From 4e7d282c10d77212e7d2477552607898dcb4c352 Mon Sep 17 00:00:00 2001 From: therealyingtong Date: Sat, 14 Jan 2023 02:34:28 -0500 Subject: [PATCH] [cleanup] Make py_plonk the root directory --- 99fault/consensus.py | 62 - LICENSE | 21 - README.md | 66 +- .../barycentric_low_degree_check.py | 32 - barycentric_low_degree_check/poly_utils.py | 207 - beacon_chain_impl/bls.py | 95 - beacon_chain_impl/full_pos.py | 513 - beacon_chain_impl/progressive_merkle_tree.py | 55 - beacon_chain_impl/simpleserialize.py | 88 - beacon_chain_impl/test.py | 53 - beacon_chain_impl/test_full_pos.py | 97 - binary_fft.py | 243 - binary_fft/binary_fft.py | 357 - binary_fft/ethereum_data_root.py | 164 - binary_fft/fast_binary_fft.pyx | 346 - binary_fft/test_binary_fft.py | 20 - binary_fft/test_ethereum_data_root.py | 10 - bitcoin_unlimited_style_sizelimits.py | 166 - blind_and_swap/blind_and_swap.py | 143 - blind_and_swap/swapsim.py | 53 - blind_and_swap/swapsim2.py | 97 - bulletproofs/ipa_commitments.py | 256 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zksnark/true_tests.txt delete mode 100644 zkstark/quadratic_prover_test.py delete mode 100644 zkstark/quadratic_provers.py diff --git a/99fault/consensus.py b/99fault/consensus.py deleted file mode 100644 index 6d3f1d9..0000000 --- a/99fault/consensus.py +++ /dev/null @@ -1,62 +0,0 @@ -# Implementation of 99% fault tolerant consensus as decribed by Leslie Lamport -# on page 391 of https://people.eecs.berkeley.edu/~luca/cs174/byzantine.pdf - -import random -from network import Network - -TIMEOUT = 10 -LATENCY = 5 -# A node in the network (not including the "commander") -class Node(): - - def __init__(self, network, id, honest=True): - self.seen = {} - self.id = id - self.network = network - self.network.add_node(self) - self.honest = honest - - # Upon receiving a message... - def on_receive(self, msg): - if self.id == 0 and len(msg) == 1: - print('Seen', msg[0], self.network.time, 'already seen', sorted(self.seen.keys())) - # Only proceed if v not in V_i... - # Byzantine nodes ignore this rule 5% of the time - if (msg[0] in self.seen) and (self.honest or random.random() < 0.95): - return - # Timeout logic (see page 399) - # Byzantine nodes ignore this rule - if (len(msg) * TIMEOUT < self.network.time) and self.honest: - return - self.seen[msg[0]] = True - new_msg = msg + [self.id] - # Broadcast v:0:j1...jk:i - # Byzantine nodes delay broadcast to split honest receiving nodes by timeout - self.network.broadcast(new_msg, at=self.network.time if self.honest else self.network.time + int(TIMEOUT / 1.5)) - - def choice(self): - return max(self.seen.keys()) - -def test(): - n = Network(LATENCY * 2) - nodes = [Node(n, i, i%4==0) for i in range(20)] - for i in range(30): - for _ in range(2): - z = random.randrange(20) - n.send_to([1000 + i], z, at=5+i*2) - for i in range(21 * LATENCY): - n.tick() - if i % 10 == 0: - print("Value sets", [sorted(node.seen.keys()) for node in nodes]) - countz = {} - maxval = "" - for node in nodes: - if node.honest: - k = str(sorted(node.seen.keys())) - countz[k] = countz.get(k, 0) + 1 - if countz[k] > countz.get(maxval, 0): - maxval = k - print("Most popular: %s" % maxval, "with %d agreeing" % countz[maxval]) - -if __name__ == '__main__': - test() diff --git a/LICENSE b/LICENSE deleted file mode 100644 index 688262d..0000000 --- a/LICENSE +++ /dev/null @@ -1,21 +0,0 @@ -The MIT License (MIT) - - Copyright (c) 2015-2018 Vitalik Buterin - - Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - - The above copyright notice and this permission notice shall be included in -all copies or substantial portions of the Software. - - THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN -THE SOFTWARE. diff --git a/README.md b/README.md index 54f168f..a4cf1be 100644 --- a/README.md +++ b/README.md @@ -1,15 +1,65 @@ -# Research +# Py_plonk - This repository is used mainly for code related to specific research questions, mostly written by @vbuterin. It is not meant as a general research repository for academic papers. +Py_plonk is a simple python implementation of the PLONK protocol as described in https://eprint.iacr.org/2019/953.pdf (see also https://vitalik.ca/general/2019/09/22/plonk.html), targeted to be close to compatible with the implementation at https://zkrepl.dev. Py_plonk includes: - An exception to this is the `papers` folder, which contains the LaTeX files for various academic papers. +* A simple programming language for describing circuits, which it can compile into the forms needed for a PLONK proof (QL, QR, QM, QO, QC, S1, S2, S3 polynomials) +* A prover that can generate proofs for this language, given a list of variable assignments +* A verifier that can verify these proofs - ## Contribute +Full compatibility is achieved in some cases: for simple programs, py_plonk is capable of outputting verification keys that _exactly_ match https://zkrepl.dev output. See the tests in test.py for some examples. - While contributions are welcome, maintaining this repository is not an active priority. The code in this repository is offered as is, without active support. +This implementation is intended for educational use, and to help reproduce and verify verification keys that are generated by other software. **IT HAS NOT BEEN AUDITED AND PROBABLY HAS BUGS, DO NOT USE BY ITSELF IN PRODUCTION.** - If you find spelling errors or have suggestions or comments, please feel free to open an issue. +Many features are missing. The parts of PLONK that are responsible for ensuring strong privacy are left out (they are easy to add, they would simply increase complexity and reduce the educational value of this implementation). - ## License +### Example - [MIT](LICENSE) © 2015-2018 Vitalik Buterin +Here is a program that lets you prove that you know two small numbers that multiply to a given number (in our example we'll use 91) without revealing what those numbers are: + +``` +n public +pb0 === pb0 * pb0 +pb1 === pb1 * pb1 +pb2 === pb2 * pb2 +pb3 === pb3 * pb3 +qb0 === qb0 * qb0 +qb1 === qb1 * qb1 +qb2 === qb2 * qb2 +qb3 === qb3 * qb3 +pb01 <== pb0 + 2 * pb1 +pb012 <== pb01 + 4 * pb2 +p <== pb012 + 8 * pb3 +qb01 <== qb0 + 2 * qb1 +qb012 <== qb01 + 4 * qb2 +q <== qb012 + 8 * qb3 +n <== p * q +``` + +Generating the verification key: + +``` +setup = utils.Setup.from_file(SETUP_FILENAME) +vk = make_verification_key(setup, 16, string_containing_the_above_code) +``` + +A setup file is in this repo. The second argument is the group order; it should be a power of two, at least 8, and at least the number of lines of code in the program. + +Proving: + +``` +assignments = compiler.fill_variable_assignments(eqs, { + 'pb3': 1, 'pb2': 1, 'pb1': 0, 'pb0': 1, + 'qb3': 0, 'qb2': 1, 'qb1': 1, 'qb0': 1, +}) +proof = prover.prove_from_witness(setup, 16, eqs, assignments) +``` + +`compiler.fill_variable_assignments` is a convenience method that executes the program to fill in any variables that you do not specify yourself. In this case, you only specify the bits of the two factors (7 and 13), the program can compute all the other intermediate and final variables for you. + +`prove_from_witness` generates a proof, passing in the full set of assignments as input. + +Verifying: + +``` +assert verifier.verify_proof(setup, 16, vk, proof, [91], optimized=True) +``` diff --git a/barycentric_low_degree_check/barycentric_low_degree_check.py b/barycentric_low_degree_check/barycentric_low_degree_check.py deleted file mode 100644 index fde0410..0000000 --- a/barycentric_low_degree_check/barycentric_low_degree_check.py +++ /dev/null @@ -1,32 +0,0 @@ -from random import randint, shuffle, choice -from poly_utils import PrimeField - -MODULUS = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 -PRIMITIVE_ROOT = 7 - -assert pow(PRIMITIVE_ROOT, (MODULUS - 1) // 2, MODULUS) != 1 -assert pow(PRIMITIVE_ROOT, MODULUS - 1, MODULUS) == 1 - -primefield = PrimeField(MODULUS) - -WIDTH = 8 - -ROOT_OF_UNITY = pow(PRIMITIVE_ROOT, (MODULUS - 1) // WIDTH, MODULUS) -DOMAIN = [pow(ROOT_OF_UNITY, i, MODULUS) for i in range(WIDTH)] - -def check(f): - result = 0 - r = randint(0, MODULUS) - rn2 = pow(r, WIDTH // 2, MODULUS) - - for i in range(WIDTH): - summand = f[i] * ((-1)**i * rn2 - 1) - summand = primefield.div(summand, DOMAIN[i * (WIDTH // 2 - 1) % WIDTH] * (r - DOMAIN[i])) - result += summand - - return result % MODULUS - -fc = [randint(0, MODULUS) for i in range(4)] -f = [primefield.eval_poly_at(fc, x) for x in DOMAIN] - -print(check(f)) \ No newline at end of file diff --git a/barycentric_low_degree_check/poly_utils.py b/barycentric_low_degree_check/poly_utils.py deleted file mode 100644 index c29d1b5..0000000 --- a/barycentric_low_degree_check/poly_utils.py +++ /dev/null @@ -1,207 +0,0 @@ -# Creates an object that includes convenience operations for numbers -# and polynomials in some prime field -class PrimeField(): - def __init__(self, modulus): - assert pow(2, modulus, modulus) == 2 - self.modulus = modulus - - def add(self, x, y): - return (x+y) % self.modulus - - def sub(self, x, y): - return (x-y) % self.modulus - - def mul(self, x, y): - return (x*y) % self.modulus - - def exp(self, x, p): - return pow(x, p, self.modulus) - - # Modular inverse using the extended Euclidean algorithm - def inv(self, a): - if a == 0: - return 0 - lm, hm = 1, 0 - low, high = a % self.modulus, self.modulus - while low > 1: - r = high//low - nm, new = hm-lm*r, high-low*r - lm, low, hm, high = nm, new, lm, low - return lm % self.modulus - - def multi_inv(self, values): - partials = [1] - for i in range(len(values)): - partials.append(self.mul(partials[-1], values[i] or 1)) - inv = self.inv(partials[-1]) - outputs = [0] * len(values) - for i in range(len(values), 0, -1): - outputs[i-1] = self.mul(partials[i-1], inv) if values[i-1] else 0 - inv = self.mul(inv, values[i-1] or 1) - return outputs - - def div(self, x, y): - return self.mul(x, self.inv(y)) - - # Evaluate a polynomial at a point - def eval_poly_at(self, p, x): - y = 0 - power_of_x = 1 - for i, p_coeff in enumerate(p): - y += power_of_x * p_coeff - power_of_x = (power_of_x * x) % self.modulus - return y % self.modulus - - # Arithmetic for polynomials - def add_polys(self, a, b): - return [((a[i] if i < len(a) else 0) + (b[i] if i < len(b) else 0)) - % self.modulus for i in range(max(len(a), len(b)))] - - def sub_polys(self, a, b): - return [((a[i] if i < len(a) else 0) - (b[i] if i < len(b) else 0)) - % self.modulus for i in range(max(len(a), len(b)))] - - def mul_by_const(self, a, c): - return [(x*c) % self.modulus for x in a] - - def mul_polys(self, a, b): - o = [0] * (len(a) + len(b) - 1) - for i, aval in enumerate(a): - for j, bval in enumerate(b): - o[i+j] += a[i] * b[j] - return [x % self.modulus for x in o] - - def div_polys(self, a, b): - assert len(a) >= len(b) - a = [x for x in a] - o = [] - apos = len(a) - 1 - bpos = len(b) - 1 - diff = apos - bpos - while diff >= 0: - quot = self.div(a[apos], b[bpos]) - o.insert(0, quot) - for i in range(bpos, -1, -1): - a[diff+i] -= b[i] * quot - apos -= 1 - diff -= 1 - return [x % self.modulus for x in o] - - def mod_polys(self, a, b): - return self.sub_polys(a, self.mul_polys(b, self.div_polys(a, b)))[:len(b)-1] - - # Build a polynomial from a few coefficients - def sparse(self, coeff_dict): - o = [0] * (max(coeff_dict.keys()) + 1) - for k, v in coeff_dict.items(): - o[k] = v % self.modulus - return o - - # Build a polynomial that returns 0 at all specified xs - def zpoly(self, xs): - root = [1] - for x in xs: - root.insert(0, 0) - for j in range(len(root)-1): - root[j] -= root[j+1] * x - return [x % self.modulus for x in root] - - # Given p+1 y values and x values with no errors, recovers the original - # p+1 degree polynomial. - # Lagrange interpolation works roughly in the following way. - # 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] - # 2. For each x, generate a polynomial which equals its corresponding - # y coordinate at that point and 0 at all other points provided. - # 3. Add these polynomials together. - - def lagrange_interp(self, xs, ys): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - root = self.zpoly(xs) - assert len(root) == len(ys) + 1 - # print(root) - # Generate per-value numerator polynomials, eg. for x=x2, - # (x - x1) * (x - x3) * ... * (x - xn), by dividing the master - # polynomial back by each x coordinate - nums = [self.div_polys(root, [-x, 1]) for x in xs] - # Generate denominators by evaluating numerator polys at each x - denoms = [self.eval_poly_at(nums[i], xs[i]) for i in range(len(xs))] - invdenoms = self.multi_inv(denoms) - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - b = [0 for y in ys] - for i in range(len(xs)): - yslice = self.mul(ys[i], invdenoms[i]) - for j in range(len(ys)): - if nums[i][j] and ys[i]: - b[j] += nums[i][j] * yslice - return [x % self.modulus for x in b] - - # Optimized poly evaluation for degree 4 - def eval_quartic(self, p, x): - xsq = x * x % self.modulus - xcb = xsq * x - return (p[0] + p[1] * x + p[2] * xsq + p[3] * xcb) % self.modulus - - # Optimized version of the above restricted to deg-4 polynomials - def lagrange_interp_4(self, xs, ys): - x01, x02, x03, x12, x13, x23 = \ - xs[0] * xs[1], xs[0] * xs[2], xs[0] * xs[3], xs[1] * xs[2], xs[1] * xs[3], xs[2] * xs[3] - m = self.modulus - eq0 = [-x12 * xs[3] % m, (x12 + x13 + x23), -xs[1]-xs[2]-xs[3], 1] - eq1 = [-x02 * xs[3] % m, (x02 + x03 + x23), -xs[0]-xs[2]-xs[3], 1] - eq2 = [-x01 * xs[3] % m, (x01 + x03 + x13), -xs[0]-xs[1]-xs[3], 1] - eq3 = [-x01 * xs[2] % m, (x01 + x02 + x12), -xs[0]-xs[1]-xs[2], 1] - e0 = self.eval_poly_at(eq0, xs[0]) - e1 = self.eval_poly_at(eq1, xs[1]) - e2 = self.eval_poly_at(eq2, xs[2]) - e3 = self.eval_poly_at(eq3, xs[3]) - e01 = e0 * e1 - e23 = e2 * e3 - invall = self.inv(e01 * e23) - inv_y0 = ys[0] * invall * e1 * e23 % m - inv_y1 = ys[1] * invall * e0 * e23 % m - inv_y2 = ys[2] * invall * e01 * e3 % m - inv_y3 = ys[3] * invall * e01 * e2 % m - return [(eq0[i] * inv_y0 + eq1[i] * inv_y1 + eq2[i] * inv_y2 + eq3[i] * inv_y3) % m for i in range(4)] - - # Optimized version of the above restricted to deg-2 polynomials - def lagrange_interp_2(self, xs, ys): - m = self.modulus - eq0 = [-xs[1] % m, 1] - eq1 = [-xs[0] % m, 1] - e0 = self.eval_poly_at(eq0, xs[0]) - e1 = self.eval_poly_at(eq1, xs[1]) - invall = self.inv(e0 * e1) - inv_y0 = ys[0] * invall * e1 - inv_y1 = ys[1] * invall * e0 - return [(eq0[i] * inv_y0 + eq1[i] * inv_y1) % m for i in range(2)] - - # Optimized version of the above restricted to deg-4 polynomials - def multi_interp_4(self, xsets, ysets): - data = [] - invtargets = [] - for xs, ys in zip(xsets, ysets): - x01, x02, x03, x12, x13, x23 = \ - xs[0] * xs[1], xs[0] * xs[2], xs[0] * xs[3], xs[1] * xs[2], xs[1] * xs[3], xs[2] * xs[3] - m = self.modulus - eq0 = [-x12 * xs[3] % m, (x12 + x13 + x23), -xs[1]-xs[2]-xs[3], 1] - eq1 = [-x02 * xs[3] % m, (x02 + x03 + x23), -xs[0]-xs[2]-xs[3], 1] - eq2 = [-x01 * xs[3] % m, (x01 + x03 + x13), -xs[0]-xs[1]-xs[3], 1] - eq3 = [-x01 * xs[2] % m, (x01 + x02 + x12), -xs[0]-xs[1]-xs[2], 1] - e0 = self.eval_quartic(eq0, xs[0]) - e1 = self.eval_quartic(eq1, xs[1]) - e2 = self.eval_quartic(eq2, xs[2]) - e3 = self.eval_quartic(eq3, xs[3]) - data.append([ys, eq0, eq1, eq2, eq3]) - invtargets.extend([e0, e1, e2, e3]) - invalls = self.multi_inv(invtargets) - o = [] - for (i, (ys, eq0, eq1, eq2, eq3)) in enumerate(data): - invallz = invalls[i*4:i*4+4] - inv_y0 = ys[0] * invallz[0] % m - inv_y1 = ys[1] * invallz[1] % m - inv_y2 = ys[2] * invallz[2] % m - inv_y3 = ys[3] * invallz[3] % m - o.append([(eq0[i] * inv_y0 + eq1[i] * inv_y1 + eq2[i] * inv_y2 + eq3[i] * inv_y3) % m for i in range(4)]) - # assert o == [self.lagrange_interp_4(xs, ys) for xs, ys in zip(xsets, ysets)] - return o diff --git a/beacon_chain_impl/bls.py b/beacon_chain_impl/bls.py deleted file mode 100644 index a55fee8..0000000 --- a/beacon_chain_impl/bls.py +++ /dev/null @@ -1,95 +0,0 @@ -try: - from hashlib import blake2s -except: - from pyblake2 import blake2s -blake = lambda x: blake2s(x).digest() -from py_ecc.optimized_bn128 import G1, G2, neg, add, multiply, FQ, FQ2, FQ12, pairing, \ - normalize, field_modulus, b, b2, is_on_curve, curve_order, final_exponentiate - -def compress_G1(pt): - x, y = normalize(pt) - return x.n + 2**255 * (y.n % 2) - -def decompress_G1(p): - if p == 0: - return (FQ(1), FQ(1), FQ(0)) - x = p % 2**255 - y_mod_2 = p // 2**255 - y = pow((x**3 + b.n) % field_modulus, (field_modulus+1)//4, field_modulus) - assert pow(y, 2, field_modulus) == (x**3 + b.n) % field_modulus - if y%2 != y_mod_2: - y = field_modulus - y - return (FQ(x), FQ(y), FQ(1)) - -# 16th root of unity -hex_root = FQ2([21573744529824266246521972077326577680729363968861965890554801909984373949499, - 16854739155576650954933913186877292401521110422362946064090026408937773542853]) - -assert hex_root ** 8 != FQ2([1,0]) -assert hex_root ** 16 == FQ2([1,0]) - -def sqrt_fq2(x): - y = x ** ((field_modulus ** 2 + 15) // 32) - while y**2 != x: - y *= hex_root - return y - -cache = {} - -def hash_to_G2(m): - if m in cache: - return cache[m] - k2 = m - while 1: - k1 = blake(k2) - k2 = blake(k1) - x1 = int.from_bytes(k1, 'big') % field_modulus - x2 = int.from_bytes(k2, 'big') % field_modulus - x = FQ2([x1, x2]) - xcb = x**3 + b2 - if xcb ** ((field_modulus ** 2 - 1) // 2) == FQ2([1,0]): - break - y = sqrt_fq2(xcb) - o = multiply((x, y, FQ2([1,0])), 2*field_modulus-curve_order) - cache[m] = o - return o - -def compress_G2(pt): - assert is_on_curve(pt, b2) - x, y = normalize(pt) - return (x.coeffs[0] + 2**255 * (y.coeffs[0] % 2), x.coeffs[1]) - -def decompress_G2(p): - x1 = p[0] % 2**255 - y1_mod_2 = p[0] // 2**255 - x2 = p[1] - x = FQ2([x1, x2]) - if x == FQ2([0, 0]): - return FQ2([1,0]), FQ2([1,0]), FQ2([0,0]) - y = sqrt_fq2(x**3 + b2) - if y.coeffs[0] % 2 != y1_mod_2: - y = y * -1 - assert is_on_curve((x, y, FQ2([1,0])), b2) - return x, y, FQ2([1,0]) - -def sign(m, k): - return compress_G2(multiply(hash_to_G2(m), k)) - -def privtopub(k): - return compress_G1(multiply(G1, k)) - -def verify(m, pub, sig): - return final_exponentiate(pairing(decompress_G2(sig), G1, False) * \ - pairing(hash_to_G2(m), neg(decompress_G1(pub)), False)) == FQ12.one() - -def aggregate_sigs(sigs): - o = FQ2([1,0]), FQ2([1,0]), FQ2([0,0]) - for s in sigs: - o = add(o, decompress_G2(s)) - return compress_G2(o) - -def aggregate_pubs(pubs): - o = FQ(1), FQ(1), FQ(0) - for p in pubs: - o = add(o, decompress_G1(p)) - return compress_G1(o) diff --git a/beacon_chain_impl/full_pos.py b/beacon_chain_impl/full_pos.py deleted file mode 100644 index 37769ab..0000000 --- a/beacon_chain_impl/full_pos.py +++ /dev/null @@ -1,513 +0,0 @@ -try: - from hashlib import blake2s -except: - from pyblake2 import blake2s -blake = lambda x: blake2s(x).digest() -import bls -import random -from bls import decompress_G1, aggregate_pubs, verify, sign, privtopub -from simpleserialize import deepcopy, serialize, to_dict - - -SHARD_COUNT = 20 -ATTESTER_COUNT = 32 -DEFAULT_BALANCE = 20000 - -class AggregateVote(): - fields = { - 'shard_id': 'int16', - 'shard_block_hash': 'hash32', - 'signer_bitmask': 'bytes', - 'aggregate_sig': ['int256'] - } - defaults = { - 'shard_id': 0, - 'shard_block_hash': b'\x00'*32, - 'signer_bitmask': b'', - 'aggregate_sig': [0,0], - } - - def __init__(self, **kwargs): - for k in self.fields.keys(): - assert k in kwargs or k in self.defaults - setattr(self, k, kwargs.get(k, self.defaults.get(k))) - -class Block(): - - fields = { - # Hash of the parent block - 'parent_hash': 'hash32', - # Number of skips (for the full PoS mechanism) - 'skip_count': 'int64', - # Randao commitment reveal - 'randao_reveal': 'hash32', - # Bitmask of who participated in the block notarization committee - 'attestation_bitmask': 'bytes', - # Their aggregate sig - 'attestation_aggregate_sig': ['int256'], - # Shard aggregate votes - 'shard_aggregate_votes': [AggregateVote], - # Reference to main chain block - 'main_chain_ref': 'hash32', - # Hash of the state - 'state_hash': 'bytes', - # Signature from signer - 'sig': ['int256'] - } - - defaults = { - 'parent_hash': b'\x00'*32, - 'skip_count': 0, - 'randao_reveal': b'\x00'*32, - 'attestation_bitmask': b'', - 'attestation_aggregate_sig': [0,0], - 'shard_aggregate_votes': [], - 'main_chain_ref': b'\x00'*32, - 'state_hash': b'\x00'*32, - 'sig': [0,0] - } - - def __init__(self, **kwargs): - for k in self.fields.keys(): - assert k in kwargs or k in self.defaults - setattr(self, k, kwargs.get(k, self.defaults.get(k))) - - def sign(self, key): - self.sig = [0,0] - self.sig = list(sign(serialize(self), key)) - - def verify(self, pub): - zig = self.sig - self.sig = [0,0] - o = verify(serialize(self), pub, tuple(zig)) - self.sig = zig - return o - -def get_shuffling(seed, validator_count, sample=None): - assert validator_count <= 16777216 - rand_max = 16777216 - 16777216 % validator_count - o = list(range(validator_count)); source = seed - i = 0 - maxvalue = sample if sample is not None else validator_count - while i < maxvalue: - source = blake(source) - for pos in range(0, 30, 3): - m = int.from_bytes(source[pos:pos+3], 'big') - remaining = validator_count - i - if remaining == 0: - break - if validator_count < rand_max: - replacement_pos = (m % remaining) + i - o[i], o[replacement_pos] = o[replacement_pos], o[i] - i += 1 - return o[:maxvalue] - -class ValidatorRecord(): - fields = { - # The validator's public key - 'pubkey': 'int256', - # What shard the validator's balance will be sent to after withdrawal - 'return_shard': 'int16', - # And what address - 'return_address': 'address', - # The validator's current RANDAO beacon commitment - 'randao_commitment': 'hash32', - # Current balance - 'balance': 'int64', - # Dynasty where the validator can (be inducted | be removed | withdraw) - 'switch_dynasty': 'int64' - } - defaults = {} - - def __init__(self, **kwargs): - for k in self.fields.keys(): - assert k in kwargs or k in self.defaults - setattr(self, k, kwargs.get(k, self.defaults.get(k))) - -class PartialCrosslinkRecord(): - - fields = { - # What shard is the crosslink being made for - 'shard_id': 'int16', - # Hash of the block - 'shard_block_hash': 'hash32', - # Which of the eligible voters are voting for it (as a bitmask) - 'voter_bitmask': 'bytes' - } - defaults = {} - - def __init__(self, **kwargs): - for k in self.fields.keys(): - assert k in kwargs or k in self.defaults, k - setattr(self, k, kwargs.get(k, self.defaults.get(k))) - - -class ActiveState(): - - fields = { - # Block height - 'height': 'int64', - # Global RANDAO beacon state - 'randao': 'hash32', - # Which validators have made FFG votes this epoch (as a bitmask) - 'ffg_voter_bitmask': 'bytes', - # Deltas to validator balances (to be processed at end of epoch) - 'balance_deltas': ['int48'], - # Storing data about crosslinks-in-progress attempted in this epoch - 'partial_crosslinks': [PartialCrosslinkRecord], - # Total number of skips (used to determine minimum timestamp) - 'total_skip_count': 'int64' - } - defaults = {'height': 0, 'randao': b'\x00'*32, - 'ffg_voter_bitmask': b'', 'balance_deltas': [], - 'partial_crosslinks': [], 'total_skip_count': 0} - - def __init__(self, **kwargs): - for k in self.fields.keys(): - assert k in kwargs or k in self.defaults - setattr(self, k, kwargs.get(k, self.defaults.get(k))) - -class CrosslinkRecord(): - fields = { - # What epoch the crosslink was submitted in - 'epoch': 'int64', - # The block hash - 'hash': 'hash32' - } - defaults = {'epoch': 0, 'hash': b'\x00'*32} - - def __init__(self, **kwargs): - for k in self.fields.keys(): - assert k in kwargs or k in self.defaults - setattr(self, k, kwargs.get(k, self.defaults.get(k))) - -class CrystallizedState(): - fields = { - # List of active validators - 'active_validators': [ValidatorRecord], - # List of joined but not yet inducted validators - 'queued_validators': [ValidatorRecord], - # List of removed validators pending withdrawal - 'exited_validators': [ValidatorRecord], - # The permutation of validators used to determine who cross-links - # what shard in this epoch - 'current_shuffling': ['int24'], - # The current epoch - 'current_epoch': 'int64', - # The last justified epoch - 'last_justified_epoch': 'int64', - # The last finalized epoch - 'last_finalized_epoch': 'int64', - # The current dynasty - 'dynasty': 'int64', - # The next shard that assignment for cross-linking will start from - 'next_shard': 'int16', - # The current FFG checkpoint - 'current_checkpoint': 'hash32', - # Records about the most recent crosslink for each shard - 'crosslink_records': [CrosslinkRecord], - # Total balance of deposits - 'total_deposits': 'int256' - } - defaults = {'active_validators': [], - 'queued_validators': [], - 'exited_validators': [], - 'current_shuffling': ['int24'], - 'current_epoch': 0, - 'last_justified_epoch': 0, - 'last_finalized_epoch': 0, - 'dynasty': 0, - 'next_shard': 0, - 'current_checkpoint': b'\x00'*32, - 'crosslink_records': [], - 'total_deposits': 0} - - def __init__(self, **kwargs): - for k in self.fields.keys(): - assert k in kwargs or k in self.defaults - setattr(self, k, kwargs.get(k, self.defaults.get(k))) - -def get_crosslink_aggvote_msg(shard_id, shard_block_hash, crystallized_state): - return shard_id.to_bytes(2, 'big') + \ - shard_block_hash + \ - crystallized_state.current_checkpoint + \ - crystallized_state.current_epoch.to_bytes(8, 'big') + \ - crystallized_state.last_justified_epoch.to_bytes(8, 'big') - -def get_attesters_and_signer(crystallized_state, active_state, skip_count): - attestation_count = min(len(crystallized_state.active_validators), ATTESTER_COUNT) - indices = get_shuffling(active_state.randao, len(crystallized_state.active_validators), - attestation_count + skip_count + 1) - return indices[:attestation_count], indices[-1] - -def get_shard_attesters(crystallized_state, shard_id): - vc = len(crystallized_state.active_validators) - return crystallized_state.current_shuffling[(vc * shard_id) // SHARD_COUNT: (vc * (shard_id + 1)) // SHARD_COUNT] - -# Get rewards and vote data -def process_ffg_deposits(crystallized_state, ffg_voter_bitmask): - total_validators = len(crystallized_state.active_validators) - finality_distance = crystallized_state.current_epoch - crystallized_state.last_finalized_epoch - online_reward = 6 if finality_distance <= 2 else 0 - offline_penalty = 3 * finality_distance - total_vote_count = 0 - total_vote_deposits = 0 - deltas = [0] * total_validators - for i in range(total_validators): - if ffg_voter_bitmask[i // 8] & (128 >> (i % 8)): - total_vote_deposits += crystallized_state.active_validators[i].balance - deltas[i] += online_reward - total_vote_count += 1 - else: - deltas[i] -= offline_penalty - print('Total voted: %d of %d validators (%.2f%%), %d of %d deposits (%.2f%%)' % - (total_vote_count, total_validators, total_vote_count * 100 / total_validators, - total_vote_deposits, crystallized_state.total_deposits, total_vote_deposits * 100 / crystallized_state.total_deposits)) - print('FFG online reward: %d, offline penalty: %d' % (online_reward, offline_penalty)) - print('Total deposit change from FFG: %d' % sum(deltas)) - # Check if we need to justify and finalize - justify = total_vote_deposits * 3 >= crystallized_state.total_deposits * 2 - finalize = False - if justify: - print('Justifying last epoch') - if crystallized_state.last_justified_epoch == crystallized_state.current_epoch - 1: - finalize = True - print('Finalizing last epoch') - return deltas, total_vote_count, total_vote_deposits, justify, finalize - -# Process rewards from crosslinks -def process_crosslinks(crystallized_state, crosslinks): - # Find the most popular crosslink in each shard - main_crosslink = {} - for c in crosslinks: - vote_count = 0 - mask = bytearray(c.voter_bitmask) - for byte in mask: - for j in range(8): - vote_count += (byte >> j) % 2 - if vote_count > main_crosslink.get(c.shard_id, (b'', 0, b''))[1]: - main_crosslink[c.shard_id] = (c.shard_block_hash, vote_count, mask) - # Adjust crosslinks - new_crosslink_records = [x for x in crystallized_state.crosslink_records] - deltas = [0] * len(crystallized_state.active_validators) - # Process shard by shard... - for shard in range(SHARD_COUNT): - indices = get_shard_attesters(crystallized_state, shard) - # Get info about the dominant crosslink for this shard - h, votes, mask = main_crosslink.get(shard, (b'', 0, bytearray((len(indices)+7)//8))) - # Calculate rewards for participants and penalties for non-participants - crosslink_distance = crystallized_state.current_epoch - crystallized_state.crosslink_records[shard].epoch - online_reward = 3 if crosslink_distance <= 2 else 0 - offline_penalty = crosslink_distance * 2 - # Go through participants and evaluate rewards/penalties - for i, index in enumerate(indices): - if mask[i//8] & (1 << (i % 8)): - deltas[i] += online_reward - else: - deltas[i] -= offline_penalty - print('Shard %d: most recent crosslink %d, reward: (%d, %d), votes: %d of %d (%.2f%%)' - % (shard, crystallized_state.crosslink_records[shard].epoch, online_reward, -offline_penalty, - votes, len(indices), votes * 100 / len(indices))) - # New crosslink - if votes * 3 >= len(indices) * 2: - new_crosslink_records[shard] = CrosslinkRecord(hash=h, epoch=crystallized_state.current_epoch) - print('New crosslink %s' % hex(int.from_bytes(h, 'big'))) - print('Total deposit change from crosslinks: %d' % sum(deltas)) - return deltas, new_crosslink_records - -def process_balance_deltas(crystallized_state, balance_deltas): - deltas = [0] * len(crystallized_state.active_validators) - for i in balance_deltas: - if i % 16777216 < 8388608: - deltas[i >> 24] += i & 16777215 - else: - deltas[i >> 24] += (i & 16777215) - 16777216 - print('Total deposit change from deltas: %d' % sum(deltas)) - return deltas - -def get_incremented_validator_sets(crystallized_state, new_active_validators): - new_active_validators = [v for v in new_active_validators] - new_exited_validators = [v for v in crystallized_state.exited_validators] - i = 0 - while i < len(new_active_validators): - if new_active_validators[i].balance <= DEFAULT_BALANCE // 2: - new_exited_validators.append(new_active_validators.pop(i)) - elif new_active_validators[i].switch_dynasty == crystallized_state.dynasty + 1: - new_exited_validators.append(new_active_validators.pop(i)) - else: - i += 1 - induct = min(len(crystallized_state.queued_validators), len(crystallized_state.active_validators) // 30 + 1) - for i in range(induct): - if crystallized_state.queued_validators[i].switch_dynasty > crystallized_state.dynasty + 1: - induct = i - break - new_active_validators.append(crystallized_state.queued_validators[i]) - new_queued_validators = crystallized_state.queued_validators[induct:] - return new_queued_validators, new_active_validators, new_exited_validators - -def process_attestations(validator_set, attestation_indices, attestation_bitmask, msg, aggregate_sig): - # Verify the attestations of the parent - pubs = [] - balance_deltas = [] - assert len(attestation_bitmask) == (len(attestation_indices) + 7) // 8 - for i, index in enumerate(attestation_indices): - if attestation_bitmask[i//8] & (128>>(i%8)): - pubs.append(validator_set[index].pubkey) - balance_deltas.append((index << 24) + 1) - assert len(balance_deltas) <= 128 - assert verify(msg, aggregate_pubs(pubs), aggregate_sig) - print('Verified aggregate sig') - return balance_deltas - - -def update_ffg_and_crosslink_progress(crystallized_state, crosslinks, ffg_voter_bitmask, votes): - # Verify the attestations of crosslink hashes - crosslink_votes = {vote.shard_block_hash + vote.shard_id.to_bytes(2, 'big'): - vote.voter_bitmask for vote in crosslinks} - new_ffg_bitmask = bytearray(ffg_voter_bitmask) - total_voters = 0 - for vote in votes: - attestation = get_crosslink_aggvote_msg(vote.shard_id, vote.shard_block_hash, crystallized_state) - indices = get_shard_attesters(crystallized_state, vote.shard_id) - votekey = vote.shard_block_hash + vote.shard_id.to_bytes(2, 'big') - if votekey not in crosslink_votes: - crosslink_votes[votekey] = bytearray((len(indices) + 7) // 8) - bitmask = crosslink_votes[votekey] - pubs = [] - for i, index in enumerate(indices): - if vote.signer_bitmask[i//8] & (128>>(i%8)): - pubs.append(crystallized_state.active_validators[index].pubkey) - if new_ffg_bitmask[index//8] & (128>>(index%8)) == 0: - new_ffg_bitmask[index//8] ^= 128>>(index%8) - bitmask[i//8] ^= 128>>(i%8) - total_voters += 1 - assert verify(attestation, aggregate_pubs(pubs), vote.aggregate_sig) - crosslink_votes[votekey] = bitmask - print('Verified aggregate vote') - new_crosslinks = [PartialCrosslinkRecord(shard_id=int.from_bytes(h[32:], 'big'), - shard_block_hash=h[:32], voter_bitmask=crosslink_votes[h]) - for h in sorted(crosslink_votes.keys())] - return new_crosslinks, new_ffg_bitmask, total_voters - -def compute_state_transition(parent_state, parent_block, block, verify_sig=True): - crystallized_state, active_state = parent_state - # Initialize a new epoch if needed - if active_state.height % SHARD_COUNT == 0: - print('Processing epoch transition') - # Process rewards from FFG/crosslink votes - new_validator_records = deepcopy(crystallized_state.active_validators) - # Who voted in the last epoch - ffg_voter_bitmask = bytearray(active_state.ffg_voter_bitmask) - # Balance changes, and total vote counts for FFG - deltas1, total_vote_count, total_vote_deposits, justify, finalize = \ - process_ffg_deposits(crystallized_state, ffg_voter_bitmask) - # Balance changes, and total vote counts for crosslinks - deltas2, new_crosslink_records = process_crosslinks(crystallized_state, active_state.partial_crosslinks) - # Process other balance deltas - deltas3 = process_balance_deltas(crystallized_state, active_state.balance_deltas) - for i, v in enumerate(new_validator_records): - v.balance += deltas1[i] + deltas2[i] + deltas3[i] - total_deposits = crystallized_state.total_deposits + sum(deltas1 + deltas2 + deltas3) - print('New total deposits: %d' % total_deposits) - - if finalize: - new_queued_validators, new_active_validators, new_exited_validators = \ - get_incremented_validator_sets(crystallized_state, new_validator_records) - else: - new_queued_validators, new_active_validators, new_exited_validators = \ - crystallized_state.queued_validators, crystallized_state.active_validators, crystallized_state.exited_validators - - crystallized_state = CrystallizedState( - queued_validators=new_queued_validators, - active_validators=new_active_validators, - exited_validators=new_exited_validators, - current_shuffling=get_shuffling(active_state.randao, len(new_active_validators)), - last_justified_epoch = crystallized_state.current_epoch if justify else crystallized_state.last_justified_epoch, - last_finalized_epoch = crystallized_state.current_epoch-1 if finalize else crystallized_state.last_finalized_epoch, - dynasty = crystallized_state.dynasty + (1 if finalize else 0), - next_shard = 0, - current_epoch = crystallized_state.current_epoch + 1, - crosslink_records = new_crosslink_records, - total_deposits = total_deposits - ) - # Reset the active state - active_state = ActiveState(height=active_state.height, - randao=active_state.randao, - ffg_voter_bitmask=bytearray((len(crystallized_state.active_validators) + 7) // 8), - balance_deltas=[], - partial_crosslinks=[], - total_skip_count=active_state.total_skip_count) - # Process the block-by-block stuff - - # Determine who the attesters and the main signer are - attestation_indices, main_signer = \ - get_attesters_and_signer(crystallized_state, active_state, block.skip_count) - - # Verify attestations - balance_deltas = process_attestations(crystallized_state.active_validators, - attestation_indices, - block.attestation_bitmask, - serialize(parent_block), - block.attestation_aggregate_sig) - # Reward main signer - balance_deltas.append((main_signer << 24) + len(balance_deltas)) - - # Verify main signature - if verify_sig: - assert block.verify(crystallized_state.active_validators[main_signer].pubkey) - print('Verified main sig') - - # Update crosslink records - new_crosslink_records, new_ffg_bitmask, voters = \ - update_ffg_and_crosslink_progress(crystallized_state, active_state.partial_crosslinks, - active_state.ffg_voter_bitmask, block.shard_aggregate_votes) - balance_deltas.append((main_signer << 24) + voters) - - o = ActiveState(height=active_state.height + 1, - randao=(int.from_bytes(active_state.randao, 'big') ^ - int.from_bytes(block.randao_reveal, 'big')).to_bytes(32, 'big'), - total_skip_count=active_state.total_skip_count + block.skip_count, - partial_crosslinks=new_crosslink_records, - ffg_voter_bitmask=new_ffg_bitmask, - balance_deltas=active_state.balance_deltas + balance_deltas) - - return crystallized_state, o - -def mk_genesis_state_and_block(pubkeys): - c = CrystallizedState( - active_validators=[ValidatorRecord( - pubkey=pub, - return_shard=0, - return_address=blake(pub.to_bytes(32, 'big'))[-20:], - randao_commitment=b'\x55'*32, - balance=DEFAULT_BALANCE, - switch_dynasty=9999999999999999999 - ) for pub in pubkeys], - queued_validators=[], - exited_validators=[], - current_shuffling=get_shuffling(b'\x35'*32, len(pubkeys)), - current_epoch=1, - last_justified_epoch=0, - last_finalized_epoch=0, - dynasty=1, - next_shard=0, - current_checkpoint=blake(b'insert EOS constitution here'), - crosslink_records=[CrosslinkRecord(hash=b'\x00'*32, epoch=0) for i in range(SHARD_COUNT)], - total_deposits=DEFAULT_BALANCE*len(pubkeys)) - a = ActiveState(height=1, - randao=b'\x45'*32, - ffg_voter_bitmask=bytearray((len(c.active_validators) + 7) // 8), - balance_deltas=[], - partial_crosslinks=[], - total_skip_count=0) - b = Block(parent_hash=b'\x00'*32, - skip_count=0, - randao_reveal=b'\x00'*32, - attestation_bitmask=b'', - attestation_aggregate_sig=[0,0], - shard_aggregate_votes=[], - main_chain_ref=b'\x00'*32, - state_hash=blake(serialize(c))+blake(serialize(a)), - sig=[0,0] - ) - return c, a, b diff --git a/beacon_chain_impl/progressive_merkle_tree.py b/beacon_chain_impl/progressive_merkle_tree.py deleted file mode 100644 index 3cb3db9..0000000 --- a/beacon_chain_impl/progressive_merkle_tree.py +++ /dev/null @@ -1,55 +0,0 @@ -from hashlib import blake2s -import binascii - -def hash(x): return blake2s(x).digest() - -zerohashes = [b'\x00' * 32] -for i in range(1, 32): - zerohashes.append(hash(zerohashes[i-1] + zerohashes[i-1])) - -# Add a value to a Merkle tree by using the algo -# that stores a branch of sub-roots -def add_value(branch, index, value): - i = 0 - while (index+1) % 2**(i+1) == 0: - i += 1 - for j in range(0, i): - value = hash(branch[j] + value) - # branch[j] = zerohashes[j] - branch[i] = value - -# Compute a Merkle root the dumb way -def merkle_root(values): - for h in range(32): - if len(values) % 2 == 1: - values.append(zerohashes[h]) - values = [hash(values[i] + values[i+1]) for i in range(0, len(values), 2)] - return values[0] - -def get_root_from_branch(branch, size): - r = b'\x00' * 32 - for h in range(32): - if (size >> h) % 2 == 1: - r = hash(branch[h] + r) - else: - r = hash(r + zerohashes[h]) - return r - -def branch_by_branch(values): - branch = zerohashes[::] - # Construct the tree using the branch-based algo - for index, value in enumerate(values): - add_value(branch, index, value) - # Return the root - return get_root_from_branch(branch, len(values)) - -testdata = [(i + 2**255).to_bytes(32, 'big') for i in range(10000)] - -# The Merkle root algo assumes trailing zero bytes -assert merkle_root(testdata[:5]) == merkle_root(testdata[:5] + [b'\x00' * 32] * 5) - -# Verify equivalence of the simple all-at-once method and the progressive method -assert branch_by_branch(testdata[:1]) == merkle_root(testdata[:1]) -assert branch_by_branch(testdata[:2]) == merkle_root(testdata[:2]) -assert branch_by_branch(testdata[:3]) == merkle_root(testdata[:3]) -assert branch_by_branch(testdata[:5049]) == merkle_root(testdata[:5049]) diff --git a/beacon_chain_impl/simpleserialize.py b/beacon_chain_impl/simpleserialize.py deleted file mode 100644 index 0788840..0000000 --- a/beacon_chain_impl/simpleserialize.py +++ /dev/null @@ -1,88 +0,0 @@ -def serialize(val, typ=None): - if typ is None and hasattr(val, 'fields'): - typ = type(val) - if typ in ('hash32', 'address'): - assert len(val) == 20 if typ == 'address' else 32 - return val - elif isinstance(typ, str) and typ[:3] == 'int': - length = int(typ[3:]) - assert length % 8 == 0 - return val.to_bytes(length // 8, 'big') - elif typ == 'bytes': - return len(val).to_bytes(4, 'big') + val - elif isinstance(typ, list): - assert len(typ) == 1 - sub = b''.join([serialize(x, typ[0]) for x in val]) - return len(sub).to_bytes(4, 'big') + sub - elif isinstance(typ, type): - sub = b''.join([serialize(getattr(val, k), typ.fields[k]) for k in sorted(typ.fields.keys())]) - return len(sub).to_bytes(4, 'big') + sub - raise Exception("Cannot serialize", val, typ) - -def _deserialize(data, start, typ): - if typ in ('hash32', 'address'): - length = 20 if typ == 'address' else 32 - assert len(data) + start >= length - return data[start: start+length], start+length - elif isinstance(typ, str) and typ[:3] == 'int': - length = int(typ[3:]) - assert length % 8 == 0 - assert len(data) + start >= length // 8 - return int.from_bytes(data[start: start+length//8], 'big'), start+length//8 - elif typ == 'bytes': - length = int.from_bytes(data[start:start+4], 'big') - assert len(data) + start >= 4+length - return data[start+4: start+4+length], start+4+length - elif isinstance(typ, list): - assert len(typ) == 1 - length = int.from_bytes(data[start:start+4], 'big') - pos, o = start + 4, [] - while pos < start + 4 + length: - result, pos = _deserialize(data, pos, typ[0]) - o.append(result) - assert pos == start + 4 + length - return o, pos - elif isinstance(typ, type): - length = int.from_bytes(data[start:start+4], 'big') - values = {} - pos = start + 4 - for k in sorted(typ.fields.keys()): - values[k], pos = _deserialize(data, pos, typ.fields[k]) - assert pos == start + 4 + length - return typ(**values), pos - raise Exception("Cannot deserialize", typ) - -def deserialize(data, typ): - return _deserialize(data, 0, typ)[0] - -def eq(x, y): - if hasattr(x, 'fields') and hasattr(y, 'fields'): - for f in x.fields: - if not eq(getattr(x, f), getattr(y, f)): - print('Unequal:', x, y, f, getattr(x, f), getattr(y, f)) - return False - return True - else: - return x == y - -def deepcopy(x): - if hasattr(x, 'fields'): - vals = {} - for f in x.fields.keys(): - vals[f] = deepcopy(getattr(x, f)) - return x.__class__(**vals) - elif isinstance(x, list): - return [deepcopy(y) for y in x] - else: - return x - -def to_dict(x): - if hasattr(x, 'fields'): - vals = {} - for f in x.fields.keys(): - vals[f] = to_dict(getattr(x, f)) - return vals - elif isinstance(x, list): - return [to_dict(y) for y in x] - else: - return x diff --git a/beacon_chain_impl/test.py b/beacon_chain_impl/test.py deleted file mode 100644 index 2aac957..0000000 --- a/beacon_chain_impl/test.py +++ /dev/null @@ -1,53 +0,0 @@ -from bls import G1, G2, hash_to_G2, compress_G1, compress_G2, \ - decompress_G1, decompress_G2, normalize, multiply, \ - sign, privtopub, aggregate_sigs, aggregate_pubs, verify - -from simpleserialize import serialize, deserialize, eq - -from full_pos import ActiveState, CheckpointRecord - -for x in (1, 5, 124, 735, 127409812145, 90768492698215092512159, 0): - print('Testing with privkey %d' % x) - p1 = multiply(G1, x) - p2 = multiply(G2, x) - msg = str(x).encode('utf-8') - msghash = hash_to_G2(msg) - assert normalize(decompress_G1(compress_G1(p1))) == normalize(p1) - assert normalize(decompress_G2(compress_G2(p2))) == normalize(p2) - assert normalize(decompress_G2(compress_G2(msghash))) == normalize(msghash) - sig = sign(msg, x) - pub = privtopub(x) - assert verify(msg, pub, sig) - -print('Testing signature aggregation') -msg = b'cow' -keys = [1, 5, 124, 735, 127409812145, 90768492698215092512159, 0] -sigs = [sign(msg, k) for k in keys] -pubs = [privtopub(k) for k in keys] -aggsig = aggregate_sigs(sigs) -aggpub = aggregate_pubs(pubs) -assert verify(msg, aggpub, aggsig) - -print('Testing basic serialization') - -assert serialize(5, 'int8') == b'\x05' -assert deserialize(b'\x05', 'int8') == 5 -assert serialize(2**32-3, 'int40') == b'\x00\xff\xff\xff\xfd' -assert deserialize(b'\x00\xff\xff\xff\xfd', 'int40') == 2**32-3 -assert serialize(b'\x35'*20, 'address') == b'\x35'*20 -assert deserialize(b'\x35'*20, 'address') == b'\x35'*20 -assert serialize(b'\x35'*32, 'hash32') == b'\x35'*32 -assert deserialize(b'\x35'*32, 'hash32') == b'\x35'*32 -assert serialize(b'cow', 'bytes') == b'\x00\x00\x00\x03cow' -assert deserialize(b'\x00\x00\x00\x03cow', 'bytes') == b'cow' - -print('Testing advanced serialization') - - -s = ActiveState() -ds = deserialize(serialize(s, type(s)), type(s)) -assert eq(s, ds) -s = ActiveState(checkpoints=[CheckpointRecord(checkpoint_hash=b'\x55'*32, bitmask=b'31337dawg')], - height=555, randao=b'\x88'*32, balance_deltas=[5,7,9,579] + [3] * 333) -ds = deserialize(serialize(s, type(s)), type(s)) -assert eq(s, ds) diff --git a/beacon_chain_impl/test_full_pos.py b/beacon_chain_impl/test_full_pos.py deleted file mode 100644 index 0a57c5f..0000000 --- a/beacon_chain_impl/test_full_pos.py +++ /dev/null @@ -1,97 +0,0 @@ -from full_pos import blake, mk_genesis_state_and_block, compute_state_transition, \ - get_attesters_and_signer, Block, get_crosslink_aggvote_msg, AggregateVote, \ - SHARD_COUNT, ATTESTER_COUNT, get_shard_attesters -import random -import bls -from simpleserialize import serialize, deserialize, eq, deepcopy -import time - -privkeys = [int.from_bytes(blake(str(i).encode('utf-8'))[:4], 'big') for i in range(100000)] -print('Generated privkeys') -keymap = {} -for i,k in enumerate(privkeys): - keymap[bls.privtopub(k)] = k - if i%50 == 0: - print("Generated %d keys" % i) - -def mock_make_child(parent_state, parent, skips, attester_share=0.8, crosslink_shards=[]): - crystallized_state, active_state = parent_state - parent_attestation = serialize(parent) - validator_count = len(crystallized_state.active_validators) - indices, main_signer = get_attesters_and_signer(crystallized_state, active_state, skips) - print('Selected indices: %r' % indices) - print('Selected main signer: %d' % main_signer) - # Randomly pick indices to include - bitfield = [1 if random.random() < attester_share else 0 for i in indices] - # Attestations - sigs = [bls.sign(parent_attestation, keymap[crystallized_state.active_validators[indices[i]].pubkey]) - for i in range(len(indices)) if bitfield[i]] - attestation_aggregate_sig = bls.aggregate_sigs(sigs) - print('Aggregated sig') - attestation_bitmask = bytearray((len(bitfield)-1) // 8 + 1) - for i, b in enumerate(bitfield): - attestation_bitmask[i//8] ^= (128 >> (i % 8)) * b - print('Aggregate bitmask:', bin(int.from_bytes(attestation_bitmask, 'big'))) - # Randomly pick indices to include for crosslinks - shard_aggregate_votes = [] - for shard, crosslinker_share in crosslink_shards: - print('Making crosslink in shard %d' % shard) - indices = get_shard_attesters(crystallized_state, shard) - print('Indices: %r' % indices) - bitfield = [1 if random.random() < crosslinker_share else 0 for i in indices] - bitmask = bytearray((len(bitfield)+7) // 8) - for i, b in enumerate(bitfield): - bitmask[i//8] ^= (128 >> (i % 8)) * b - print('Bitmask:', bin(int.from_bytes(bitmask, 'big'))) - shard_block_hash = blake(bytes([shard])) - crosslink_attestation_hash = get_crosslink_aggvote_msg(shard, shard_block_hash, crystallized_state) - sigs = [bls.sign(crosslink_attestation_hash, keymap[crystallized_state.active_validators[indices[i]].pubkey]) - for i in range(len(indices)) if bitfield[i]] - v = AggregateVote(shard_id=shard, - shard_block_hash=shard_block_hash, - signer_bitmask=bitmask, - aggregate_sig=list(bls.aggregate_sigs(sigs))) - shard_aggregate_votes.append(v) - print('Added %d shard aggregate votes' % len(crosslink_shards)) - # State calculations - o = Block(parent_hash=blake(parent_attestation), - skip_count=skips, - randao_reveal=blake(str(random.random()).encode('utf-8')), - attestation_bitmask=attestation_bitmask, - attestation_aggregate_sig=list(attestation_aggregate_sig), - shard_aggregate_votes=shard_aggregate_votes, - main_chain_ref=b'\x00'*32, - state_hash=b'\x00'*64) - print('Generated preliminary block header') - new_crystallized_state, new_active_state = \ - compute_state_transition((crystallized_state, active_state), parent, o, verify_sig=False) - print('Calculated state transition') - if crystallized_state == new_crystallized_state: - o.state_hash = blake(parent.state_hash[:32] + blake(serialize(new_active_state))) - else: - o.state_hash = blake(blake(serialize(new_crystallized_state)) + blake(serialize(new_active_state))) - # Main signature - o.sign(keymap[crystallized_state.active_validators[main_signer].pubkey]) - print('Signed') - return o, new_crystallized_state, new_active_state - -c, a, block = mk_genesis_state_and_block(keymap.keys()) -print('Generated genesis state') -print('Crystallized state length:', len(serialize(c))) -print('Active state length:', len(serialize(a))) -print('Block size:', len(serialize(block))) -block2, c2, a2 = mock_make_child((c, a), block, 0, 0.8, []) -t = time.time() -assert compute_state_transition((c, a), block, block2) -print("Normal block (basic attestation only) processed in %.4f sec" % (time.time() - t)) -print('Verified a block!') -block3, c3, a3 = mock_make_child((c2, a2), block2, 0, 0.8, [(0, 0.75)]) -print('Verified a block with a committee!') -while a3.height % SHARD_COUNT > 0: - block3, c3, a3 = mock_make_child((c3, a3), block3, 0, 0.8, [(a3.height, 0.6 + 0.02 * a3.height)]) - print('Height: %d' % a3.height) -print('FFG bitmask:', bin(int.from_bytes(a3.ffg_voter_bitmask, 'big'))) -block4, c4, a4 = mock_make_child((c3, a3), block3, 1, 0.55, []) -t = time.time() -assert compute_state_transition((c3, a3), block3, block4) -print("Epoch transition processed in %.4f sec" % (time.time() - t)) diff --git a/binary_fft.py b/binary_fft.py deleted file mode 100644 index 71c6800..0000000 --- a/binary_fft.py +++ /dev/null @@ -1,243 +0,0 @@ -def log2(x): - return 0 if x <= 1 else 1 + log2(x // 2) - -def raw_mul(a, b): - if a*b == 0: - return 0 - o = 0 - for i in range(log2(b) + 1): - if b & (1<= blog: - if a & (1<= len(b) - a = [x for x in a] - o = [] - apos = len(a) - 1 - bpos = len(b) - 1 - diff = apos - bpos - while diff >= 0: - quot = self.div(a[apos], b[bpos]) - o.insert(0, quot) - for i in range(bpos, -1, -1): - a[diff+i] ^= self.mul(b[i], quot) - apos -= 1 - diff -= 1 - return o - - # Build a polynomial that returns 0 at all specified xs - def zpoly(self, xs): - root = [1] - for x in xs: - root.insert(0, 0) - for j in range(len(root)-1): - root[j] ^= self.mul(root[j+1], x) - return root - - # Given p+1 y values and x values with no errors, recovers the original - # p+1 degree polynomial. - # Lagrange interpolation works roughly in the following way. - # 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] - # 2. For each x, generate a polynomial which equals its corresponding - # y coordinate at that point and 0 at all other points provided. - # 3. Add these polynomials together. - - def lagrange_interp(self, xs, ys): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - root = self.zpoly(xs) - assert len(root) == len(ys) + 1 - # print(root) - # Generate per-value numerator polynomials, eg. for x=x2, - # (x - x1) * (x - x3) * ... * (x - xn), by dividing the master - # polynomial back by each x coordinate - nums = [self.div_polys(root, [x, 1]) for x in xs] - # Generate denominators by evaluating numerator polys at each x - denoms = [self.eval_poly_at(nums[i], xs[i]) for i in range(len(xs))] - invdenoms = self.multi_inv(denoms) - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - b = [0 for y in ys] - for i in range(len(xs)): - yslice = self.mul(ys[i], invdenoms[i]) - for j in range(len(ys)): - if nums[i][j] and ys[i]: - b[j] ^= self.mul(nums[i][j], yslice) - return b - -def _simple_ft(field, vals): - assert len(vals) == 2**field.height - return [field.eval_poly_at(vals, i) for i in range(2**field.height)] - -# Returns `evens` and `odds` such that: -# poly(x) = evens(x^2+kx) + x * odds(x^2+kx) -# poly(x+k) = evens(x^2+kx) + (x+k) * odds(x^2+kx) -# -# Note that this satisfies two other invariants: -# -# poly(x+k) - poly(x) = k * odds(x^2+kx) -# poly(x)*(x+k) - poly(x+k)*x = k * evens(x^2+kx) - -def cast(field, poly, k): - if len(poly) <= 2: - return ([poly[0]], [poly[1] if len(poly) == 2 else 0]) - mod_power = 2 - while mod_power * 2 < len(poly): - mod_power *= 2 - half_mod_power = mod_power // 2 - k_to_half_mod_power = field.exp(k, half_mod_power) - low = poly + [0] * (mod_power * 2 - len(poly)) - high = low[len(low)-half_mod_power:] - low = low[:len(low)-mod_power] + [low[i] ^ field.mul(low[i+half_mod_power], k_to_half_mod_power) for i in range(len(low)-mod_power, len(low)-half_mod_power)] - high = low[len(low)-half_mod_power:] + high - low = low[:len(low)-mod_power] + [low[i] ^ field.mul(low[i+half_mod_power], k_to_half_mod_power) for i in range(len(low)-mod_power, len(low)-half_mod_power)] - low_cast = cast(field, low, k) - high_cast = cast(field, high, k) - return (low_cast[0] + high_cast[0], low_cast[1] + high_cast[1]) - -# Returns a polynomial p2 such that p2(x) = poly(x^2+kx) -def compose(field, poly, k): - if len(poly) == 1: - return poly + [0] - mod_power = 1 - while mod_power * 2 < len(poly): - mod_power *= 2 - k_to_mod_power = field.exp(k, mod_power) - low = compose(field, poly[:mod_power], k) + [0] * mod_power * 3 - high = compose(field, poly[mod_power:], k) + [0] * mod_power * 3 - return [low[i] ^ field.mul(high[i-mod_power], k_to_mod_power) ^ high[i-2*mod_power] for i in range(mod_power*4)] - -# Equivalent to [field.eval_poly_at(poly, x) for x in domain] -def fft(field, poly, domain): - # Base case: constant polynomials - if len(domain) == 1: - return [poly[0]] - # Split the domain into two cosets A and B, where for x in A, x+offset is in B - offset = domain[1] - # Get evens, odds such that: - # poly(x) = evens(x^2+offset*x) + x * odds(x^2+offset*x) - # poly(x+k) = evens(x^2+offset*x) + (x+k) * odds(x^2+offset*x) - evens, odds = cast(field, poly, offset) - # The smaller domain D = [x**2 - offset*x for x in A] = [x**2 - offset*x for x in B] - casted_domain = [field.mul(x, offset ^ x) for x in domain][::2] - # Two half-size sub-problems over the smaller domain, recovering - # evaluations of evens and odds over the smaller domain - even_points = fft(field, evens, casted_domain) - odd_points = fft(field, odds, casted_domain) - # Combine the evaluations of evens and odds into evaluations of poly - L = [e ^ field.mul(d, o) for d,e,o in zip(domain[::2], even_points, odd_points)] - R = [e ^ field.mul(d, o) for d,e,o in zip(domain[1::2], even_points, odd_points)] - return [R[i//2] if i%2 else L[i//2] for i in range(len(domain))] - -# The inverse function of fft, does the steps backwards -def invfft(field, vals, domain): - # Base case: constant polynomials - if len(domain) == 1: - return [vals[0]] - # Split the domain into two cosets A and B, where for x in A, x+offset is in B - offset = domain[1] - # Compute the evaluations of the evens and odds polynomials using the invariants: - # poly(x+k) - poly(x) = k * odds(x^2+kx) - # poly(x)*(x+k) - poly(x+k)*x = k * evens(x^2+kx) - L, R = vals[::2], vals[1::2] - even_points = [field.div(field.mul(l, d ^ offset) ^ field.mul(r, d), offset) for d, l, r in zip(domain[::2], L, R)] - odd_points = [field.div(l ^ r, offset) for d, l, r in zip(domain[::2], L, R)] - # The smaller domain D = [x**2 - offset*x for x in A] = [x**2 - offset*x for x in B] - casted_domain = [field.mul(x, offset ^ x) for x in domain][::2] - # Two half-size problems over the smaller domains, recovering - # the polynomials evens and odds - evens = invfft(field, even_points, casted_domain) - odds = invfft(field, odd_points, casted_domain) - # Given evens and odds where poly(x) = evens(x^2+offset*x) + x * odds(x^2+offset*x), - # recover poly - composed_evens = compose(field, evens, offset) + [0] - composed_odds = compose(field, odds, offset) + [0] - o = [composed_evens[i] ^ composed_odds[i-1] for i in range(len(vals))] - return o diff --git a/binary_fft/binary_fft.py b/binary_fft/binary_fft.py deleted file mode 100644 index ee6f009..0000000 --- a/binary_fft/binary_fft.py +++ /dev/null @@ -1,357 +0,0 @@ -def log2(x): - o = 0 - while x > 1: - x //= 2 - o += 1 - return o - -def is_power_of_2(x): - return x > 0 and x&(x-1) == 0 - -def raw_mul(a, b): - if a*b == 0: - return 0 - o = 0 - for i in range(log2(b) + 1): - if b & (1<= blog: - if a & (1<= len(b) - a = [x for x in a] - o = [] - apos = len(a) - 1 - bpos = len(b) - 1 - diff = apos - bpos - while diff >= 0: - quot = self.div(a[apos], b[bpos]) - o.insert(0, quot) - for i in range(bpos, -1, -1): - a[diff+i] ^= self.mul(b[i], quot) - apos -= 1 - diff -= 1 - return o - - # Build a polynomial that returns 0 at all specified xs - def zpoly(self, xs): - root = [1] - for x in xs: - root.insert(0, 0) - for j in range(len(root)-1): - root[j] ^= self.mul(root[j+1], x) - return root - - # Given p+1 y values and x values with no errors, recovers the original - # p+1 degree polynomial. - # Lagrange interpolation works roughly in the following way. - # 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] - # 2. For each x, generate a polynomial which equals its corresponding - # y coordinate at that point and 0 at all other points provided. - # 3. Add these polynomials together. - - def lagrange_interp(self, xs, ys): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - root = self.zpoly(xs) - assert len(root) == len(ys) + 1 - # print(root) - # Generate per-value numerator polynomials, eg. for x=x2, - # (x - x1) * (x - x3) * ... * (x - xn), by dividing the master - # polynomial back by each x coordinate - nums = [self.div_polys(root, [x, 1]) for x in xs] - # Generate denominators by evaluating numerator polys at each x - denoms = [self.eval_poly_at(nums[i], xs[i]) for i in range(len(xs))] - invdenoms = self.multi_inv(denoms) - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - b = [0 for y in ys] - for i in range(len(xs)): - yslice = self.mul(ys[i], invdenoms[i]) - for j in range(len(ys)): - if nums[i][j] and ys[i]: - b[j] ^= self.mul(nums[i][j], yslice) - return b - -def _simple_ft(field, domain, poly): - return [field.eval_poly_at(poly, i) for i in domain] - -# Returns `evens` and `odds` such that: -# poly(x) = evens(x**2+kx) + x * odds(x**2+kx) -# poly(x+k) = evens(x**2+kx) + (x+k) * odds(x**2+kx) -# -# Note that this satisfies two other invariants: -# -# poly(x+k) - poly(x) = k * odds(x**2+kx) -# poly(x)*(x+k) - poly(x+k)*x = k * evens(x**2+kx) - -def cast(field, poly, k): - if len(poly) <= 2: - return ([poly[0]], [poly[1] if len(poly) == 2 else 0]) - assert is_power_of_2(len(poly)) - mod_power = len(poly)//2 - half_mod_power = mod_power // 2 - k_to_half_mod_power = field.exp(k, half_mod_power) - # Calculate low = poly % (x**2 - k*x)**half_mod_power - # and high = poly // (x**2 - k*x)**half_mod_power - # Note that (x**2 - k*x)**n = x**2n - k**n * x**n in binary fields - low_and_high = poly[::] - for i in range(mod_power, half_mod_power*3): - low_and_high[i] ^= field.mul(low_and_high[i+half_mod_power], k_to_half_mod_power) - for i in range(half_mod_power, mod_power): - low_and_high[i] ^= field.mul(low_and_high[i+half_mod_power], k_to_half_mod_power) - # Recursively compute two half-size sub-problems, low and high - low_cast = cast(field, low_and_high[:mod_power], k) - high_cast = cast(field, low_and_high[mod_power:], k) - # Combine the results - return (low_cast[0] + high_cast[0], low_cast[1] + high_cast[1]) - -# Returns a polynomial p2 such that p2(x) = poly(x**2+kx) -def compose(field, poly, k): - if len(poly) == 2: - return [poly[0], field.mul(poly[1], k), poly[1], 0] - if len(poly) == 1: - return poly + [0] - # Largest mod_power=2**k such that mod_power >= len(poly)/2 - assert is_power_of_2(len(poly)) - mod_power = len(poly)//2 - k_to_mod_power = field.exp(k, mod_power) - # Recursively compute two half-size sub-problems, the bottom and top half - # of the polynomial - low = compose(field, poly[:mod_power], k) - high = compose(field, poly[mod_power:], k) - # Combine them together, multiplying the top one by (x**2-k*x)**n - # Note that (x**2 - k*x)**n = x**2n - k**n * x**n in binary fields - o = [0] * len(poly) * 2 - for i, (L, H) in enumerate(zip(low, high)): - o[i] ^= L - o[i+mod_power] ^= field.mul(H, k_to_mod_power) - o[i+2*mod_power] ^= H - return o - -# Equivalent to [field.eval_poly_at(poly, x) for x in domain] -# Special thanks to www.math.clemson.edu/~sgao/papers/GM10.pdf for insights -# though this algorithm is not exactly identical to any algorithm in the paper -def fft(field, domain, poly): - # Base case: constant polynomials - # if len(domain) == 1: - # return [poly[0]] - if len(domain) <= 8: - return _simple_ft(field, domain, poly) - # Split the domain into two cosets A and B, where for x in A, x+offset is in B - offset = domain[1] - # Get evens, odds such that: - # poly(x) = evens(x**2+offset*x) + x * odds(x**2+offset*x) - # poly(x+k) = evens(x**2+offset*x) + (x+k) * odds(x**2+offset*x) - evens, odds = cast(field, poly, offset) - # The smaller domain D = [x**2 - offset*x for x in A] = [x**2 - offset*x for x in B] - casted_domain = [field.mul(x, offset ^ x) for x in domain[::2]] - # Two half-size sub-problems over the smaller domain, recovering - # evaluations of evens and odds over the smaller domain - even_points = fft(field, casted_domain, evens) - odd_points = fft(field, casted_domain, odds) - # Combine the evaluations of evens and odds into evaluations of poly - o = [] - for i in range(len(domain)//2): - o.append(even_points[i] ^ field.mul(domain[i*2], odd_points[i])) - o.append(even_points[i] ^ field.mul(domain[i*2+1], odd_points[i])) - return o - -# The inverse function of fft, does the steps backwards -def invfft(field, domain, vals): - # Base case: constant polynomials - if len(domain) == 1: - return [vals[0]] - # if len(domain) <= 4: - # return field.lagrange_interp(domain, vals) - # Split the domain into two cosets A and B, where for x in A, x+offset is in B - offset = domain[1] - # Compute the evaluations of the evens and odds polynomials using the invariants: - # poly(x+k) - poly(x) = k * odds(x**2+kx) - # poly(x)*(x+k) - poly(x+k)*x = k * evens(x**2+kx) - even_points = [0] * (len(vals)//2) - odd_points = [0] * (len(vals)//2) - for i in range(len(domain)//2): - p_of_x, p_of_x_plus_k = vals[i*2], vals[i*2+1] - x = domain[i*2] - even_points[i] = field.div(field.mul(p_of_x, x ^ offset) ^ field.mul(p_of_x_plus_k, x), offset) - odd_points[i] = field.div(p_of_x ^ p_of_x_plus_k, offset) - casted_domain = [field.mul(x, offset ^ x) for x in domain[::2]] - # Two half-size problems over the smaller domains, recovering - # the polynomials evens and odds - evens = invfft(field, casted_domain, even_points) - odds = invfft(field, casted_domain, odd_points) - # Given evens and odds where poly(x) = evens(x**2+offset*x) + x * odds(x**2+offset*x), - # recover poly - composed_evens = compose(field, evens, offset) + [0] - composed_odds = [0] + compose(field, odds, offset) - o = [composed_evens[i] ^ composed_odds[i] for i in range(len(vals))] - return o - -# shift_polys[i][j] is the 2**j degree coefficient of the polynomial that evaluates to [1,1...1, 0,0....0] with 2**(i-1) ones and 2**(i-1) zeroes -shift_polys = [[], [1], [32755, 32755], [52774, 60631, 8945], [38902, 5560, 44524, 12194], [55266, 46488, 60321, 5401, 40130], [21827, 32224, 51565, 15072, 8277, 64379], [59460, 15452, 60370, 24737, 20321, 35516, 39606], [42623, 56997, 25925, 15351, 16625, 47045, 38250, 17462], [7575, 27410, 32434, 22187, 28933, 15447, 37964, 38186, 4776], [39976, 61188, 42456, 2155, 6178, 34033, 52305, 14913, 2896, 48908], [6990, 12021, 36054, 16198, 17011, 14018, 58553, 13272, 25318, 5288, 21429], [16440, 34925, 14360, 22561, 43883, 36645, 7613, 26531, 8597, 59502, 61283, 53412]] - -def invfft2(field, vals): - if len(vals) == 1: - return [vals[0]] - L = invfft2(field, vals[:len(vals)//2]) - R = shift(field, invfft2(field, vals[len(vals)//2:]), len(vals)//2) - o = [0] * len(vals) - for j, (l, r) in enumerate(zip(L, R)): - o[j] ^= l - for i, coeff in enumerate(shift_polys[log2(len(vals))]): - o[2**i+j] ^= field.mul(l ^ r, coeff) - # print(vals, o) - return o - -# def invfft(field, domain, vals): return invfft2(field, vals) - -# Multiplies two polynomials using the FFT method -def mul(field, domain, p1, p2): - assert len(p1) <= len(domain) and len(p2) <= len(domain) - values1 = fft(field, domain, p1) - values2 = fft(field, domain, p2) - values3 = [field.mul(v1, v2) for v1, v2 in zip(values1, values2)] - return invfft(field, domain, values3) - -# Generates the polynomial `p(x) = (x - xs[0]) * (x - xs[1]) * ...` -def zpoly(field, xs): - if len(xs) == 0: - # print([1], domain, xs) - return [1] - if len(xs) == 1: - # print([xs[0], 1], domain, xs) - return [xs[0], 1] - domain = list(range(2**log2(max(xs)+1) * 2)) - offset = domain[1] - zL = zpoly(field, xs[::2]) - zR = zpoly(field, xs[1::2]) - o = mul(field, domain, zL, zR) - # print(o, domain, xs) - return o - -# Returns q(x) = p(x + k) -def shift(field, poly, k): - if len(poly) == 1: - return poly - # Largest mod_power=2**k such that mod_power >= len(poly)/2 - assert is_power_of_2(len(poly)) - mod_power = len(poly)//2 - k_to_mod_power = field.exp(k, mod_power) - # Calculate low = poly % (x+k)**mod_power - # and high = poly // (x+k)**mod_power - # Note that (x+k)**n = x**n + k**n for power-of-two powers in binary fields - low_and_high = poly[::] - for i in range(mod_power): - low_and_high[i] ^= field.mul(low_and_high[i+mod_power], k_to_mod_power) - return shift(field, low_and_high[:mod_power], k) + shift(field, low_and_high[mod_power:], k) - -# Interpolates the polynomial where `p(xs[i]) = vals[i]` -def interpolate(field, xs, vals): - domain_size = 2**(log2(max(xs)) + 1) - assert domain_size * 2 <= 2**field.height - domain = list(range(domain_size)) - big_domain = list(range(domain_size * 2)) - z = zpoly(field, [x for x in domain if x not in xs]) - # print("z = ", z) - z_values = fft(field, big_domain, z) - # print("z_values = ", z_values) - p_times_z_values = [0] * len(domain) - for v, d in zip(vals, xs): - p_times_z_values[d] = field.mul(v, z_values[d]) - # print("p_times_z_values = ", p_times_z_values) - p_times_z = invfft(field, domain, p_times_z_values) - # print("p_times_z = ", p_times_z) - shifted_p_times_z_values = fft(field, big_domain, p_times_z)[domain_size:] - # print("shifted_p_times_z_values =", shifted_p_times_z_values) - shifted_p_values = [field.div(x, y) for x,y in zip(shifted_p_times_z_values, z_values[domain_size:])] - # print("shifted_p_values =", shifted_p_values) - shifted_p = invfft(field, domain, shifted_p_values) - return shift(field, shifted_p, domain_size) diff --git a/binary_fft/ethereum_data_root.py b/binary_fft/ethereum_data_root.py deleted file mode 100644 index 8cd7955..0000000 --- a/binary_fft/ethereum_data_root.py +++ /dev/null @@ -1,164 +0,0 @@ -# import fast_binary_fft as b -import binary_fft as b -f = b.BinaryField(65579) -from hashlib import sha256 -def hash(x): return sha256(x).digest() - -log2 = b.log2 - -# Alternative optimized/simplified inverse-FFT implementation - -# shift_polys[i][j] is the 2**j degree coefficient of the polynomial that evaluates to [1,1...1, 0,0....0] with 2**(i-1) ones and 2**(i-1) zeroes -shift_polys = [[], [1], [32755, 32755], [52774, 60631, 8945], [38902, 5560, 44524, 12194], [55266, 46488, 60321, 5401, 40130], [21827, 32224, 51565, 15072, 8277, 64379], [59460, 15452, 60370, 24737, 20321, 35516, 39606], [42623, 56997, 25925, 15351, 16625, 47045, 38250, 17462], [7575, 27410, 32434, 22187, 28933, 15447, 37964, 38186, 4776], [39976, 61188, 42456, 2155, 6178, 34033, 52305, 14913, 2896, 48908], [6990, 12021, 36054, 16198, 17011, 14018, 58553, 13272, 25318, 5288, 21429], [16440, 34925, 14360, 22561, 43883, 36645, 7613, 26531, 8597, 59502, 61283, 53412]] - -def invfft2(field, vals): - if len(vals) == 1: - return [vals[0]] - L = invfft2(field, vals[:len(vals)//2]) - R = b.shift(field, invfft2(field, vals[len(vals)//2:]), len(vals)//2) - o = [0] * len(vals) - for j, (l, r) in enumerate(zip(L, R)): - o[j] ^= l - for i, coeff in enumerate(shift_polys[log2(len(vals))]): - o[2**i+j] ^= field.mul(l ^ r, coeff) - # print(vals, o) - return o - -# Alternative simplified but less efficient FFT implementation -def p_mod_shift(field, poly): - shift_poly = shift_polys[log2(len(poly))] - half_height = len(poly)//2 - low = poly[::] - high = [] - while len(high) < half_height: - high.insert(0, field.div(low[-1], shift_poly[-1])) - for i, coeff in enumerate(shift_poly[:-1]): - low[-half_height-1+2**i] ^= field.mul(high[0], coeff) - low.pop() - return high, low - -def fft2(field, poly): - # if len(poly) == 1: - # return [poly[0]] - if len(poly) <= 8: - return b._simple_ft(field, list(range(len(poly))), poly) - # p(x) = high(x) * s(x) + low(x) - high, low = p_mod_shift(field, poly) - # p(x) = g(x) * (s(x)+1) + h(x) * s(x) - g, h = low, [x^y for x,y in zip(high, low)] - # print(poly, g, h) - g_values = fft2(field, g) - h_values = fft2(field, b.shift(field, h, len(poly)//2)) - return g_values + h_values - -def eval_polynomial_at(poly, x): - return f.eval_poly_at(poly, x) - -def interpolate(xs, values): - if xs == list(range(len(xs))): - return invfft2(f, values) - else: - return b.interpolate(f, xs, values) - -def next_power_of_two(n): - return 2**log2(n-1) * 2 - -def multi_evaluate(xs, poly): - # degree = next_power_of_two(max(xs)+1) - extended_values = b.fft(f, list(range(next_power_of_two(max(xs)+1))), poly) - # extended_values = fft2(f, poly + [0] * (degree - len(poly))) - return [extended_values[x] for x in xs] - -def get_merkle_root(values): - extended_length = 2**log2(len(values)) - tree = [None] * extended_length + values + [b'\x00'*32] * (extended_length - len(values)) - for i in range(extended_length - 1, 0, -1): - tree[i] = hash(tree[i*2] + tree[i*2+1]) - return tree[1] - -def int_to_bytes(i, n): - return i.to_bytes(n, 'little') - -def bytes_to_int(b): - return int.from_bytes(b, 'little') - -def integer_squareroot(n: int) -> int: - """ - The largest integer ``x`` such that ``x**2`` is less than or equal to ``n``. - """ - assert n >= 0 - x = n - y = (x + 1) // 2 - while y < x: - x = y - y = (x + n // x) // 2 - return x - -Bytes32 = 0 -List = {int: 1, Bytes32: 2, 2: 2} -FIELD_ELEMENT_BITS = 16 -ZERO_HASH = b'\x00' * 32 - -def fill(xs: List[int], values: List[int], length: int) -> List[int]: - """ - Takes the minimal polynomial that returns values[i] at xs[i] and computes - its outputs for all values in range(0, length) - """ - poly = interpolate(xs, values) - # o = values + multi_evaluate(list(range(len(values))), b.shift(f, poly, len(values))) - # return o - return multi_evaluate(list(range(length)), poly) - -def fill_axis(xs: List[int], values: List[Bytes32], length: int) -> List[Bytes32]: - """ - Interprets a series of 32-byte chunks as a series of ordered packages of field - elements. For each i, treats the set of i'th field elements in each chunk as - evaluations of a polynomial. Evaluates the polynomials on the extended domain - range(0, length) and provides the 32-byte chunks that are the packages of the - extended evaluations of every polynomial at each coordinate. - """ - data = [[bytes_to_int(a[i: i + FIELD_ELEMENT_BITS//8]) for a in values] for i in range(0, 32, FIELD_ELEMENT_BITS//8)] - newdata = [fill(xs, d, length) for d in data] - return [b''.join([int_to_bytes(n[i], FIELD_ELEMENT_BITS//8) for n in newdata]) for i in range(length)] - -def get_data_square(data: bytes) -> List[List[Bytes32]]: - """ - Converts data into a 2**k x 2**k square, padding with zeroes if necessary. - """ - print("Data length:", len(data)) - chunks = [data[i: i+32] for i in range(0, len(data), 32)] - if len(chunks[-1]) < 32: - chunks[-1] += b'\x00' * (32 - len(chunks[-1])) - print("Chunks:", len(chunks)) - target_size = 4**(log2(len(chunks) - 1) // 2 + 1) - chunks.extend([ZERO_HASH for i in range(len(chunks), target_size)]) - print("Extended to:", len(chunks)) - side_length = integer_squareroot(len(chunks)) - print("Side length:", side_length) - return [chunks[i: i + side_length] for i in range(0, len(chunks), side_length)] - -def extend_data_square(square: List[List[Bytes32]]) -> List[List[Bytes32]]: - """ - Extends a 2**k x 2**k square to 2**(k+1) x 2**(k+1) using `fill_axis` to - fill rows and columns. - """ - L = len(square) - # Extend each row - square = [fill_axis(list(range(L)), row, L * 2) for row in square] - # Flip rows and columns - square = [[square[j][i] for i in range(L)] for j in range(len(square))] - # Extend each column - square = [fill_axis(list(range(L)), row, L * 2) for row in square] - # Flip back to row form - square = [[square[j][i] for i in range(L)] for j in range(len(square))] - return square - -def mk_data_root(data: bytes) -> Bytes32: - """ - Computes the root of the package of rows and colums of a given piece of data. - """ - square = extend_data_square(get_data_square(data)) - row_roots = [get_merkle_root(r) for r in square] - transposed_square = [[square[j][i] for i in range(len(square))] for j in range(len(square))] - column_roots = [get_merkle_root(r) for r in transposed_square] - return hash(get_merkle_root(row_roots) + get_merkle_root(column_roots)) diff --git a/binary_fft/fast_binary_fft.pyx b/binary_fft/fast_binary_fft.pyx deleted file mode 100644 index d76ec7f..0000000 --- a/binary_fft/fast_binary_fft.pyx +++ /dev/null @@ -1,346 +0,0 @@ -from libcpp.vector cimport vector - -def is_power_of_2(int x): - return x > 0 and x&(x-1) == 0 - -def log2(int x): - cdef int o = 0 - while x > 1: - x //= 2 - o += 1 - return o - -def raw_mul(int a, int b): - if a*b == 0: - return 0 - cdef int o = 0 - for i in range(log2(b) + 1): - if b & (1<= blog: - if a & (1<= len(b) - cdef vector[int] a = [x for x in _a] - cdef vector[int] o = [] - cdef int apos = len(a) - 1 - cdef int bpos = len(b) - 1 - cdef int diff = apos - bpos - cdef int quot - while diff >= 0: - quot = self.div(a[apos], b[bpos]) - o = [quot] + o - for i in range(bpos, -1, -1): - a[diff+i] ^= self.mul(b[i], quot) - apos -= 1 - diff -= 1 - return o - - # Build a polynomial that returns 0 at all specified xs - def zpoly(self, vector[int] xs): - cdef vector[int] root = [1] - for x in xs: - root = [0] + root - for j in range(len(root)-1): - root[j] ^= self.mul(root[j+1], x) - return root - - # Given p+1 y values and x values with no errors, recovers the original - # p+1 degree polynomial. - # Lagrange interpolation works roughly in the following way. - # 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] - # 2. For each x, generate a polynomial which equals its corresponding - # y coordinate at that point and 0 at all other points provided. - # 3. Add these polynomials together. - - def lagrange_interp(self, vector[int] xs, vector[int] ys): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - cdef vector[int] root = self.zpoly(xs) - assert len(root) == len(ys) + 1 - # print(root) - # Generate per-value numerator polynomials, eg. for x=x2, - # (x - x1) * (x - x3) * ... * (x - xn), by dividing the master - # polynomial back by each x coordinate - cdef vector[vector[int]] nums = [self.div_polys(root, [x, 1]) for x in xs] - # Generate denominators by evaluating numerator polys at each x - cdef vector[int] denoms = [self.eval_poly_at(nums[i], xs[i]) for i in range(len(xs))] - cdef vector[int] invdenoms = self.multi_inv(denoms) - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - cdef vector[int] b = [0 for y in ys] - cdef int yslice - for i in range(len(xs)): - yslice = self.mul(ys[i], invdenoms[i]) - for j in range(len(ys)): - if nums[i][j] and ys[i]: - b[j] ^= self.mul(nums[i][j], yslice) - return b - -def _simple_ft(field, vector[int] domain, vector[int] poly): - cdef vector[int] o = [field.eval_poly_at(poly, i) for i in domain] - return o - -# Returns `evens` and `odds` such that: -# poly(x) = evens(x**2+kx) + x * odds(x**2+kx) -# poly(x+k) = evens(x**2+kx) + (x+k) * odds(x**2+kx) -# -# Note that this satisfies two other invariants: -# -# poly(x+k) - poly(x) = k * odds(x**2+kx) -# poly(x)*(x+k) - poly(x+k)*x = k * evens(x**2+kx) - -def cast(field, poly, int k): - if len(poly) <= 2: - return ([poly[0]], [poly[1] if len(poly) == 2 else 0]) - assert is_power_of_2(len(poly)) - mod_power = len(poly)//2 - half_mod_power = mod_power // 2 - k_to_half_mod_power = field.exp(k, half_mod_power) - # Calculate low = poly % (x**2 - k*x)**half_mod_power - # and high = poly // (x**2 - k*x)**half_mod_power - # Note that (x**2 - k*x)**n = x**2n - k**n * x**n in binary fields - low_and_high = poly[::] - for i in range(mod_power, half_mod_power*3): - low_and_high[i] ^= field.mul(low_and_high[i+half_mod_power], k_to_half_mod_power) - for i in range(half_mod_power, mod_power): - low_and_high[i] ^= field.mul(low_and_high[i+half_mod_power], k_to_half_mod_power) - # Recursively compute two half-size sub-problems, low and high - low_cast = cast(field, low_and_high[:mod_power], k) - high_cast = cast(field, low_and_high[mod_power:], k) - # Combine the results - return (low_cast[0] + high_cast[0], low_cast[1] + high_cast[1]) - -# Returns a polynomial p2 such that p2(x) = poly(x**2+kx) -def compose(field, poly, k): - if len(poly) == 2: - return [poly[0], field.mul(poly[1], k), poly[1], 0] - if len(poly) == 1: - return poly + [0] - # Largest mod_power=2**k such that mod_power >= len(poly)/2 - assert is_power_of_2(len(poly)) - mod_power = len(poly)//2 - k_to_mod_power = field.exp(k, mod_power) - # Recursively compute two half-size sub-problems, the bottom and top half - # of the polynomial - low = compose(field, poly[:mod_power], k) - high = compose(field, poly[mod_power:], k) - # Combine them together, multiplying the top one by (x**2-k*x)**n - # Note that (x**2 - k*x)**n = x**2n - k**n * x**n in binary fields - o = [0] * len(poly) * 2 - for i, (L, H) in enumerate(zip(low, high)): - o[i] ^= L - o[i+mod_power] ^= field.mul(H, k_to_mod_power) - o[i+2*mod_power] ^= H - return o - -# Equivalent to [field.eval_poly_at(poly, x) for x in domain] -# Special thanks to www.math.clemson.edu/~sgao/papers/GM10.pdf for insights -# though this algorithm is not exactly identical to any algorithm in the paper -def fft(field, domain, poly): - # Base case: constant polynomials - # if len(domain) == 1: - # return [poly[0]] - if len(domain) <= 8: - return _simple_ft(field, domain, poly) - # Split the domain into two cosets A and B, where for x in A, x+offset is in B - offset = domain[1] - # Get evens, odds such that: - # poly(x) = evens(x**2+offset*x) + x * odds(x**2+offset*x) - # poly(x+k) = evens(x**2+offset*x) + (x+k) * odds(x**2+offset*x) - evens, odds = cast(field, poly, offset) - # The smaller domain D = [x**2 - offset*x for x in A] = [x**2 - offset*x for x in B] - casted_domain = [field.mul(x, offset ^ x) for x in domain[::2]] - # Two half-size sub-problems over the smaller domain, recovering - # evaluations of evens and odds over the smaller domain - even_points = fft(field, casted_domain, evens) - odd_points = fft(field, casted_domain, odds) - # Combine the evaluations of evens and odds into evaluations of poly - L = [e ^ field.mul(d, o) for d,e,o in zip(domain[::2], even_points, odd_points)] - R = [e ^ field.mul(d, o) for d,e,o in zip(domain[1::2], even_points, odd_points)] - return [R[i//2] if i%2 else L[i//2] for i in range(len(domain))] - -# The inverse function of fft, does the steps backwards -def invfft(field, domain, vals): - # Base case: constant polynomials - if len(domain) == 1: - return [vals[0]] - # if len(domain) <= 4: - # return field.lagrange_interp(domain, vals) - # Split the domain into two cosets A and B, where for x in A, x+offset is in B - offset = domain[1] - # Compute the evaluations of the evens and odds polynomials using the invariants: - # poly(x+k) - poly(x) = k * odds(x**2+kx) - # poly(x)*(x+k) - poly(x+k)*x = k * evens(x**2+kx) - L, R = vals[::2], vals[1::2] - even_points = [field.div(field.mul(l, d ^ offset) ^ field.mul(r, d), offset) for d, l, r in zip(domain[::2], L, R)] - odd_points = [field.div(l ^ r, offset) for d, l, r in zip(domain[::2], L, R)] - # The smaller domain D = [x**2 - offset*x for x in A] = [x**2 - offset*x for x in B] - casted_domain = [field.mul(x, offset ^ x) for x in domain][::2] - # Two half-size problems over the smaller domains, recovering - # the polynomials evens and odds - evens = invfft(field, casted_domain, even_points) - odds = invfft(field, casted_domain, odd_points) - # Given evens and odds where poly(x) = evens(x**2+offset*x) + x * odds(x**2+offset*x), - # recover poly - composed_evens = compose(field, evens, offset) + [0] - composed_odds = compose(field, odds, offset) + [0] - o = [composed_evens[i] ^ composed_odds[i-1] for i in range(len(vals))] - return o - -# Multiplies two polynomials using the FFT method -def mul(field, domain, p1, p2): - assert len(p1) <= len(domain) and len(p2) <= len(domain) - values1 = fft(field, domain, p1) - values2 = fft(field, domain, p2) - values3 = [field.mul(v1, v2) for v1, v2 in zip(values1, values2)] - return invfft(field, domain, values3) - -# Generates the polynomial `p(x) = (x - xs[0]) * (x - xs[1]) * ...` -def zpoly(field, xs): - if len(xs) == 0: - # print([1], domain, xs) - return [1] - if len(xs) == 1: - # print([xs[0], 1], domain, xs) - return [xs[0], 1] - domain = list(range(2**log2(max(xs)) * 2)) - offset = domain[1] - zL = zpoly(field, xs[::2]) - zR = zpoly(field, xs[1::2]) - o = mul(field, domain, zL, zR) - # print(o, domain, xs) - return o - -# Returns q(x) = p(x + k) -def shift(field, poly, k): - if len(poly) == 1: - return poly - # Largest mod_power=2**k such that mod_power >= len(poly)/2 - mod_power = 1 - while mod_power * 2 < len(poly): - mod_power *= 2 - k_to_mod_power = field.exp(k, mod_power) - # Calculate low = poly % (x+k)**mod_power - # and high = poly // (x+k)**mod_power - # Note that (x+k)**n = x**n + k**n for power-of-two powers in binary fields - high = poly[mod_power:] + [0] * (2 * mod_power - len(poly)) - low = [poly[i] ^ field.mul(poly[i + mod_power], k_to_mod_power) for i in range(mod_power)] - return shift(field, low, k) + shift(field, high, k) - -# Interpolates the polynomial where `p(xs[i]) = vals[i]` -def interpolate(field, xs, vals): - domain_size = 2**(log2(max(xs)) + 1) - assert domain_size * 2 <= 2**field.height - domain = list(range(domain_size)) - big_domain = list(range(domain_size * 2)) - z = zpoly(field, [x for x in domain if x not in xs]) - # print("z = ", z) - z_values = fft(field, big_domain, z) - # print("z_values = ", z_values) - p_times_z_values = [0] * len(domain) - for v, d in zip(vals, xs): - p_times_z_values[d] = field.mul(v, z_values[d]) - # print("p_times_z_values = ", p_times_z_values) - p_times_z = invfft(field, domain, p_times_z_values) - # print("p_times_z = ", p_times_z) - shifted_p_times_z_values = fft(field, big_domain, p_times_z)[domain_size:] - # print("shifted_p_times_z_values =", shifted_p_times_z_values) - shifted_p_values = [field.div(x, y) for x,y in zip(shifted_p_times_z_values, z_values[domain_size:])] - # print("shifted_p_values =", shifted_p_values) - shifted_p = invfft(field, domain, shifted_p_values) - return shift(field, shifted_p, domain_size) diff --git a/binary_fft/test_binary_fft.py b/binary_fft/test_binary_fft.py deleted file mode 100644 index be04b52..0000000 --- a/binary_fft/test_binary_fft.py +++ /dev/null @@ -1,20 +0,0 @@ -import binary_fft - -bigf = binary_fft.BinaryField(1033) -poly = [x**9 % 1024 for x in range(1024)] -z = binary_fft.fft(bigf, range(1024), poly) -z2 = binary_fft._simple_ft(bigf, range(1024), poly) -assert z == z2 -poly2 = binary_fft.invfft(bigf, range(1024), z) -assert poly2 == poly -print("Invfft and fft tests passed") -poly3 = [x**9 % 1024 for x in range(25)] -xs = [x*11 % 32 for x in range(25)] -ys = [bigf.eval_poly_at(poly3, x) for x in xs] -poly4 = binary_fft.interpolate(bigf, xs, ys) -assert poly4[:len(poly3)] == poly3 -xs = [x*11 % 32 for x in range(1, 25)] -ys = [bigf.eval_poly_at(poly3, x) for x in xs] -poly5 = binary_fft.interpolate(bigf, xs, ys) -assert poly5[:len(poly3)] == poly3 -print("Interpolation tests passed") diff --git a/binary_fft/test_ethereum_data_root.py b/binary_fft/test_ethereum_data_root.py deleted file mode 100644 index 9d323a4..0000000 --- a/binary_fft/test_ethereum_data_root.py +++ /dev/null @@ -1,10 +0,0 @@ -import ethereum_data_root as e -import sys -import os -from hashlib import sha256 -datastream = b''.join([sha256(bytes([i])).digest() for i in range(256)]) - -if __name__ == '__main__': - L = int(sys.argv[1]) - data = (datastream * (L // len(datastream) + 1))[:L] - print(e.mk_data_root(data)) diff --git a/bitcoin_unlimited_style_sizelimits.py b/bitcoin_unlimited_style_sizelimits.py deleted file mode 100644 index 9b9699b..0000000 --- a/bitcoin_unlimited_style_sizelimits.py +++ /dev/null @@ -1,166 +0,0 @@ -# The purpose of this script is to create an evolutionary -# model to study the equilibrium effects of Bitcoin Unlimited-style -# "emergent consensus". Note that the model is not yet quite -# complete as it does not take into account the benefits of -# mining "sister blocks" that steal transaction fees, though it -# does give a rough idea of what equilibrium behavior -# among the various miner policy dimensions (block accept size, -# override depth, block creation size) looks like -import random - -# Block reward -REWARD = 1000 -# Call this function to get a tx with the right fee -TX_FEE_DISTRIBUTION = lambda: (10000 // random.randrange(5, 250)) * 0.01 -# TX_FEE_DISTRIBUTION = lambda: 20 -# Propagation time -PROPTIME_FACTOR = 1 - -# List of tuples: -# (default limit, n-block limit, acceptance depth, creation limit) -strategies = [] -for i in range(4): - for j in range(4): - strategies.append([2 + i * 2, 100, 3, 10 + j * 4]) - -class Block(): - def __init__(self, parent, size, fees, miner): - self.hash = random.randrange(10**20) - self.parent = parent - self.score = 1 if self.parent is None else parent.score + 1 - self.miner = miner - self.size = size - self.fees = fees - -class Miner(): - def __init__(self, strategy, id): - self.limit, self.big_limit, self.accept_depth, self.creation_limit = strategy - self.chain = {} - self.big_chain = {} - self.head = None - self.big_head = None - self.id = id - self.future = {} - self.children = {} - self.created = 0 - - def process_history(self, time): - deletes = [] - for t in self.future: - if t <= time: - for b in self.future[t]: - self.process_block(b) - deletes.append(t) - for t in deletes: - del self.future[t] - - def add_block(self, block, time): - self.process_history(time) - if time + int(block.size * PROPTIME_FACTOR) not in self.future: - self.future[time + int(block.size * PROPTIME_FACTOR)] = [block] - else: - self.future[time + int(block.size * PROPTIME_FACTOR)].append(block) - - def process_block(self, block): - if block.size <= self.limit and (block.parent is None or block.parent.hash in self.chain): - self.chain[block.hash] = block - if block.score > (self.head.score if self.head else 0): - self.head = block - if block.size <= self.big_limit and (block.parent is None or block.parent.hash in self.big_chain): - self.big_chain[block.hash] = block - if block.score > (self.big_head.score if self.big_head else 0): - self.big_head = block - if block.score > (self.head.score if self.head else 0) + self.accept_depth: - self.head = block - self.chain[block.hash] = block - if block.parent and block.parent.hash not in self.chain and block.parent.hash not in self.big_chain: - if block.parent.hash not in self.children: - self.children[block.parent.hash] = [block] - else: - self.children[block.parent.hash].append(block) - if block.hash in self.children: - for c in self.children[block.hash]: - self.process_block(c) - del self.children[block.hash] - - def create_block(self, backlog, time): - self.process_history(time) - fees = sum(backlog[:self.creation_limit]) - # print 'Creating block of size %d (fees %d, seq %d)' % (self.creation_limit, fees, self.head.score + 1 if self.head else 1) - self.created += 1 - return Block(self.head, self.creation_limit, fees, self.id) - - -def simulate(strats): - miners = [Miner(strat, i) for i, strat in enumerate(strats)] - backlog = [] - for i in range(100000): - if i % 10000 == 0: - print 'Progress %d' % i - backlog.append(TX_FEE_DISTRIBUTION()) - if random.random() < 0.01: - backlog = sorted(backlog)[::-1] - miner = random.choice(miners) - b = miner.create_block(backlog, i) - backlog = backlog[b.size:] - for m in miners: - m.add_block(b, i) - rewards = [0] * len(miners) - blocks = [0] * len(miners) - h = miners[0].head - sz = 0 - while h is not None: - rewards[h.miner] += REWARD + h.fees - blocks[h.miner] += 1 - h = h.parent - sz += 1 - return rewards, blocks, [m.created for m in miners] - -for r in range(200): - tests = [] - for s in strategies: - tests.append(s) - tests.append((s[0] - 2, s[1], s[2], s[3])) - tests.append((s[0] + 2, s[1], s[2], s[3])) - tests.append((s[0], s[1], s[2] - 1, s[3])) - tests.append((s[0], s[1], s[2] + 1, s[3])) - tests.append((s[0], s[1], s[2], s[3] - 2)) - tests.append((s[0], s[1], s[2], s[3] + 2)) - NUM_TESTS = 7 - print 'Starting simulation' - results, blks, created = simulate(tests) - for i, s in enumerate(strategies): - base = results[i * NUM_TESTS] - if results[i * NUM_TESTS + 1] < base < results[i * NUM_TESTS + 2]: - print 'Increasing base accept size beneficial at %r' % s - s[0] += 2 - if results[i * NUM_TESTS + 1] > base > results[i * NUM_TESTS + 2] and s[0] > 2: - print 'Decreasing base accept size beneficial at %r' % s - s[0] -= 2 - if results[i * NUM_TESTS + 3] < base < results[i * NUM_TESTS + 4]: - print 'Increasing override depth beneficial at %r' % s - s[2] += 1 - if results[i * NUM_TESTS + 3] > base > results[i * NUM_TESTS + 4] and s[2] > 1: - print 'Decreasing override depth beneficial at %r' % s - s[2] -= 1 - if results[i * NUM_TESTS + 5] < base < results[i * NUM_TESTS + 6]: - print 'Increasing creation size beneficial at %r' % s - s[3] += 2 - if results[i * NUM_TESTS + 5] > base > results[i * NUM_TESTS + 6] and s[3] > 2: - print 'Decreasing creation size beneficial at %r' % s - s[3] -= 2 - for s in strategies: - print s - print 'Chain quality (per miner):', [(b * 100 / c) if c else 0 for b, c in zip(blks, created)] - print 'Chain quality (total, non-perturbed miners only):', sum(blks[::NUM_TESTS]) * 1.0 / sum(created[::NUM_TESTS]) - if r % 20 == 0: - print 'Control round' - results, blks, created = simulate(strategies) - print 'Chain quality (per miner):', [(b * 100 / c) if c else 0 for b, c in zip(blks, created)] - print 'Chain quality (total):', sum(blks) * 1.0 / sum(created) - - - -# results = simulate(strategies) -# for s, r in zip(strategies, results): -# print s[0], s[3], r diff --git a/blind_and_swap/blind_and_swap.py b/blind_and_swap/blind_and_swap.py deleted file mode 100644 index e43d3b2..0000000 --- a/blind_and_swap/blind_and_swap.py +++ /dev/null @@ -1,143 +0,0 @@ -# THIS IS EXPERIMENTAL CODE. DO NOT USE IN PRODUCTION! - -from hashlib import sha256 -hash_to_int = lambda x: int.from_bytes(sha256(x).digest(), 'little') - -from py_ecc import bn128 as curve -POINT = tuple -SIG2 = tuple -SIG3 = tuple - -def serialize_int(x): - return x.to_bytes(32, 'little') - -def serialize_point(pt): - x, y = pt - return x.n.to_bytes(32, 'little') + y.n.to_bytes(32, 'little') - -def privtopub(key): - return curve.multiply(curve.G1, key) - -# Linear combination of a list of points and values -def lincomb(pts: list, values: list) -> POINT: - o = curve.Z1 - for pt, value in zip(pts, values): - o = curve.add(o, curve.multiply(pt, value)) - return o - -# Make a Schnorr signature -def sign(msg: bytes, key: int) -> SIG2: - r = hash_to_int(msg + serialize_int(key)) - R = curve.multiply(curve.G1, r) - e = hash_to_int(serialize_point(R) + msg) - s = (r - key * e) % curve.curve_order - return (s, e) - -# Verify a Schnorr signature -def verify(msg: bytes, KEY: POINT, sig: SIG2) -> bool: - s, e = sig - # Gs + Ke = G(r - ke) + Ke = Gr - Ke + Ke = R - R = curve.add(curve.multiply(curve.G1, s), curve.multiply(KEY, e)) - new_e = hash_to_int(serialize_point(R) + msg) - return new_e == e - -# Make a 1-of-2 signature, knowing the first of 2 keys -def sign_firstof2(msg: bytes, key1: int, KEY2: POINT, BASE: POINT =curve.G1) -> SIG3: - r1 = hash_to_int(msg + serialize_int(key1)) - R1 = curve.multiply(BASE, r1) - e1 = hash_to_int(serialize_point(R1) + msg) - s2 = hash_to_int(msg + serialize_int(key1) + b'\x01') % curve.curve_order - R2 = curve.add(curve.multiply(BASE, s2), curve.multiply(KEY2, e1)) - new_e = hash_to_int(serialize_point(R2) + msg) - s1 = (r1 - key1 * new_e) % curve.curve_order - return (s1, s2, new_e) - -# Make a 1-of-2 signature, knowing the second of 2 keys -def sign_secondof2(msg: bytes, KEY1: POINT, key2: int, BASE: POINT =curve.G1) -> SIG3: - r2 = hash_to_int(msg + serialize_int(key2)) - R2 = curve.multiply(BASE, r2) - e2 = hash_to_int(serialize_point(R2) + msg) - s1 = hash_to_int(msg + serialize_int(key2) + b'\x01') % curve.curve_order - R1 = curve.add(curve.multiply(BASE, s1), curve.multiply(KEY1, e2)) - new_e = hash_to_int(serialize_point(R1) + msg) - s2 = (r2 - key2 * new_e) % curve.curve_order - return (s1, s2, e2) - -# Verify a 1-of-2 signature -def verify_1of2(msg: bytes, KEY1: POINT, KEY2: POINT, sig: SIG3, BASE: POINT =curve.G1) -> bool: - s1, s2, e = sig - R1 = curve.add(curve.multiply(BASE, s1), curve.multiply(KEY1, e)) - new_e = hash_to_int(serialize_point(R1) + msg) - R2 = curve.add(curve.multiply(BASE, s2), curve.multiply(KEY2, new_e)) - newer_e = hash_to_int(serialize_point(R2) + msg) - return newer_e == e - -# Generate points C1, D1, C2, D2, which equal -# EITHER (A1*f, B1*f, A2*f, B2*f) OR (A2*f, B2*f, A1*f, B1*f) -# And generate a proof that this was done correctly -def prove_blind_and_swap(A1: POINT, B1: POINT, A2: POINT, B2: POINT, factor: int, swap=False): - # Compute the blind-and-swap - if not swap: - C1, D1, C2, D2 = (curve.multiply(P, factor) for P in (A1, B1, A2, B2)) - else: - C1, D1, C2, D2 = (curve.multiply(P, factor) for P in (A2, B2, A1, B1)) - # Fiat shamir to choose a random linear combination - msg = b''.join(serialize_point(x) for x in (A1, B1, A2, B2, C1, C2, D1, D2)) - r = hash_to_int(msg + b'\x01') - # Take that linear combination of the base - BASE = lincomb((A1, B1, A2, B2), (1, r, r**2, r**3)) - # The PUB_NOSWAP point is the same linear combination of (C1, D1, C2, D2) - # The PUB_WITHSWAP point is the same linear combination of (C2, D2, C1, D1) - # If you are not swapping, then PUB_NOSWAP = factor * BASE - # If you are swapping, then PUB_WITHSWAP = factor * BASE - # So we now transformed the problem into a 1-of-2 ringsig - if not swap: - PUB_WITHSWAP = lincomb((C2, D2, C1, D1), (1, r, r**2, r**3)) - proof = sign_firstof2(msg, factor, PUB_WITHSWAP, BASE) - else: - PUB_NOSWAP = lincomb((C1, D1, C2, D2), (1, r, r**2, r**3)) - proof = sign_secondof2(msg, PUB_NOSWAP, factor, BASE) - return C1, D1, C2, D2, proof - -# Verify a proof of a blind-and-swap operation -def verify_blind_and_swap(A1: POINT, B1: POINT, A2: POINT, B2: POINT, - C1: POINT, D1: POINT, C2: POINT, D2: POINT, - proof: SIG3): - msg = b''.join(serialize_point(x) for x in (A1, B1, A2, B2, C1, C2, D1, D2)) - r = hash_to_int(msg + b'\x01') - BASE = lincomb((A1, B1, A2, B2), (1, r, r**2, r**3)) - PUB_NOSWAP = lincomb((C1, D1, C2, D2), (1, r, r**2, r**3)) - PUB_WITHSWAP = lincomb((C2, D2, C1, D1), (1, r, r**2, r**3)) - return verify_1of2(msg, PUB_NOSWAP, PUB_WITHSWAP, proof, BASE) - -def test(): - # Basic schnorr - key1, key2 = 1337, 42069 - KEY1, KEY2 = privtopub(key1), privtopub(key2) - sig = sign(b'cow', key1) - assert verify(b'cow', KEY1, sig) - print("Passed basic schnorr test") - # 1-of-2 signatures - BASE = curve.multiply(curve.G1, 1) - firstof2_sig = sign_firstof2(b'cow', key1, KEY2, BASE) - secondof2_sig = sign_secondof2(b'cow', KEY1, key2, BASE) - assert verify_1of2(b'cow', KEY1, KEY2, firstof2_sig, BASE) - assert verify_1of2(b'cow', KEY1, KEY2, secondof2_sig, BASE) - print("Passed 1 of 2 signature test") - # Blind and swap proofs - A1, B1, A2, B2 = (curve.multiply(curve.G1, x) for x in (31337, 69042, 8675309, 299792458)) - factor = 5 - C1, D1, C2, D2, proof = prove_blind_and_swap(A1, B1, A2, B2, factor, False) - FAKE_POINT = curve.multiply(curve.G1, 98765432123456789) - assert (C1, D1, C2, D2) == tuple(curve.multiply(P, factor) for P in (A1, B1, A2, B2)) - assert verify_blind_and_swap(A1, B1, A2, B2, C1, D1, C2, D2, proof) - assert not verify_blind_and_swap(A1, B1, A2, B2, C1, FAKE_POINT, C2, D2, proof) - factor2 = 7 - E1, F1, E2, F2, proof = prove_blind_and_swap(C1, D1, C2, D2, factor2, True) - assert (E1, F1, E2, F2) == tuple(curve.multiply(P, factor2) for P in (C2, D2, C1, D1)) - assert verify_blind_and_swap(C1, D1, C2, D2, E1, F1, E2, F2, proof) - assert not verify_blind_and_swap(C1, D1, C2, D2, E1, F1, E2, FAKE_POINT, proof) - print("Passed blind-and-swap test") - -if __name__ == '__main__': - test() diff --git a/blind_and_swap/swapsim.py b/blind_and_swap/swapsim.py deleted file mode 100644 index 9670da8..0000000 --- a/blind_and_swap/swapsim.py +++ /dev/null @@ -1,53 +0,0 @@ -import random, sys - -def run(width, rounds, swaps_per_round, extract_positions): - array = list(range(width)) - o = [] - for r in range(rounds): - # Swap - offsets = [(r*2+1)*i for i in range(swaps_per_round)] - swap_indices = [(extract_positions[r-1] + offset) % width for offset in offsets] - rotation = random.randrange(len(swap_indices)) - _buffer = [array[index] for index in swap_indices] - _buffer = _buffer[rotation:] + _buffer[:rotation] - for index, new_value in zip(swap_indices, _buffer): - array[index] = new_value - # Extract - extraction_index = extract_positions[r] - o.append(array[extraction_index]) - array[extraction_index] = width + r - return o - -def test(width, rounds, swaps_per_round, runs): - extract_positions = [random.randrange(width) for _ in range(rounds + swaps_per_round)] - outputs = [{} for _ in range(rounds)] - for r in range(runs): - output = run(width, rounds, swaps_per_round, extract_positions) - if r % 10 == 0: - print("Round {}".format(r)) - for store, val in zip(outputs, output): - store[val] = store.get(val, 0) + 1 - thresholds = [] - for store in outputs: - top_freqs = sorted(store.values(), reverse=True) - # print(top_freqs) - await_count = sum(top_freqs) * 0.2 - for i in range(len(top_freqs)): - await_count -= top_freqs[i] - if await_count <= 0: - thresholds.append(i+1) - break - if thresholds[-1] == 1: - print(top_freqs[:20]) - # print(thresholds[-1]) - return thresholds - -if __name__ == '__main__': - width, swaps_per_round, runs = int(sys.argv[1]), int(sys.argv[2]), 1000 - rounds = width * 4 - thresholds = test(width, rounds, swaps_per_round, runs) - for i in range(0, rounds, 10): - print("After {} rounds, need to DoS {} validators for 20% chance of killing proposer".format(i, thresholds[i])) - second_half = thresholds[len(thresholds)//2:] - print("Average of second half: {}".format(sum(second_half) / len(second_half))) - print("Frequency of 1 in second half: {}".format(second_half.count(1) / len(second_half))) diff --git a/blind_and_swap/swapsim2.py b/blind_and_swap/swapsim2.py deleted file mode 100644 index acbba45..0000000 --- a/blind_and_swap/swapsim2.py +++ /dev/null @@ -1,97 +0,0 @@ -import copy, sys, random - -LOG_LEVEL = [None] -FUNCTION = (lambda: 0).__class__ - -DEFAULTS = { - 'width': 256, - 'rounds': 512, - 'swaps_per_round': 15, - 'log_level': 1 -} - -def merge_probs(*probs): - L = len(probs) - #if isinstance(probs[0], list): - # return [sum(prob[i]) / len(probs) - o = {} - for prob in probs: - for k,v in prob.items(): - o[k] = o.get(k, 0) + v / L - return o - -def simplify_dict(obj): - o = {} - for x in sorted(obj.keys(), key=lambda z: obj[z], reverse=True)[:4]: - o[x] = round(obj[x], 3) - if sum(o.values()) < 1: - o['other'] = round(obj[x], 3) - return o - -def log(contents, level): - if level <= LOG_LEVEL[0]: - if isinstance(contents, FUNCTION): - contents = contents() - print(contents) - -def run(width, rounds, swaps_per_round): - extract_positions = [random.randrange(width) for _ in range(rounds + swaps_per_round)] - extract_offsets = [random.randrange(width//2) * 2 + 1 for _ in range(rounds + swaps_per_round)] - array = [{i: 1} for i in range(width)] - o = [] - if bin(width).count('1') != 1: - raise Exception("Width must be a power of 2") - if bin(swaps_per_round + 1).count('1') != 1: - raise Exception("swaps_per_round must be a power of 2 minus 1") - log_swaps = len(bin(swaps_per_round + 1)) - 3 - for r in range(rounds): - log(" ------ ", 1) - log("Round {}".format(r), 1) - for depth in range(log_swaps): - pivot = extract_positions[r - depth - 1] - offset = extract_offsets[r - depth - 1] - log("Depth {}: pivot {} offset {}".format(depth, pivot, offset), 2) - for i in range(2**depth): - L = (pivot + offset * i) % width - R = (pivot + offset * (i + 2**depth)) % width - log("Swapping {} and {}".format(L, R), 2) - new_prob = merge_probs(array[L], array[R]) - array[L] = new_prob - array[R] = new_prob - extraction_index = extract_positions[r] - o.append(array[extraction_index]) - array[extraction_index] = {width+r: 1} - log("New index: {}, Pivot: {}, offset: {}".format(width+r, extraction_index, extract_offsets[r]), 2) - log(lambda: [simplify_dict(x) for x in array], 3) - return o - -def test(width, rounds, swaps_per_round): - thresholds = [] - outputs = run(width, rounds, swaps_per_round) - for store in outputs: - top_freqs = sorted(store.values(), reverse=True) - await_count = sum(top_freqs) * 0.2 - for i in range(len(top_freqs)): - await_count -= top_freqs[i] - if await_count <= 0: - thresholds.append(i+1) - break - return thresholds - -if __name__ == '__main__': - args = {} - for x in sys.argv: - if '=' in x: - prefix, postfix = x[:x.index('=')], x[x.index('=')+1:] - args[prefix] = int(postfix) - for arg, val in DEFAULTS.items(): - if arg not in args: - print("Arg {} defaulted to {}".format(arg, val)) - args[arg] = val - LOG_LEVEL[0] = args['log_level'] - thresholds = test(args['width'], args['rounds'], args['swaps_per_round']) - for i in range(0, args['rounds'], 10): - print("After {} rounds, need to DoS {} validators for 20% chance of killing proposer".format(i, thresholds[i])) - second_half = thresholds[len(thresholds)//2:] - print("Average 20%-diffusion of proposer: {}".format(sum(second_half) / len(second_half))) - print("Frequency of 20%-diffusion = 1: {}".format(second_half.count(1) / len(second_half))) diff --git a/bulletproofs/ipa_commitments.py b/bulletproofs/ipa_commitments.py deleted file mode 100644 index 67c3de9..0000000 --- a/bulletproofs/ipa_commitments.py +++ /dev/null @@ -1,256 +0,0 @@ -from py_ecc import optimized_bls12_381 as b -from hashlib import sha256 -from dataclasses import dataclass -from multicombs import lincomb -import time - -# See page 25 and 29 of https://eprint.iacr.org/2020/1536.pdf and -# page 49-50 of https://eprint.iacr.org/2020/499.pdf - -# ----------------------------------------------------------------------- # -# THIS IS AN EDUCATIONAL IMPLEMENTATION ONLY. DO NOT USE IN PRODUCTION!!! # -# ----------------------------------------------------------------------- # - - -BLS12_381_COFACTOR = 76329603384216526031706109802092473003 - - -def hash(x): - return sha256(x).digest() - - -# Creates the generator points. This is a public procedure that can be repeated -# by anyone, so it is NOT a trusted setup -def mk_generator_points(count): - points = [] - x = b.FQ(1) - while len(points) < count: - y = (x ** 3 + b.b) ** ((b.field_modulus + 1) // 4) - if b.is_on_curve((x, y, b.FQ(1)), b.b): - points.append(b.multiply((x, y, b.FQ(1)), BLS12_381_COFACTOR)) - x += b.FQ(1) - return points - - -# Commit to some polynomial -def commit(generator_points, poly): - # Equivalent (but faster) to this: - # reduce( - # b.add, - # [b.multiply(pt, cf) for pt, cf in zip(generator_points[:len(poly)], poly)], - # b.Z1 - # ) - return lincomb(generator_points[:len(poly)], poly, b.add, b.Z1) - - -# Returne True iff x is a power of two -def is_power_of_two(x): - return x and (x & (x-1) == 0) - - -# Serializes an elliptic curve point. Used for Fiat-Shamir. -def serialize_point(pt): - pt = b.normalize(pt) - return pt[0].n.to_bytes(64, 'little') + pt[1].n.to_bytes(64, 'little') - - -# Returns the (left|right) half of something -def left_half(x): - return x[:len(x)//2] - - -def right_half(x): - return x[len(x)//2:] - - -# The data structure for a proof -@dataclass -class Proof(): - L: list - R: list - tip: int - - -# Prove that `commitment` actually is the commitment to a polynomial -# (it does not prove _which_ polynomial) -def prove(points, commitment, poly): - assert is_power_of_two(len(poly)) - # Crop the base points to just what we need - points = points[:len(poly)] - # Left-side points for the proof - L = [] - # Right-side points for the proof - R = [] - # Fiat-shamir randomness value - r = hash(serialize_point(commitment)) - # log(n) rounds... - while len(poly) > 1: - # Generate the left-side and right-side points - polyL, polyR = left_half(poly), right_half(poly) - pointsL, pointsR = left_half(points), right_half(points) - yL = commit(pointsR, polyL) - yR = commit(pointsL, polyR) - L.append(yL) - R.append(yR) - # Generate random coefficient for recombining the L and R and commitment - r = hash(r + serialize_point(yL) + serialize_point(yR)) - a = int.from_bytes(r, 'little') % b.curve_order - # print('a value: ', a) - # Generate half-size polynomial and points for the next round - poly = [(cL + cR * a) % b.curve_order for (cL, cR) in zip(polyL, polyR)] - points = [b.add(b.multiply(pL, a), pR) for (pL, pR) in zip(pointsL, pointsR)] - # print('intermediate commitment:', commit(points, poly)) - return Proof(L, R, poly[0]) - - -def verify(points, commitment, proof): - # Crop the base points to just what we need - points = points[:2**len(proof.L)] - # Fiat-shamir randomness value - r = hash(serialize_point(commitment)) - # For verification, we need to generate the same random linear combination of - # base points that the prover did.. But because we don't need to use it until - # the end, we do it more efficiently here: when we progress through the rounds, - # we keep track of how many times each points[i] will appear in the final - # result... - points_coeffs = [1] - # log(n) rounds, just like the prover... - for i in range(len(proof.L)): - r = hash(r + serialize_point(proof.L[i]) + serialize_point(proof.R[i])) - # Generate random coefficient for recombining (same as the prover) - a = int.from_bytes(r, 'little') % b.curve_order - # print('a value: ', a) - # Add L and R into the commitment, applying the appropriate coefficients - commitment = b.add( - proof.L[i], - b.add( - b.multiply(commitment, a), - b.multiply(proof.R[i], a**2) - ) - ) - # print('intermediate commitment:', commitment) - # Update the coefficients (points_coeffs[i] = how many times points[i] will - # appear in the single base point of the last round) - points_coeffs = sum([[(x*a) % b.curve_order, x] for x in points_coeffs], []) - # Finally, we do the linear combination - combined_point = lincomb(points, points_coeffs, b.add, b.Z1) - # Base case check: base_point * coefficient ?= commitment - return b.eq(b.multiply(combined_point, proof.tip), commitment) - - -# Prove that `commitment` actually is the commitment to a polynomial -# `p` such that `p(x) = y` -def prove_evaluation(points, commitment, poly, x, y): - assert is_power_of_two(len(poly)) - # Crop the base points to just what we need. We add an additional base point, - # which we will use to mix in the _evaluation_ of the polynomial. - points, H = points[:len(poly)], points[len(poly)] - # Alongside the base points, we track the powers of the x coordinate we are - # proving an evaluation for. These points get manipulated in the same way as the - # base points do. - xpowers = [pow(x, i, b.curve_order) for i in range(len(poly))] - # Left-side points for the proof - L = [] - # Right-side points for the proof - R = [] - # Fiat-shamir randomness value - r = hash(serialize_point(commitment) + x.to_bytes(32, 'little') + y.to_bytes(32, 'little')) - # For security, we randomize H - H = b.multiply(H, int.from_bytes(r, 'little') % b.curve_order) - while len(poly) > 1: - # Generate the left-side and right-side points, except we also mix in a similarly - # constructed "commitment" that uses `H * powers of x` as its base instead of the - # base points. - polyL, polyR = left_half(poly), right_half(poly) - pointsL, pointsR = left_half(points), right_half(points) - xpowersL, xpowersR = left_half(xpowers), right_half(xpowers) - yL = commit(pointsR, polyL) - yR = commit(pointsL, polyR) - L.append(b.add(yL, b.multiply(H, sum(a*b for a,b in zip(xpowersR, polyL))))) - R.append(b.add(yR, b.multiply(H, sum(a*b for a,b in zip(xpowersL, polyR))))) - # Generate random coefficient for recombining the L and R and commitment - r = hash(r + serialize_point(L[-1]) + serialize_point(R[-1])) - a = int.from_bytes(r, 'little') % b.curve_order - # print('a value: ', a) - # Generate half-size polynomial and points for the next round. Notice how we treat - # the powers of x the same way that we do the base points - poly = [(cL + cR * a) % b.curve_order for (cL, cR) in zip(polyL, polyR)] - points = [b.add(b.multiply(pL, a), pR) for (pL, pR) in zip(pointsL, pointsR)] - xpowers = [(xL * a + xR) % b.curve_order for (xL, xR) in zip(xpowersL, xpowersR)] - # print('intermediate commitment:', b.add(commit(points, poly), b.multiply(H, sum(a*b for a,b in zip(xpowers, poly))))) - return Proof(L, R, poly[0]) - - -# Verify a proof of an evaluation made using the above protocol -def verify_evaluation(points, commitment, proof, x, y): - # Crop the base points to just what we need. We add an additional base point, - # which we will use to mix in the _evaluation_ of the polynomial. - points, H = points[:2**len(proof.L)], points[2**len(proof.L)] - # Powers of x, as in the prover - xpowers = [pow(x, i, b.curve_order) for i in range(len(poly))] - # Fiat-shamir randomness value - r = hash(serialize_point(commitment) + x.to_bytes(32, 'little') + y.to_bytes(32, 'little')) - # For security, we randomize H - H = b.multiply(H, int.from_bytes(r, 'little') % b.curve_order) - # We "mix in" H * the claimed evaluation P(x) = y. Notice that `H * P(x)` equals the - # dot-product of `H * powers of x` and the polynomial coefficients, so it has the - # "same format" as the polynomial commitment itself. This allows us to verify the - # evaluation using the same technique that we use to just prove that the commitment - # is valid - commitment = b.add(commitment, b.multiply(H, y)) - # Track the linear combination so we can generate the final-round point and xpower, - # just as before - points_coeffs = [1] - for i in range(len(proof.L)): - # Generate random coefficient for recombining (same as the prover) - r = hash(r + serialize_point(proof.L[i]) + serialize_point(proof.R[i])) - a = int.from_bytes(r, 'little') % b.curve_order - # print('a value: ', a) - # Add L and R into the commitment, applying the appropriate coefficients - commitment = b.add( - proof.L[i], - b.add( - b.multiply(commitment, a), - b.multiply(proof.R[i], a**2) - ) - ) - # print('intermediate commitment:', commitment) - # Update the coefficients (as in basic verification above) - points_coeffs = sum([[(x*a) % b.curve_order, x] for x in points_coeffs], []) - # Finally, we do the linear combination; same one for base points and x powers - combined_point = lincomb(points, points_coeffs, b.add, b.Z1) - combined_x_powers = sum(p*c for p,c in zip(xpowers, points_coeffs)) - # Base case check: base_point * coefficient ?= commitment. Note that here we - # have to also mix H * the combined xpower into the final base point - return b.eq( - b.add( - b.multiply(combined_point, proof.tip), - b.multiply(H, (proof.tip * combined_x_powers) % b.curve_order) - ), - commitment - ) - - -time_cache = [time.time()] - - -def get_time_delta(): - time_cache.append(time.time()) - return time_cache[-1] - time_cache[-2] - -if __name__ == '__main__': - get_time_delta() - points = mk_generator_points(32) - print("Generated generator points: {:.3f}s".format(get_time_delta())) - poly = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3] - commitment = commit(points, poly) - print("Simple commitment generated: {:.3f}s".format(get_time_delta())) - proof = prove(points, commitment, poly) - print("Proof generated: {:.3f}s".format(get_time_delta())) - print(proof) - assert verify(points, commitment, proof) - print("Proof verified: {:.3f}s".format(get_time_delta())) - proof2 = prove_evaluation(points, commitment, poly, 10, 3979853562951413) - print("Evaluation proof generated: {:.3f}s".format(get_time_delta())) - assert verify_evaluation(points, commitment, proof2, 10, 3979853562951413) - print("Evaluation proof verified: {:.3f}s".format(get_time_delta())) diff --git a/casper4/basic_validation_code.se.py b/casper4/basic_validation_code.se.py deleted file mode 100644 index e1dd96d..0000000 --- a/casper4/basic_validation_code.se.py +++ /dev/null @@ -1,3 +0,0 @@ -~calldatacopy(0, 0, 128) -~call(3000, 1, 0, 0, 128, 0, 32) -return(~mload(0) == 0xfe2ec957647679d210034b65e9c7db2452910b0c) diff --git a/casper4/diag1.png b/casper4/diag1.png deleted file mode 100644 index 85ebe279229cdea06800e6c3ef89f89952a4adcd..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 29529 zcmc$_bxfo|*Du(}00V=|;0!kCV2!)GyEC}EySux)ySqDsyAJN|Znx+C?q)an_9i!* z?Cu|=NGDzWJf}{b^OLGjS!oe?SZr7T001v0Dku*CfL{XuV2Uu{pihYO@0>uxR~u0^ zdjJ5T7xdQymK&yC0RY&;i3##4x@4TMe^Eu#z=6K12a|Aic7{_G6(#ozTvjCyi?prQ 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zuPwOF$1f@H%iZpKK9_$hb~PGZz@8sSjn8>eb{uLt&h5Cz+ghBpyQ*s4jTO3U((95c z`tRPjHTwdRV_%lOD}4a$IaY~-R*pL`lSnrIXFu8O9Ql5}Su)TN22WQ%mvv4FO#p3( BD2o69 diff --git a/casper4/fixed_address_creator.py b/casper4/fixed_address_creator.py deleted file mode 100644 index 17e135a..0000000 --- a/casper4/fixed_address_creator.py +++ /dev/null @@ -1,42 +0,0 @@ - -import serpent -import rlp -from ethereum import utils -from ethereum import tester -from ethereum import transactions - -sighash = serpent.compile('sighash.se.py') - -tests = [ - [b"\x01"], - [b"\x80", "a"], - [b"\x81", "b"], - [b""], - [b"", b"\x01", b""], - [b"", b"\x81", b""], - [b"dog", b"c" * 54, b"\x01"], - [b"\x01", b"c" * 55, b"pig"], - [b"moose", b"c" * 56, b"\x00"], - [b'\x01', b'55555555555555555555555555555555', b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00', b'', b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00', b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x1b\x88\xa7\x85r\x1b3\x17\xcaP\x96\xca\xd3S\xfcgM\xec\xe0\xf5!\xc8\xb4m\xd9\xb7E\xf3\x81d\x87\x93VD\xe0Ej\xcd\xec\x80\x11\x86(qZ\x9b\x80\xbf\xce\xe5*\r\x9d.o\xcd\x11s\xc5\xbc\x8c\xcb\xb9\xa9 '] -] - -s = tester.state() -c = s.evm(sighash, sender=tester.k0, endowment=0) - -for test in tests: - z = s.send(tester.k0, c, 0, rlp.encode(test)) - assert z == utils.sha3(rlp.encode(test[:-1])) - print("Passed test, gas consumed: ", s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used - s.last_tx.intrinsic_gas_used) - -# Create transaction -t = transactions.Transaction(0, 30 * 10**9, 2999999, '', 0, sighash) -t.startgas = t.intrinsic_gas_used + 50000 + 200 * len(sighash) -t.v = 27 -t.r = 45 -t.s = 79 -print("Sighash") -print('Send %d wei to %s' % (t.startgas * t.gasprice, - '0x'+utils.encode_hex(t.sender))) - -print('Contract address: 0x'+utils.encode_hex(utils.mk_contract_address(t.sender, 0))) -print('Code: 0x'+utils.encode_hex(rlp.encode(t))) diff --git a/casper4/griefing_factor_calculator.py b/casper4/griefing_factor_calculator.py deleted file mode 100644 index b51af75..0000000 --- a/casper4/griefing_factor_calculator.py +++ /dev/null @@ -1,75 +0,0 @@ -# Computes griefing factors of various parameter sets for Casper the -# Friendly Finality Gadget - -# Case 1: <1/3 non-commit (optimal if epsilon participate) -def gf1(x1, x2, x3, x4, x5): - return x2 / x1 - -# Case 2: censor <1/3 committers (optimal if 1/3 get censored) -def gf2(x1, x2, x3, x4, x5): - return 1.5 * (x1 + x2 / 3) / x2 - -# Generalized case 2 -#k = 0.25 -#def gf2(x1, x2, x3, x4, x5): -# return (x1 * k + x2 * k**2) / (x2 * k * (1-k)) - -# Case 3: <1/3 non-prepare (optimal if epsilon participate) -def gf3(x1, x2, x3, x4, x5): - return x4 / x3 - -# Case 4: censor <1/3 preparers (optimal if 1/3 get censored) -def gf4(x1, x2, x3, x4, x5): - return 1.5 * (x3 + x4 / 3) / x4 - -# Case 5: finality preventing 1/3 non-commits -def gf5(x1, x2, x3, x4, x5): - return 2 * (x5 + x2 / 3) / (x5 + x1 + x2 / 3) - -# Case 6: censor commits -def gf6(x1, x2, x3, x4, x5): - # Case 6a: 51% participate - return max(1 + x2 / (x5 + x1 + x2 / 2), - # Case 6b: 67% participate - (x5 + x1 + x2 / 3) / (x5 + x2 / 3) / 2) - -# Case 7: finality and commit-preventing 1/3 non-prepares -def gf7(x1, x2, x3, x4, x5): - return 2 * (x5 + x4 / 3) / (x5 + x3 + x4 / 3) - -gfs = (gf1, gf2, gf3, gf4, gf5, gf6, gf7) - -# Get the maximum griefing factor of a set of parameters -def getmax(*args): - return max([f(*args) for f in gfs]) - -# Get the maximum <50% griefing factor, and enforce a bound -# of MAX_CENSOR_GF on the griefing factor of >50% coalitions -def getmax2(*args): - MAX_CENSOR_GF = 2 - if gf2(*args) > MAX_CENSOR_GF or gf4(*args) > MAX_CENSOR_GF or \ - gf6(*args) > MAX_CENSOR_GF: - return 999999999999999999 - - return max(gf1(*args), gf3(*args), gf5(*args), gf7(*args)) - -# Range to test for each parameter -my_range = [i/12. for i in range(1, 61)] - -best_vals = (1, 0, 0, 0, 0) -best_score = 999999999999999999 - -# print([f(5, 6, 5, 6, 0) for f in gfs]) - -for x1 in my_range: - for x2 in my_range: - for x3 in my_range: - for x4 in my_range: - o = getmax2(x1, x2, x3, x4, 1) - if o < best_score: - best_score = o - best_vals = (x1, x2, x3, x4, 1) - if o <= 1: - print((x1, x2, x3, x4, 1), [f(x1, x2, x3, x4, 1) for f in gfs]) -print('result', best_vals, best_score) -print([f(*best_vals) for f in gfs]) diff --git a/casper4/griefing_one_third_offline_simulator.py b/casper4/griefing_one_third_offline_simulator.py deleted file mode 100644 index bf5c4f7..0000000 --- a/casper4/griefing_one_third_offline_simulator.py +++ /dev/null @@ -1,35 +0,0 @@ -import math - -# Length of an epoch in seconds -epoch_len = 1400 -# In-protocol penalization parameter -increment = 0.00002 - -# Parameters -NFP = 0 -NCP = 3 -NCCP = 3 -NPP = 3 -NPCP = 3 - -def sim_offline(p): - online, offline = 1-p, p - for i in range(1, 999999): - # Lost by offline validators - offline_loss = NFP + NPP + NPCP * (offline / (online + offline)) - # Lost by online validators - online_loss = NFP + NPCP * (offline / (online + offline)) - online *= 1 - increment * math.log(i) * online_loss - offline *= 1 - increment * math.log(i) * offline_loss - if i % 100 == 0 or online >= 2 * offline: - print("%d epochs (%.2f days): online %.4f offline %.4f" % - (i, epoch_len * i / 86400, online, offline)) - # If the remaining validators can commit, break - if online >= 2 * offline: - return (1-p, online, epoch_len * i / 86400) - -sim_offline(0.4) - -#results = [sim_offline(i * 0.01) for i in range(34, 100)] -#for col in results: -# print("%.4f, %.4f, %.4f" % col) diff --git a/casper4/rlp_decoder.se.py b/casper4/rlp_decoder.se.py deleted file mode 100644 index bd965ed..0000000 --- a/casper4/rlp_decoder.se.py +++ /dev/null @@ -1,77 +0,0 @@ -macro calldatachar($x): - div(calldataload($x), 2**248) - -macro calldatabytes_as_int($x, $b): - div(calldataload($x), 256**(32-$b)) - -def any(): - # Positions of the values that we are changing - positions = array(256) - # Index of the next position we are adding to - positionIndex = 0 - # Output data (main part) - data = string(~calldatasize() + 1024) - # Index of where we are adding data - dataPos = 0 - # Can only parse lists; check the length of the list and set the index - # in calldata to the right start position - c = calldatachar(0) - if c < 192: - ~invalid() - if c < 248: - if ~calldatasize() != 1 + (c - 192): - ~invalid() - i = 1 - else: - L = calldatabytes_as_int(i + 1, c - 247) - if ~calldatasize() != 1 + (c - 247) + L: - ~invalid() - i = 1 + (c - 247) - # Main loop - while i < ~calldatasize(): - # Get type (single byte, short, long) - c = calldatachar(i) - positions[positionIndex] = dataPos - positionIndex += 1 - # Single byte < 0x80 - if c < 128: - mstore(data + dataPos, 1) - calldatacopy(data + dataPos + 32, i, 1) - i += 1 - dataPos += 33 - # Short (up to 55 bytes) - elif c < 184: - mstore(data + dataPos, c - 128) - calldatacopy(data + dataPos + 32, i + 1, c - 128) - # Output could have been in single-byte format - if c == 129: - if calldatachar(i + 1) < 128: - ~invalid() - i += c - 128 + 1 - dataPos += (c - 128) + 32 - # Long (56 or more bytes) - elif c < 192: - L = calldatabytes_as_int(i + 1, c - 183) - # Forbid leading zero byte - if calldatachar(i + 1) == 0: - ~invalid() - # Forbid too short values - if L < 56: - ~invalid() - mstore(data + dataPos, L) - calldatacopy(data + dataPos + 32, i + 1 + c - 183, L) - i += (c - 183) + 1 + L - dataPos += L + 32 - else: - # Not handling nested arrays - ~invalid() - if positionIndex > 32: - ~invalid() - positions[positionIndex] = dataPos - output = string(2048) - i = 0 - while i <= positionIndex: - output[i] = positions[i] + positionIndex * 32 + 32 - i += 1 - mcopy(output + positionIndex * 32 + 32, data, dataPos) - ~return(output, positionIndex * 32 + dataPos + 32) diff --git a/casper4/sighash.se.py b/casper4/sighash.se.py deleted file mode 100644 index e496628..0000000 --- a/casper4/sighash.se.py +++ /dev/null @@ -1,64 +0,0 @@ -# Fetches the char from calldata at position $x -macro calldatachar($x): - div(calldataload($x), 2**248) - -# Fetches the next $b bytes from calldata starting at position $x -# Assumes that there is nothing important in memory at bytes 0..63 -macro calldatabytes_as_int($x, $b): - ~mstore(32-$b, calldataload($x)) - ~mload(0) - -# Position in calldata -with pos = 0: - # First char in calldata - with c0 = calldatachar(0): - # The start of the array must be in 192...255 because it represents - # a list length - # Length ++ body case - if c0 < 248: - pos = 1 - # Length of length ++ length ++ body case - else: - pos = (c0 - 246) - # Start position of the list (save it) - with startpos = pos: - # Start position of the previous element - with lastpos = 0: - # Keep looping until we hit the end of the input - while pos < ~calldatasize(): - # Next char in calldata - with c = calldatachar(pos): - lastpos = pos - # Single byte 0x00...0x7f body case - if c < 128: - pos += 1 - # Length ++ body case - elif c < 184: - pos += c - 127 - # Length of length ++ length ++ body case - elif c < 192: - pos += calldatabytes_as_int(pos + 1, c - 183) + (c - 182) - - # Length of new RLP list - with newlen = lastpos - startpos: - # Length ++ body case - if newlen < 56: - # Store length in the first byte - ~mstore8(0, 192 + newlen) - # Copy calldata right after length - ~calldatacopy(1, startpos, newlen) - # Return the hash - return(~sha3(0, 1 + newlen)) - else: - # The log256 of the length (ie. length of length) - # Can't go higher than 16777216 bytes due to gas limits - with _log = if(newlen < 256, 1, if(newlen < 65536, 2, 3)): - # Store the length - ~mstore(0, newlen) - # Store the length of the length right before the length - with 31minuslog = 31 - _log: - ~mstore8(31minuslog, 247 + _log) - # Store the rest of the data - ~calldatacopy(32, startpos, newlen) - # Return the hash - return(~sha3(31minuslog, 1 + _log + newlen)) diff --git a/casper4/simple_casper.v.py b/casper4/simple_casper.v.py deleted file mode 100644 index d6dfcab..0000000 --- a/casper4/simple_casper.v.py +++ /dev/null @@ -1,559 +0,0 @@ -# Information about validators -validators: public({ - # Amount of wei the validator holds - deposit: wei_value, - # The dynasty the validator is joining - dynasty_start: num, - # The dynasty the validator joined for the first time - original_dynasty_start: num, - # The dynasty the validator is leaving - dynasty_end: num, - # The timestamp at which the validator can withdraw - withdrawal_epoch: num, - # The address which the validator's signatures must verify to (to be later replaced with validation code) - addr: address, - # Addess to withdraw to - withdrawal_addr: address, - # Previous epoch in which this validator committed - prev_commit_epoch: num -}[num]) - -# The current dynasty (validator set changes between dynasties) -dynasty: public(num) - -# Amount of wei added to the total deposits in the next dynasty -next_dynasty_wei_delta: wei_value - -# Amount of wei added to the total deposits in the dynasty after that -second_next_dynasty_wei_delta: wei_value - -# Total deposits during this dynasty -total_deposits: public(wei_value[num]) - -# Mapping of dynasty to start epoch of that dynasty -dynasty_start_epoch: public(num[num]) - -# Mapping of epoch to what dynasty it is -dynasty_in_epoch: public(num[num]) - -# Information for use in processing cryptoeconomic commitments -consensus_messages: public({ - # How many prepares are there for this hash (hash of message hash + view source) from the current dynasty - prepares: wei_value[bytes32], - # Bitmap of which validator IDs have already prepared - prepare_bitmap: num256[num][bytes32], - # From the previous dynasty - prev_dyn_prepares: wei_value[bytes32], - # Is a prepare referencing the given ancestry hash justified? - ancestry_hash_justified: bool[bytes32], - # Is a commit on the given hash justified? - hash_justified: bool[bytes32], - # How many commits are there for this hash - commits: wei_value[bytes32], - # And from the previous dynasty - prev_dyn_commits: wei_value[bytes32], - # Was the block committed? - committed: bool, - # Value used to calculate the per-epoch fee that validators should be charged - deposit_scale_factor: decimal -}[num]) # index: epoch - -# A bitmap, where the ith bit of dynasty_mark[arg1][arg2] shows -# whether or not validator arg1 is active during dynasty arg2*256+i -dynasty_mask: num256[num][num] - -# ancestry[x][y] = k > 0: x is a kth generation ancestor of y -ancestry: public(num[bytes32][bytes32]) - -# Number of validators -nextValidatorIndex: public(num) - -# Time between blocks -block_time: timedelta - -# Length of an epoch in blocks -epoch_length: num - -# Withdrawal delay -withdrawal_delay: timedelta - -# Delay after which a message can be slashed due to absence of justification -insufficiency_slash_delay: timedelta - -# Current epoch -current_epoch: public(num) - -# Can withdraw destroyed deposits -owner: address - -# Total deposits destroyed -total_destroyed: wei_value - -# Sighash calculator library address -sighasher: address - -# Purity checker library address -purity_checker: address - -# Reward for preparing or committing, as fraction of deposit size -reward_factor: public(decimal) - -# Desired total ether given out assuming 1M ETH deposited -reward_at_1m_eth: decimal - -# Have I already been initialized? -initialized: bool - -# Log topic for prepare -prepare_log_topic: bytes32 - -# Log topic for commit -commit_log_topic: bytes32 - -def initiate(): - assert not self.initialized - self.initialized = True - # Set Casper parameters - self.block_time = 14 - self.epoch_length = 100 - # Only ~11.5 days, for testing purposes - self.withdrawal_delay = 1000000 - # Only ~1 day, for testing purposes - self.insufficiency_slash_delay = 86400 - # Temporary backdoor for testing purposes (to allow recovering destroyed deposits) - self.owner = 0x1Db3439a222C519ab44bb1144fC28167b4Fa6EE6 - # Add an initial validator - self.validators[0] = { - deposit: as_wei_value(3, ether), - dynasty_start: 0, - dynasty_end: 1000000000000000000000000000000, - original_dynasty_start: 0, - withdrawal_epoch: 1000000000000000000000000000000, - addr: 0x1Db3439a222C519ab44bb1144fC28167b4Fa6EE6, - withdrawal_addr: 0x1Db3439a222C519ab44bb1144fC28167b4Fa6EE6, - prev_commit_epoch: 0, - } - self.nextValidatorIndex = 1 - # Initialize the epoch counter - self.current_epoch = block.number / self.epoch_length - # Set the sighash calculator address - self.sighasher = 0x476c2cA9a7f3B16FeCa86512276271FAf63B6a24 - # Set the purity checker address - self.purity_checker = 0xD7a3BD6C9eA32efF147d067f907AE6b22d436F91 - # Set an initial root of the epoch hash chain - self.consensus_messages[0].ancestry_hash_justified[0x0000000000000000000000000000000000000000000000000000000000000000] = True - # self.consensus_messages[0].committed = True - # Set initial total deposit counter - self.total_deposits[0] = as_wei_value(3, ether) - # Set deposit scale factor - self.consensus_messages[0].deposit_scale_factor = 1000000000000000000.0 - # Total ETH given out assuming 1m ETH deposits - self.reward_at_1m_eth = 12.5 - # Log topics for prepare and commit - self.prepare_log_topic = sha3("prepare()") - self.commit_log_topic = sha3("commit()") - -# Called at the start of any epoch -def initialize_epoch(epoch: num): - # Check that the epoch actually has started - computed_current_epoch = block.number / self.epoch_length - assert epoch <= computed_current_epoch and epoch == self.current_epoch + 1 - # Set the epoch number - self.current_epoch = epoch - # Increment the dynasty - if self.consensus_messages[epoch - 1].committed: - self.dynasty += 1 - self.total_deposits[self.dynasty] = self.total_deposits[self.dynasty - 1] + self.next_dynasty_wei_delta - self.next_dynasty_wei_delta = self.second_next_dynasty_wei_delta - self.second_next_dynasty_wei_delta = 0 - self.dynasty_start_epoch[self.dynasty] = epoch - self.dynasty_in_epoch[epoch] = self.dynasty - # Compute square root factor - ether_deposited_as_number = self.total_deposits[self.dynasty] / as_wei_value(1, ether) - sqrt = ether_deposited_as_number / 2.0 - for i in range(20): - sqrt = (sqrt + (ether_deposited_as_number / sqrt)) / 2 - # Reward factor is the reward given for preparing or committing as a - # fraction of that validator's deposit size - base_coeff = 1.0 / sqrt * (self.reward_at_1m_eth / 1000) - # Rules: - # * You are penalized 2x per epoch - # * If you prepare, you get 1.5x, and if you commit you get another 1.5x - # Hence, assuming 100% performance, your reward per epoch is x - self.reward_factor = 1.5 * base_coeff - self.consensus_messages[epoch].deposit_scale_factor = self.consensus_messages[epoch - 1].deposit_scale_factor * (1 - 2 * base_coeff) - -# Send a deposit to join the validator set -def deposit(validation_addr: address, withdrawal_addr: address): - assert self.current_epoch == block.number / self.epoch_length - assert extract32(raw_call(self.purity_checker, concat('\xa1\x90>\xab', as_bytes32(validation_addr)), gas=500000, outsize=32), 0) != as_bytes32(0) - self.validators[self.nextValidatorIndex] = { - deposit: msg.value, - dynasty_start: self.dynasty + 2, - original_dynasty_start: self.dynasty + 2, - dynasty_end: 1000000000000000000000000000000, - withdrawal_epoch: 1000000000000000000000000000000, - addr: validation_addr, - withdrawal_addr: withdrawal_addr, - prev_commit_epoch: 0, - } - self.nextValidatorIndex += 1 - self.second_next_dynasty_wei_delta += msg.value - -# Log in or log out from the validator set. A logged out validator can log -# back in later, if they do not log in for an entire withdrawal period, -# they can get their money out -def flick_status(logout_msg: bytes <= 1024): - assert self.current_epoch == block.number / self.epoch_length - # Get hash for signature, and implicitly assert that it is an RLP list - # consisting solely of RLP elements - sighash = extract32(raw_call(self.sighasher, logout_msg, gas=200000, outsize=32), 0) - # Extract parameters - values = RLPList(logout_msg, [num, num, bool, bytes]) - validator_index = values[0] - epoch = values[1] - login_flag = values[2] - sig = values[3] - assert self.current_epoch == epoch - # Signature check - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash, sig), gas=500000, outsize=32), 0) == as_bytes32(1) - # Logging in - if login_flag: - # Check that we are logged out - assert self.validators[validator_index].dynasty_end < self.dynasty - # Check that we logged out for less than 3840 dynasties (min: ~2 months) - assert self.validators[validator_index].dynasty_end >= self.dynasty - 3840 - # Apply the per-epoch deposit penalty - prev_login_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_start] - prev_logout_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_end + 1] - self.validators[validator_index].deposit = \ - floor(self.validators[validator_index].deposit * - (self.consensus_messages[prev_logout_epoch].deposit_scale_factor / - self.consensus_messages[prev_login_epoch].deposit_scale_factor)) - # Log back in - # Go through the dynasty mask to clear out the ineligible dynasties - old_ds = self.validators[validator_index].dynasty_end - new_ds = self.dynasty + 2 - for i in range(old_ds / 256, old_ds / 256 + 16): - if old_ds > i * 256: - s = old_ds % 256 - else: - s = 0 - if new_ds < i * 256 + 256: - e = new_ds % 256 - else: - e = 256 - self.dynasty_mask[validator_index][i] = num256_sub(shift(as_num256(1), e), shift(as_num256(1), s)) - if e < 256: - break - self.validators[validator_index].dynasty_start = new_ds - self.validators[validator_index].dynasty_end = 1000000000000000000000000000000 - self.second_next_dynasty_wei_delta += self.validators[validator_index].deposit - # Logging out - else: - # Check that we haven't already withdrawn - assert self.validators[validator_index].dynasty_end >= self.dynasty + 2 - # Set the end dynasty - self.validators[validator_index].dynasty_end = self.dynasty + 2 - self.second_next_dynasty_wei_delta -= self.validators[validator_index].deposit - # Set the withdrawal date - self.validators[validator_index].withdrawal_epoch = self.current_epoch + self.withdrawal_delay / self.block_time / self.epoch_length - -# Removes a validator from the validator pool -def delete_validator(validator_index: num): - self.validators[validator_index] = { - deposit: 0, - dynasty_start: 0, - dynasty_end: 0, - original_dynasty_start: 0, - withdrawal_epoch: 0, - addr: None, - withdrawal_addr: None, - prev_commit_epoch: 0, - } - -# Withdraw deposited ether -def withdraw(validator_index: num): - # Check that we can withdraw - assert self.current_epoch >= self.validators[validator_index].withdrawal_epoch - # Apply the per-epoch deposit penalty - prev_login_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_start] - prev_logout_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_end + 1] - self.validators[validator_index].deposit = \ - floor(self.validators[validator_index].deposit * - (self.consensus_messages[prev_logout_epoch].deposit_scale_factor / - self.consensus_messages[prev_login_epoch].deposit_scale_factor)) - # Withdraw - send(self.validators[validator_index].withdrawal_addr, self.validators[validator_index].deposit) - self.delete_validator(validator_index) - -# Checks if a given validator could have prepared in a given epoch -def check_eligible_in_epoch(validator_index: num, epoch: num) -> num(const): - # Time limit for submitting a prepare - assert epoch > self.current_epoch - 3840 - # Original starting dynasty of the validator; fail if before - do = self.validators[validator_index].original_dynasty_start - # Ending dynasty of the current login period - de = self.validators[validator_index].dynasty_end - # Dynasty of the prepare - dc = self.dynasty_in_epoch[epoch] - # Dynasty before the prepare (for prev dynasty checking) - dp = dc - 1 - # Check against mask to see if the dynasty was eligible before - cur_in_mask = bitwise_and(self.dynasty_mask[validator_index][dc / 256], shift(as_num256(1), dc % 256)) - prev_in_mask = bitwise_and(self.dynasty_mask[validator_index][dp / 256], shift(as_num256(1), dp % 256)) - o = 0 - # Return result as bitmask, bit 1 = in_current_dynasty, bit 0 = in_prev_dynasty - if ((do <= dc and cur_in_mask == as_num256(0)) and dc < de): - o += 2 - if ((do <= dp and prev_in_mask == as_num256(0)) and dp < de): - o += 1 - return o - -# Process a prepare message -def prepare(prepare_msg: bytes <= 1024): - # Get hash for signature, and implicitly assert that it is an RLP list - # consisting solely of RLP elements - sighash = extract32(raw_call(self.sighasher, prepare_msg, gas=200000, outsize=32), 0) - # Extract parameters - values = RLPList(prepare_msg, [num, num, bytes32, bytes32, num, bytes32, bytes]) - validator_index = values[0] - epoch = values[1] - hash = values[2] - ancestry_hash = values[3] - source_epoch = values[4] - source_ancestry_hash = values[5] - sig = values[6] - new_ancestry_hash = sha3(concat(hash, ancestry_hash)) - # Hash for purposes of identifying this (epoch, hash, ancestry_hash, source_epoch, source_ancestry_hash) combination - sourcing_hash = sha3(concat(as_bytes32(epoch), hash, ancestry_hash, as_bytes32(source_epoch), source_ancestry_hash)) - # Check the signature - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash, sig), gas=500000, outsize=32), 0) == as_bytes32(1) - # Check that we are in an epoch after we started validating - assert self.current_epoch >= self.dynasty_start_epoch[self.validators[validator_index].dynasty_start] - # Check that this prepare has not yet been made - assert not bitwise_and(self.consensus_messages[epoch].prepare_bitmap[sourcing_hash][validator_index / 256], - shift(as_num256(1), validator_index % 256)) - # Check that we are at least (epoch length / 4) blocks into the epoch - # assert block.number % self.epoch_length >= self.epoch_length / 4 - # Check that this validator was active in either the previous dynasty or the current one - epochcheck = self.check_eligible_in_epoch(validator_index, epoch) - in_current_dynasty = epochcheck >= 2 - in_prev_dynasty = (epochcheck % 2) == 1 - assert in_current_dynasty or in_prev_dynasty - # Check that the prepare is on top of a justified prepare - assert self.consensus_messages[source_epoch].ancestry_hash_justified[source_ancestry_hash] - # Check that we have not yet prepared for this epoch - # Pay the reward if the prepare was submitted in time and the blockhash is correct - this_validators_deposit = self.validators[validator_index].deposit - if self.current_epoch == epoch: #if blockhash(epoch * self.epoch_length) == hash: - reward = floor(this_validators_deposit * self.reward_factor) - self.validators[validator_index].deposit += reward - self.total_deposits[self.dynasty] += reward - # Can't prepare for this epoch again - self.consensus_messages[epoch].prepare_bitmap[sourcing_hash][validator_index / 256] = \ - bitwise_or(self.consensus_messages[epoch].prepare_bitmap[sourcing_hash][validator_index / 256], - shift(as_num256(1), validator_index % 256)) - # self.validators[validator_index].max_prepared = epoch - # Record that this prepare took place - curdyn_prepares = self.consensus_messages[epoch].prepares[sourcing_hash] - if in_current_dynasty: - curdyn_prepares += this_validators_deposit - self.consensus_messages[epoch].prepares[sourcing_hash] = curdyn_prepares - prevdyn_prepares = self.consensus_messages[epoch].prev_dyn_prepares[sourcing_hash] - if in_prev_dynasty: - prevdyn_prepares += this_validators_deposit - self.consensus_messages[epoch].prev_dyn_prepares[sourcing_hash] = prevdyn_prepares - # If enough prepares with the same epoch_source and hash are made, - # then the hash value is justified for commitment - if (curdyn_prepares >= self.total_deposits[self.dynasty] * 2 / 3 and \ - prevdyn_prepares >= self.total_deposits[self.dynasty - 1] * 2 / 3) and \ - not self.consensus_messages[epoch].ancestry_hash_justified[new_ancestry_hash]: - self.consensus_messages[epoch].ancestry_hash_justified[new_ancestry_hash] = True - self.consensus_messages[epoch].hash_justified[hash] = True - # Add a parent-child relation between ancestry hashes to the ancestry table - if not self.ancestry[ancestry_hash][new_ancestry_hash]: - self.ancestry[ancestry_hash][new_ancestry_hash] = 1 - raw_log([self.prepare_log_topic], prepare_msg) - -# Process a commit message -def commit(commit_msg: bytes <= 1024): - sighash = extract32(raw_call(self.sighasher, commit_msg, gas=200000, outsize=32), 0) - # Extract parameters - values = RLPList(commit_msg, [num, num, bytes32, num, bytes]) - validator_index = values[0] - epoch = values[1] - hash = values[2] - prev_commit_epoch = values[3] - sig = values[4] - # Check the signature - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash, sig), gas=500000, outsize=32), 0) == as_bytes32(1) - # Check that we are in the right epoch - assert self.current_epoch == block.number / self.epoch_length - assert self.current_epoch == epoch - # Check that we are at least (epoch length / 2) blocks into the epoch - # assert block.number % self.epoch_length >= self.epoch_length / 2 - # Check that the commit is justified - assert self.consensus_messages[epoch].hash_justified[hash] - # Check that this validator was active in either the previous dynasty or the current one - epochcheck = self.check_eligible_in_epoch(validator_index, epoch) - in_current_dynasty = epochcheck >= 2 - in_prev_dynasty = (epochcheck % 2) == 1 - assert in_current_dynasty or in_prev_dynasty - # Check that we have not yet committed for this epoch - assert self.validators[validator_index].prev_commit_epoch == prev_commit_epoch - assert prev_commit_epoch < epoch - self.validators[validator_index].prev_commit_epoch = epoch - this_validators_deposit = self.validators[validator_index].deposit - # Pay the reward if the blockhash is correct - if True: #if blockhash(epoch * self.epoch_length) == hash: - reward = floor(this_validators_deposit * self.reward_factor) - self.validators[validator_index].deposit += reward - self.total_deposits[self.dynasty] += reward - # Can't commit for this epoch again - # self.validators[validator_index].max_committed = epoch - # Record that this commit took place - if in_current_dynasty: - self.consensus_messages[epoch].commits[hash] += this_validators_deposit - if in_prev_dynasty: - self.consensus_messages[epoch].prev_dyn_commits[hash] += this_validators_deposit - # Record if sufficient commits have been made for the block to be finalized - if (self.consensus_messages[epoch].commits[hash] >= self.total_deposits[self.dynasty] * 2 / 3 and \ - self.consensus_messages[epoch].prev_dyn_commits[hash] >= self.total_deposits[self.dynasty - 1] * 2 / 3) and \ - not self.consensus_messages[epoch].committed: - self.consensus_messages[epoch].committed = True - raw_log([self.commit_log_topic], commit_msg) - -# Cannot make two prepares in the same epoch -def double_prepare_slash(prepare1: bytes <= 1000, prepare2: bytes <= 1000): - # Get hash for signature, and implicitly assert that it is an RLP list - # consisting solely of RLP elements - sighash1 = extract32(raw_call(self.sighasher, prepare1, gas=200000, outsize=32), 0) - sighash2 = extract32(raw_call(self.sighasher, prepare2, gas=200000, outsize=32), 0) - # Extract parameters - values1 = RLPList(prepare1, [num, num, bytes32, bytes32, num, bytes32, bytes]) - values2 = RLPList(prepare2, [num, num, bytes32, bytes32, num, bytes32, bytes]) - validator_index = values1[0] - epoch1 = values1[1] - sig1 = values1[6] - assert validator_index == values2[0] - epoch2 = values2[1] - sig2 = values2[6] - # Check the signatures - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash1, sig1), gas=500000, outsize=32), 0) == as_bytes32(1) - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash2, sig2), gas=500000, outsize=32), 0) == as_bytes32(1) - # Check that they're from the same epoch - assert epoch1 == epoch2 - # Check that they're not the same message - assert sighash1 != sighash2 - # Delete the offending validator, and give a 4% "finder's fee" - validator_deposit = self.validators[validator_index].deposit - send(msg.sender, validator_deposit / 25) - self.total_destroyed += validator_deposit * 24 / 25 - self.total_deposits[self.dynasty] -= (validator_deposit - validator_deposit / 25) - self.delete_validator(validator_index) - -def prepare_commit_inconsistency_slash(prepare_msg: bytes <= 1024, commit_msg: bytes <= 1024): - # Get hash for signature, and implicitly assert that it is an RLP list - # consisting solely of RLP elements - sighash1 = extract32(raw_call(self.sighasher, prepare_msg, gas=200000, outsize=32), 0) - sighash2 = extract32(raw_call(self.sighasher, commit_msg, gas=200000, outsize=32), 0) - # Extract parameters - values1 = RLPList(prepare_msg, [num, num, bytes32, bytes32, num, bytes32, bytes]) - values2 = RLPList(commit_msg, [num, num, bytes32, num, bytes]) - validator_index = values1[0] - prepare_epoch = values1[1] - prepare_source_epoch = values1[4] - sig1 = values1[6] - assert validator_index == values2[0] - commit_epoch = values2[1] - sig2 = values2[4] - # Check the signatures - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash1, sig1), gas=500000, outsize=32), 0) == as_bytes32(1) - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash2, sig2), gas=500000, outsize=32), 0) == as_bytes32(1) - # Check that the prepare refers to something older than the commit - assert prepare_source_epoch < commit_epoch - # Check that the prepare is newer than the commit - assert commit_epoch < prepare_epoch - # Delete the offending validator, and give a 4% "finder's fee" - validator_deposit = self.validators[validator_index].deposit - send(msg.sender, validator_deposit / 25) - self.total_destroyed += validator_deposit * 24 / 25 - self.total_deposits[self.dynasty] -= validator_deposit - self.delete_validator(validator_index) - -def commit_non_justification_slash(commit_msg: bytes <= 1024): - sighash = extract32(raw_call(self.sighasher, commit_msg, gas=200000, outsize=32), 0) - # Extract parameters - values = RLPList(commit_msg, [num, num, bytes32, num, bytes]) - validator_index = values[0] - epoch = values[1] - hash = values[2] - sig = values[4] - # Check the signature - assert len(sig) == 96 - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash, sig), gas=500000, outsize=32), 0) == as_bytes32(1) - # Check that the commit is old enough - assert self.current_epoch == block.number / self.epoch_length - assert (self.current_epoch - epoch) * self.epoch_length * self.block_time > self.insufficiency_slash_delay - assert not self.consensus_messages[epoch].hash_justified[hash] - # Delete the offending validator, and give a 4% "finder's fee" - validator_deposit = self.validators[validator_index].deposit - send(msg.sender, validator_deposit / 25) - self.total_destroyed += validator_deposit * 24 / 25 - self.total_deposits[self.dynasty] -= validator_deposit - self.delete_validator(validator_index) - -# Fill in the table for which hash is what-degree ancestor of which other hash -def derive_parenthood(older: bytes32, hash: bytes32, newer: bytes32): - assert sha3(concat(hash, older)) == newer - self.ancestry[older][newer] = 1 - -# Fill in the table for which hash is what-degree ancestor of which other hash -def derive_ancestry(oldest: bytes32, middle: bytes32, recent: bytes32): - assert self.ancestry[middle][recent] - assert self.ancestry[oldest][middle] - self.ancestry[oldest][recent] = self.ancestry[oldest][middle] + self.ancestry[middle][recent] - -def prepare_non_justification_slash(prepare_msg: bytes <= 1024) -> num: - # Get hash for signature, and implicitly assert that it is an RLP list - # consisting solely of RLP elements - sighash = extract32(raw_call(self.sighasher, prepare_msg, gas=200000, outsize=32), 0) - # Extract parameters - values = RLPList(prepare_msg, [num, num, bytes32, bytes32, num, bytes32, bytes]) - validator_index = values[0] - epoch = values[1] - hash = values[2] - ancestry_hash = values[3] - source_epoch = values[4] - source_ancestry_hash = values[5] - sig = values[6] - # Check the signature - assert extract32(raw_call(self.validators[validator_index].addr, concat(sighash, sig), gas=500000, outsize=32), 0) == as_bytes32(1) - # Check that the view change is old enough - assert self.current_epoch == block.number / self.epoch_length - assert (self.current_epoch - epoch) * self.block_time * self.epoch_length > self.insufficiency_slash_delay - # Check that the source ancestry hash not had enough prepares, OR that there is not the - # correct ancestry link between the current ancestry hash and source ancestry hash - c1 = self.consensus_messages[source_epoch].ancestry_hash_justified[source_ancestry_hash] - if epoch - 1 > source_epoch: - c2 = self.ancestry[source_ancestry_hash][ancestry_hash] == epoch - 1 - source_epoch - else: - c2 = source_ancestry_hash == ancestry_hash - assert not (c1 and c2) - # Delete the offending validator, and give a 4% "finder's fee" - validator_deposit = self.validators[validator_index].deposit - send(msg.sender, validator_deposit / 25) - self.total_destroyed += validator_deposit * 24 / 25 - self.total_deposits[self.dynasty] -= validator_deposit - self.delete_validator(validator_index) - -# Temporary backdoor for testing purposes (to allow recovering destroyed deposits) -def owner_withdraw(): - send(self.owner, self.total_destroyed) - self.total_destroyed = 0 - -# Change backdoor address (set to zero to remove entirely) -def change_owner(new_owner: address): - if self.owner == msg.sender: - self.owner = new_owner diff --git a/casper4/simple_casper_tester.py b/casper4/simple_casper_tester.py deleted file mode 100644 index 61433c3..0000000 --- a/casper4/simple_casper_tester.py +++ /dev/null @@ -1,400 +0,0 @@ -from ethereum import tester as t -from ethereum import utils, state_transition, transactions, abi -from viper import compiler -import serpent -from ethereum.slogging import LogRecorder, configure_logging, set_level -config_string = ':info,eth.vm.log:trace,eth.vm.op:trace,eth.vm.stack:trace,eth.vm.exit:trace,eth.pb.msg:trace,eth.pb.tx:debug' -#configure_logging(config_string=config_string) -import rlp -s = t.state() -t.languages['viper'] = compiler.Compiler() -t.gas_limit = 9999999 - -EPOCH_LENGTH = 100 - -def inject_tx(txhex): - tx = rlp.decode(utils.decode_hex(txhex[2:]), transactions.Transaction) - s.state.set_balance(tx.sender, tx.startgas * tx.gasprice) - state_transition.apply_transaction(s.state, tx) - contract_address = utils.mk_contract_address(tx.sender, 0) - assert s.state.get_code(contract_address) - return contract_address - -code_template = """ -~calldatacopy(0, 0, 128) -~call(3000, 1, 0, 0, 128, 0, 32) -return(~mload(0) == %s) -""" - -def mk_validation_code(address): - return serpent.compile(code_template % (utils.checksum_encode(address))) - -# Install RLP decoder library -rlp_decoder_address = inject_tx( '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') - -# Install sig hasher - -s.state.set_balance('0x6e7406512b244843c1171840dfcd3d7532d979fe', 7291200000000000) - -sighasher_address = inject_tx( '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') - -# Install purity checker - -purity_checker_address = inject_tx( '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') - -ct = abi.ContractTranslator([{'name': 'check(address)', 'type': 'function', 'constant': True, 'inputs': [{'name': 'addr', 'type': 'address'}], 'outputs': [{'name': 'out', 'type': 'bool'}]}, {'name': 'submit(address)', 'type': 'function', 'constant': False, 'inputs': [{'name': 'addr', 'type': 'address'}], 'outputs': [{'name': 'out', 'type': 'bool'}]}]) -# Check that the RLP decoding library and the sig hashing library are "pure" -assert utils.big_endian_to_int(s.send(t.k0, purity_checker_address, 0, ct.encode('submit', [rlp_decoder_address]))) == 1 -assert utils.big_endian_to_int(s.send(t.k0, purity_checker_address, 0, ct.encode('submit', [sighasher_address]))) == 1 - -k1_valcode_addr = s.send(t.k0, "", 0, mk_validation_code(t.a0)) -assert utils.big_endian_to_int(s.send(t.k0, purity_checker_address, 0, ct.encode('submit', [k1_valcode_addr]))) == 1 - -# Install Casper - -casper_code = open('simple_casper.v.py').read().replace('0x1Db3439a222C519ab44bb1144fC28167b4Fa6EE6', utils.checksum_encode(k1_valcode_addr)) \ - .replace('0x476c2cA9a7f3B16FeCa86512276271FAf63B6a24', utils.checksum_encode(sighasher_address)) \ - .replace('0xD7a3BD6C9eA32efF147d067f907AE6b22d436F91', utils.checksum_encode(purity_checker_address)) - -print('Casper code length', len(compiler.compile(casper_code))) - -casper = s.abi_contract(casper_code, language='viper', startgas=5555555) - -print('Gas consumed to launch Casper', s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used) - -# Helper functions for making a prepare, commit, login and logout message - -def mk_prepare(validator_index, epoch, hash, ancestry_hash, source_epoch, source_ancestry_hash, key): - sighash = utils.sha3(rlp.encode([validator_index, epoch, hash, ancestry_hash, source_epoch, source_ancestry_hash])) - v, r, s = utils.ecdsa_raw_sign(sighash, key) - sig = utils.encode_int32(v) + utils.encode_int32(r) + utils.encode_int32(s) - return rlp.encode([validator_index, epoch, hash, ancestry_hash, source_epoch, source_ancestry_hash, sig]) - -def mk_commit(validator_index, epoch, hash, prev_commit_epoch, key): - sighash = utils.sha3(rlp.encode([validator_index, epoch, hash, prev_commit_epoch])) - v, r, s = utils.ecdsa_raw_sign(sighash, key) - sig = utils.encode_int32(v) + utils.encode_int32(r) + utils.encode_int32(s) - return rlp.encode([validator_index, epoch, hash, prev_commit_epoch, sig]) - -def mk_status_flicker(validator_index, epoch, login, key): - sighash = utils.sha3(rlp.encode([validator_index, epoch, login])) - v, r, s = utils.ecdsa_raw_sign(sighash, key) - sig = utils.encode_int32(v) + utils.encode_int32(r) + utils.encode_int32(s) - return rlp.encode([validator_index, epoch, login, sig]) - -# Begin the test - -print("Starting tests") -casper.initiate() -# Initialize the first epoch -s.state.block_number = EPOCH_LENGTH -print('foo', casper.initialize_epoch(1)) -assert casper.get_nextValidatorIndex() == 1 -start = s.snapshot() -print("Epoch initialized") -print("Reward factor: %.8f" % (casper.get_reward_factor() * 2 / 3)) -# Send a prepare message -#configure_logging(config_string=config_string) -casper.prepare(mk_prepare(0, 1, '\x35' * 32, '\x00' * 32, 0, '\x00' * 32, t.k0)) -print('Gas consumed for a prepare: %d (including %d intrinsic gas)' % - (s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used, s.last_tx.intrinsic_gas_used)) -epoch_1_anchash = utils.sha3(b'\x35' * 32 + b'\x00' * 32) -assert casper.get_consensus_messages__hash_justified(1, b'\x35' * 32) -assert casper.get_consensus_messages__ancestry_hash_justified(1, epoch_1_anchash) -print("Prepare message processed") -try: - casper.prepare(mk_prepare(0, 1, '\x35' * 32, '\x00' * 32, 0, '\x00' * 32, t.k0)) - success = True -except: - success = False -assert not success -print("Prepare message fails the second time") -# Send a commit message -casper.commit(mk_commit(0, 1, '\x35' * 32, 0, t.k0)) -print('Gas consumed for a commit: %d (including %d intrinsic gas)' % - (s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used, s.last_tx.intrinsic_gas_used)) -# Check that we committed -assert casper.get_consensus_messages__committed(1) -print("Commit message processed") -# Initialize the second epoch -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(2) -# Check that the dynasty increased as expected -assert casper.get_dynasty() == 1 -assert casper.get_total_deposits(1) == casper.get_total_deposits(0) > 0 -print("Second epoch initialized, dynasty increased as expected") -# Send a prepare message -casper.prepare(mk_prepare(0, 2, '\x45' * 32, epoch_1_anchash, 1, epoch_1_anchash, t.k0)) -# Send a commit message -epoch_2_commit = mk_commit(0, 2, '\x45' * 32, 1, t.k0) -casper.commit(epoch_2_commit) -epoch_2_anchash = utils.sha3(b'\x45' * 32 + epoch_1_anchash) -assert casper.get_consensus_messages__ancestry_hash_justified(2, epoch_2_anchash) -# Check that we committed -assert casper.get_consensus_messages__committed(2) -# Initialize the third epoch -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(3) -print("Second epoch prepared and committed, third epoch initialized") -# Test the NO_DBL_PREPARE slashing condition -p1 = mk_prepare(0, 3, '\x56' * 32, epoch_2_anchash, 2, epoch_2_anchash, t.k0) -p2 = mk_prepare(0, 3, '\x57' * 32, epoch_2_anchash, 2, epoch_2_anchash, t.k0) -snapshot = s.snapshot() -casper.double_prepare_slash(p1, p2) -s.revert(snapshot) -print("NO_DBL_PREPARE slashing condition works") -# Test the PREPARE_COMMIT_CONSISTENCY slashing condition -p3 = mk_prepare(0, 3, '\x58' * 32, epoch_2_anchash, 0, b'\x00' * 32, t.k0) -snapshot = s.snapshot() -casper.prepare_commit_inconsistency_slash(p3, epoch_2_commit) -s.revert(snapshot) -print("PREPARE_COMMIT_CONSISTENCY slashing condition works") -# Finish the third epoch -casper.prepare(p1) -casper.commit(mk_commit(0, 3, '\x56' * 32, 2, t.k0)) -epoch_3_anchash = utils.sha3(b'\x56' * 32 + epoch_2_anchash) -assert casper.get_consensus_messages__ancestry_hash_justified(3, epoch_3_anchash) -assert casper.get_consensus_messages__committed(3) -# Initialize the fourth epoch. Not doing prepares or commits during this epoch. -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(4) -assert casper.get_dynasty() == 3 -epoch_4_anchash = utils.sha3(b'\x67' * 32 + epoch_3_anchash) -# Not publishing this prepare for the time being -p4 = mk_prepare(0, 4, '\x78' * 32, '\x12' * 32, 3, '\x24' * 32, t.k0) -# Initialize the fifth epoch -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(5) -print("Epochs up to 5 initialized") -# Dynasty not incremented because no commits were made -assert casper.get_dynasty() == 3 -epoch_5_anchash = utils.sha3(b'\x78' * 32 + epoch_4_anchash) -p5 = mk_prepare(0, 5, '\x78' * 32, epoch_4_anchash, 3, epoch_3_anchash, t.k0) -casper.prepare(p5) -# Test the COMMIT_REQ slashing condition -kommit = mk_commit(0, 5, b'\x80' * 32, 3, t.k0) -epoch_inc = 1 + int(86400 / 14 / EPOCH_LENGTH) -s.state.block_number += EPOCH_LENGTH * epoch_inc -print("Speeding up time to test remaining two slashing conditions") -for i in range(6, 6 + epoch_inc): - casper.initialize_epoch(i) -print("Epochs up to %d initialized" % (6 + epoch_inc)) -snapshot = s.snapshot() -casper.commit_non_justification_slash(kommit) -s.revert(snapshot) -try: - casper.commit_non_justification_slash(0, epoch_2_commit) - success = True -except: - success = False -assert not success -print("COMMIT_REQ slashing condition works") -# Test the PREPARE_REQ slashing condition -casper.derive_parenthood(epoch_3_anchash, b'\x67' * 32, epoch_4_anchash) -assert casper.get_ancestry(epoch_3_anchash, epoch_4_anchash) == 1 -assert casper.get_ancestry(epoch_4_anchash, epoch_5_anchash) == 1 -casper.derive_ancestry(epoch_3_anchash, epoch_4_anchash, epoch_5_anchash) -assert casper.get_ancestry(epoch_3_anchash, epoch_5_anchash) == 2 -snapshot = s.snapshot() -casper.prepare_non_justification_slash(p4) -s.revert(snapshot) -try: - casper.prepare_non_justification_slash(p5) - success = True -except: - success = False -assert not success -print("PREPARE_REQ slashing condition works") - -print("Restarting the chain for test 2") -# Restart the chain -s.revert(start) -assert casper.get_dynasty() == 0 -assert casper.get_current_epoch() == 1 -assert casper.get_consensus_messages__ancestry_hash_justified(0, b'\x00' * 32) -print("Epoch 1 initialized") -for k in (t.k1, t.k2, t.k3, t.k4, t.k5, t.k6): - valcode_addr = s.send(t.k0, '', 0, mk_validation_code(utils.privtoaddr(k))) - assert utils.big_endian_to_int(s.send(t.k0, purity_checker_address, 0, ct.encode('submit', [valcode_addr]))) == 1 - casper.deposit(valcode_addr, utils.privtoaddr(k), value=3 * 10**18) -print("Processed 6 deposits") -casper.prepare(mk_prepare(0, 1, b'\x10' * 32, b'\x00' * 32, 0, b'\x00' * 32, t.k0)) -casper.commit(mk_commit(0, 1, b'\x10' * 32, 0, t.k0)) -epoch_1_anchash = utils.sha3(b'\x10' * 32 + b'\x00' * 32) -assert casper.get_consensus_messages__committed(1) -print("Prepared and committed") -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(2) -print("Epoch 2 initialized") -assert casper.get_dynasty() == 1 -casper.prepare(mk_prepare(0, 2, b'\x20' * 32, epoch_1_anchash, 1, epoch_1_anchash, t.k0)) -casper.commit(mk_commit(0, 2, b'\x20' * 32, 1, t.k0)) -epoch_2_anchash = utils.sha3(b'\x20' * 32 + epoch_1_anchash) -assert casper.get_consensus_messages__committed(2) -print("Confirmed that one key is still sufficient to prepare and commit") -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(3) -print("Epoch 3 initialized") -assert casper.get_dynasty() == 2 -assert 3 * 10**18 <= casper.get_total_deposits(0) < 4 * 10**18 -assert 3 * 10**18 <= casper.get_total_deposits(1) < 4 * 10**18 -assert 21 * 10**18 <= casper.get_total_deposits(2) < 22 * 10**18 -print("Confirmed new total_deposits") -try: - # Try to log out, but sign with the wrong key - casper.flick_status(mk_status_flicker(0, 3, 0, t.k1)) - success = True -except: - success = False -assert not success -# Log out -casper.flick_status(mk_status_flicker(4, 3, 0, t.k4)) -casper.flick_status(mk_status_flicker(5, 3, 0, t.k5)) -casper.flick_status(mk_status_flicker(6, 3, 0, t.k6)) -print("Logged out three validators") -# Validators leave the fwd validator set in dynasty 4 -assert casper.get_validators__dynasty_end(4) == 4 -epoch_3_anchash = utils.sha3(b'\x30' * 32 + epoch_2_anchash) -# Prepare from one validator -casper.prepare(mk_prepare(0, 3, b'\x30' * 32, epoch_2_anchash, 2, epoch_2_anchash, t.k0)) -# Not prepared yet -assert not casper.get_consensus_messages__hash_justified(3, b'\x30' * 32) -print("Prepare from one validator no longer sufficient") -# Prepare from 3 more validators -for i, k in ((1, t.k1), (2, t.k2), (3, t.k3)): - casper.prepare(mk_prepare(i, 3, b'\x30' * 32, epoch_2_anchash, 2, epoch_2_anchash, k)) -# Still not prepared -assert not casper.get_consensus_messages__hash_justified(3, b'\x30' * 32) -print("Prepare from four of seven validators still not sufficient") -# Prepare from a fifth validator -casper.prepare(mk_prepare(4, 3, b'\x30' * 32, epoch_2_anchash, 2, epoch_2_anchash, t.k4)) -# NOW we're prepared! -assert casper.get_consensus_messages__hash_justified(3, b'\x30' * 32) -print("Prepare from five of seven validators sufficient!") -# Five commits -for i, k in enumerate([t.k0, t.k1, t.k2, t.k3, t.k4]): - casper.commit(mk_commit(i, 3, b'\x30' * 32, 2 if i == 0 else 0, k)) -# And we committed! -assert casper.get_consensus_messages__committed(3) -print("Commit from five of seven validators sufficient") -# Start epoch 4 -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(4) -assert casper.get_dynasty() == 3 -print("Epoch 4 initialized") -# Prepare and commit -epoch_4_anchash = utils.sha3(b'\x40' * 32 + epoch_3_anchash) -for i, k in enumerate([t.k0, t.k1, t.k2, t.k3, t.k4]): - casper.prepare(mk_prepare(i, 4, b'\x40' * 32, epoch_3_anchash, 3, epoch_3_anchash, k)) -for i, k in enumerate([t.k0, t.k1, t.k2, t.k3, t.k4]): - casper.commit(mk_commit(i, 4, b'\x40' * 32, 3, k)) -assert casper.get_consensus_messages__committed(4) -print("Prepared and committed") -# Start epoch 5 / dynasty 4 -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(5) -print("Epoch 5 initialized") -assert casper.get_dynasty() == 4 -assert 21 * 10**18 <= casper.get_total_deposits(3) <= 22 * 10**18 -assert 12 * 10**18 <= casper.get_total_deposits(4) <= 13 * 10**18 -epoch_5_anchash = utils.sha3(b'\x50' * 32 + epoch_4_anchash) -# Do three prepares -for i, k in enumerate([t.k0, t.k1, t.k2]): - casper.prepare(mk_prepare(i, 5, b'\x50' * 32, epoch_4_anchash, 4, epoch_4_anchash, k)) -# Three prepares are insufficient because there are still five validators in the rear validator set -assert not casper.get_consensus_messages__hash_justified(5, b'\x50' * 32) -print("Three prepares insufficient, as rear validator set still has seven") -# Do two more prepares -for i, k in [(3, t.k3), (4, t.k4)]: - casper.prepare(mk_prepare(i, 5, b'\x50' * 32, epoch_4_anchash, 4, epoch_4_anchash, k)) -# Now we're good! -assert casper.get_consensus_messages__hash_justified(5, b'\x50' * 32) -print("Five prepares sufficient") -for i, k in enumerate([t.k0, t.k1, t.k2, t.k3, t.k4]): - casper.commit(mk_commit(i, 5, b'\x50' * 32, 4, k)) -# Committed! -assert casper.get_consensus_messages__committed(5) -# Start epoch 6 / dynasty 5 -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(6) -assert casper.get_dynasty() == 5 -print("Epoch 6 initialized") -# Log back in -old_deposit_start = casper.get_dynasty_start_epoch(casper.get_validators__dynasty_start(4)) -old_deposit_end = casper.get_dynasty_start_epoch(casper.get_validators__dynasty_end(4) + 1) -old_deposit = casper.get_validators__deposit(4) -# Explanation: -# * During dynasty 0, the validator deposited, so he joins the current set in dynasty 2 -# (epoch 3), and the previous set in dynasty 3 (epoch 4) -# * During dynasty 2, the validator logs off, so he leaves the current set in dynasty 4 -# (epoch 5) and the previous set in dynasty 5 (epoch 6) -assert [casper.check_eligible_in_epoch(4, i) for i in range(7)] == [0, 0, 0, 2, 3, 1, 0] -casper.flick_status(mk_status_flicker(4, 6, 1, t.k4)) -# Explanation: -# * During dynasty 7, the validator will log on again. Hence, the dynasty mask -# should include dynasties 4, 5, 6 -assert [casper.check_eligible_in_epoch(4, i) for i in range(7)] == [0, 0, 0, 2, 3, 1, 0] -new_deposit = casper.get_validators__deposit(4) -print("One validator logging back in") -print("Penalty from %d epochs: %.4f" % (old_deposit_end - old_deposit_start, 1 - new_deposit / old_deposit)) -assert casper.get_validators__dynasty_start(4) == 7 -# Here three prepares and three commits should be sufficient! -epoch_6_anchash = utils.sha3(b'\x60' * 32 + epoch_5_anchash) -for i, k in enumerate([t.k0, t.k1, t.k2]): - casper.prepare(mk_prepare(i, 6, b'\x60' * 32, epoch_5_anchash, 5, epoch_5_anchash, k)) -for i, k in enumerate([t.k0, t.k1, t.k2]): - casper.commit(mk_commit(i, 6, b'\x60' * 32, 5, k)) -assert casper.get_consensus_messages__committed(6) -print("Three of four prepares and commits sufficient") -# Start epoch 7 / dynasty 6 -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(7) -assert casper.get_dynasty() == 6 -print("Epoch 7 initialized") -# Here three prepares and three commits should be sufficient! -epoch_7_anchash = utils.sha3(b'\x70' * 32 + epoch_6_anchash) -for i, k in enumerate([t.k0, t.k1, t.k2]): - #if i == 1: - # configure_logging(config_string=config_string) - casper.prepare(mk_prepare(i, 7, b'\x70' * 32, epoch_6_anchash, 6, epoch_6_anchash, k)) - #if i == 1: - # import sys - # sys.exit() -print('Gas consumed for first prepare', s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used) -print('Gas consumed for second prepare', s.state.receipts[-2].gas_used - s.state.receipts[-3].gas_used) -print('Gas consumed for third prepare', s.state.receipts[-3].gas_used - s.state.receipts[-4].gas_used) -for i, k in enumerate([t.k0, t.k1, t.k2]): - casper.commit(mk_commit(i, 7, b'\x70' * 32, 6, k)) -print('Gas consumed for first commit', s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used) -print('Gas consumed for second commit', s.state.receipts[-2].gas_used - s.state.receipts[-3].gas_used) -print('Gas consumed for third commit', s.state.receipts[-3].gas_used - s.state.receipts[-4].gas_used) -assert casper.get_consensus_messages__committed(7) -print("Three of four prepares and commits sufficient") -# Start epoch 8 / dynasty 7 -s.state.block_number += EPOCH_LENGTH -casper.initialize_epoch(8) -assert casper.get_dynasty() == 7 -print("Epoch 8 initialized") -assert 12 * 10**18 <= casper.get_total_deposits(6) <= 13 * 10**18 -assert 15 * 10**18 <= casper.get_total_deposits(7) <= 16 * 10**18 -epoch_8_anchash = utils.sha3(b'\x80' * 32 + epoch_7_anchash) -# Do three prepares -for i, k in enumerate([t.k0, t.k1, t.k2]): - casper.prepare(mk_prepare(i, 8, b'\x80' * 32, epoch_7_anchash, 7, epoch_7_anchash, k)) -# Three prepares are insufficient because there are still five validators in the rear validator set -assert not casper.get_consensus_messages__hash_justified(8, b'\x80' * 32) -print("Three prepares no longer sufficient, as the forward validator set has five validators") -# Do one more prepare -for i, k in [(3, t.k3)]: - casper.prepare(mk_prepare(i, 8, b'\x80' * 32, epoch_7_anchash, 7, epoch_7_anchash, k)) -# Now we're good! -assert casper.get_consensus_messages__hash_justified(8, b'\x80' * 32) -print("Four of five prepares sufficient") -for i, k in enumerate([t.k0, t.k1, t.k2, t.k3, t.k4]): - casper.commit(mk_commit(i, 8, b'\x80' * 32, 7 if i < 3 else 5, k)) -assert casper.get_consensus_messages__committed(8) -print("Committed") -# Validator rejoins current validator set in epoch 8 -assert [casper.check_eligible_in_epoch(4, i) for i in range(9)] == [0, 0, 0, 2, 3, 1, 0, 0, 2] - -print("All tests passed") diff --git a/casper4/simulator.py b/casper4/simulator.py deleted file mode 100644 index 6040b82..0000000 --- a/casper4/simulator.py +++ /dev/null @@ -1,378 +0,0 @@ -# Implements Minimal Slashing Conditions and dynamic validator sets, descriptions here: -# Slashing Conditions: https://docs.google.com/document/d/1ecFPYhe7YsKNQUAx48S8hoyK9Y4Rbe9be_lCe_vj2ek -# Dynamic Validator Sets: https://medium.com/@VitalikButerin/safety-under-dynamic-validator-sets-ef0c3bbdf9f6#.igylifcm9 - -import random - -POOL_SIZE = 10 -VALIDATOR_IDS = range(0, POOL_SIZE*2) -INITIAL_VALIDATORS = range(0, POOL_SIZE) -BLOCK_TIME = 100 -EPOCH_LENGTH = 5 -AVG_LATENCY = 255 - -def poisson_latency(latency): - return lambda: 1 + int(random.gammavariate(1, 1) * latency) - -class Network(): - def __init__(self, latency): - self.nodes = [] - self.latency = latency - self.time = 0 - self.msg_arrivals = {} - - def broadcast(self, msg): - for i, n in enumerate(self.nodes): - delay = self.latency() - if self.time + delay not in self.msg_arrivals: - self.msg_arrivals[self.time + delay] = [] - self.msg_arrivals[self.time + delay].append((i, msg)) - - def tick(self): - if self.time in self.msg_arrivals: - for node_index, msg in self.msg_arrivals[self.time]: - self.nodes[node_index].on_receive(msg) - del self.msg_arrivals[self.time] - for n in self.nodes: - n.tick(self.time) - self.time += 1 - -class Block(): - def __init__(self, parent=None, finalized_dynasties=None): - self.hash = random.randrange(10**30) - # If we are genesis block, set initial values - if not parent: - self.number = 0 - self.prevhash = 0 - self.prev_dynasty = self.current_dynasty = Dynasty(INITIAL_VALIDATORS) - self.next_dynasty = self.generate_next_dynasty(self.current_dynasty.number) - return - # Set our block number and our prevhash - self.number = parent.number + 1 - self.prevhash = parent.hash - # Generate a random next dynasty - self.next_dynasty = self.generate_next_dynasty(parent.current_dynasty.number) - # If the current_dynasty was finalized, we advance to the next dynasty - if parent.current_dynasty in finalized_dynasties: - self.prev_dynasty = parent.current_dynasty - self.current_dynasty = parent.next_dynasty - return - # `current_dynasty` has not yet been finalized so we don't rotate validators - self.prev_dynasty = parent.prev_dynasty - self.current_dynasty = parent.current_dynasty - - @property - def epoch(self): - return self.number // EPOCH_LENGTH - - def generate_next_dynasty(self, prev_dynasty_number): - random.seed(self.hash) - next_dynasty = Dynasty(random.sample(VALIDATOR_IDS, POOL_SIZE), prev_dynasty_number+1) - random.seed() - return next_dynasty - -class Prepare(): - def __init__(self, view, _hash, view_source, sender): - self.view = view - self.hash = random.randrange(10**30) - self.blockhash = _hash - self.view_source = view_source - self.sender = sender - -class Commit(): - def __init__(self, view, _hash, sender): - self.view = view - self.hash = random.randrange(10**30) - self.blockhash = _hash - self.sender = sender - -class Dynasty(): - def __init__(self, validators, number=0): - self.validators = validators - self.number = number - - def __hash__(self): - return hash(str(self.number) + str(self.validators)) - - def __eq__(self, other): - return (str(self.number) + str(self.validators)) == (str(other.number) + str(other.validators)) - -GENESIS = Block() - -# Fork choice rule: -# 1. HEAD = genesis -# 2. Find the descendant with the highest number of commits -# 3. Repeat 2 until 0 commits -# 4. Longest chain rule - -class Node(): - def __init__(self, network, id): - # List of highest-commit descendants along with their commit counts, in oldest-to-newest order - self.checkpoints = [GENESIS.hash] - # Received blocks - self.received = {GENESIS.hash: GENESIS} - # Messages that will be processed once a given message is received - self.dependencies = {} - # Checkpoint to view source to prepare count - self.prepare_count = {} - # Checkpoints that can be committed - self.committable = {} - # Commits for any given checkpoint - # Genesis is an immutable start of the chain - self.commits = {GENESIS.hash: INITIAL_VALIDATORS} - # Set of finalized dynasties - self.finalized_dynasties = set() - self.finalized_dynasties.add(Dynasty(INITIAL_VALIDATORS)) - # My current epoch - self.current_epoch = 0 - # My highest committed epoch and hash - self.highest_committed_epoch = -1 - self.highest_committed_hash = GENESIS.hash - # Network I am connected to - self.network = network - network.nodes.append(self) - # Longest tail from each checkpoint - self.tails = {GENESIS.hash: GENESIS} - # Tail that each block belongs to - self.tail_membership = {GENESIS.hash: GENESIS.hash} - # This node's ID - self.id = id - - @property - def head(self): - latest_checkpoint = self.checkpoints[-1] - latest_block = self.tails[latest_checkpoint] - return latest_block - - # Get the checkpoint immediately before a given checkpoint - def get_checkpoint_parent(self, block): - if block.number == 0: - return None - return self.received[self.tail_membership[block.prevhash]] - - # If we received an object but did not receive some dependencies - # needed to process it, save it to be processed later - def add_dependency(self, _hash, obj): - if _hash not in self.dependencies: - self.dependencies[_hash] = [] - self.dependencies[_hash].append(obj) - - # Is a given checkpoint an ancestor of another given checkpoint? - def is_ancestor(self, anc, desc): - if not isinstance(anc, Block): - anc = self.received[anc] - if not isinstance(desc, Block): - desc = self.received[desc] - assert anc.number % EPOCH_LENGTH == 0 - assert desc.number % EPOCH_LENGTH == 0 - while True: - if desc is None: - return False - if desc.hash == anc.hash: - return True - desc = self.get_checkpoint_parent(desc) - - def get_last_committed_checkpoint(self): - z = len(self.checkpoints) - 1 - while self.score_checkpoint(self.received[self.checkpoints[z]]) < 1: - z -= 1 - return self.checkpoints[z] - - # Called on receiving a block - def accept_block(self, block): - # If we didn't receive the block's parent yet, wait - if block.prevhash not in self.received: - self.add_dependency(block.prevhash, block) - return False - # We recived the block - self.received[block.hash] = block - # print(self.id, 'got a block', block.number, block.hash) - # If it's an epoch block (in general) - if block.number % EPOCH_LENGTH == 0: - # Start a tail object for it - self.tail_membership[block.hash] = block.hash - self.tails[block.hash] = block - # Otherwise... - else: - # See if it's part of the longest tail, if so set the tail accordingly - assert block.prevhash in self.received - assert block.prevhash in self.tail_membership - self.tail_membership[block.hash] = self.tail_membership[block.prevhash] - if block.number > self.tails[self.tail_membership[block.hash]].number: - self.tails[self.tail_membership[block.hash]] = block - self.check_checkpoints(self.received[self.tail_membership[block.hash]]) - self.maybe_prepare_last_checkpoint() - return True - - def maybe_prepare_last_checkpoint(self): - target_block = self.received[self.checkpoints[-1]] - # If the block is an epoch block of a higher epoch than what we've seen so far - if target_block.epoch > self.current_epoch: - print('now in epoch %d' % target_block.epoch) - # Increment our epoch - self.current_epoch = target_block.epoch - # If our highest committed hash is in the main chain (in most cases - # it should be), then send a prepare - last_committed_checkpoint = self.get_last_committed_checkpoint() - if self.is_ancestor(self.highest_committed_hash, last_committed_checkpoint): - print('Preparing %d for epoch %d with view source %d' % - (target_block.hash, target_block.epoch, self.received[last_committed_checkpoint].epoch)) - self.network.broadcast(Prepare(target_block.epoch, target_block.hash, self.received[last_committed_checkpoint].epoch, self.id)) - assert self.received[target_block.hash] - - # Pick a checkpoint by number of commits first, epoch number - # (ie. longest chain rule) second - def score_checkpoint(self, block): - # Choose the dynasty (current or previous) with the minimum number of commits - current_dynasty_number_of_commits = len(list(set(block.current_dynasty.validators) & set(self.commits.get(block.hash, [])))) - prev_dynasty_number_of_commits = len(list(set(block.prev_dynasty.validators) & set(self.commits.get(block.hash, [])))) - number_of_commits = min(current_dynasty_number_of_commits, prev_dynasty_number_of_commits) - return number_of_commits + 0.000000001 * self.tails[block.hash].number - - # See if a given epoch block requires us to reorganize our checkpoint list - def check_checkpoints(self, block): - # Is this hash already in our main chain? Then do nothing - if block.hash in self.checkpoints: - # prev_checkpoint = self.received[self.checkpoints[self.checkpoints.index(block.hash) - 1]] - # if score_checkpoint(block) < score_checkpoint(prev_checkpoint): - return - # Figure out how many of our checkpoints we need to revert - z = len(self.checkpoints) - 1 - new_score = self.score_checkpoint(block) - while new_score > self.score_checkpoint(self.received[self.checkpoints[z]]): - z -= 1 - # If none, do nothing - if z == len(self.checkpoints) - 1 and block.number <= self.received[self.checkpoints[z-1]].number: - return - # Delete the checkpoints that need to be superseded - self.checkpoints = self.checkpoints[:z + 1] - # Re-run the fork choice rule - while 1: - # Find the descendant with the highest score (commits first, epoch second) - max_score = 0 - max_descendant = None - for _hash in self.tails: - if self.is_ancestor(self.checkpoints[-1], _hash) and _hash != self.checkpoints[-1]: - new_score = self.score_checkpoint(self.received[_hash]) - if new_score > max_score: - max_score = new_score - max_descendant = _hash - # Append to the chain that checkpoint, and all checkpoints between the - # last checkpoint and the new one - if max_descendant: - new_chain = [max_descendant] - while new_chain[0] != self.checkpoints[-1]: - new_chain.insert(0, self.get_checkpoint_parent(self.received[new_chain[0]]).hash) - self.checkpoints.extend(new_chain[1:]) - # If there were no suitable descendants found, break - else: - break - print('New checkpoints: %r' % [self.received[b].epoch for b in self.checkpoints]) - - # Called on receiving a prepare message - def accept_prepare(self, prepare): - if self.id == 0: - print('got a prepare', prepare.view, prepare.view_source, prepare.blockhash, prepare.blockhash in self.received) - # If the block has not yet been received, wait - if prepare.blockhash not in self.received: - self.add_dependency(prepare.blockhash, prepare) - return False - # If the sender is not in the prepare's dynasty, ignore the prepare - if prepare.sender not in self.received[prepare.blockhash].current_dynasty.validators and \ - prepare.sender not in self.received[prepare.blockhash].prev_dynasty.validators: - return False - # Add to the prepare count - if prepare.blockhash not in self.prepare_count: - self.prepare_count[prepare.blockhash] = {} - self.prepare_count[prepare.blockhash][prepare.view_source] = self.prepare_count[prepare.blockhash].get(prepare.view_source, 0) + 1 - # If there are enough prepares and the previous dynasty is finalized... - if self.prepare_count[prepare.blockhash][prepare.view_source] > (POOL_SIZE * 2) // 3 and \ - self.received[prepare.blockhash].prev_dynasty in self.finalized_dynasties and \ - prepare.blockhash not in self.committable: - # Mark it as committable - self.committable[prepare.blockhash] = True - # Start counting commits - self.commits[prepare.blockhash] = [] - # If there are dependencies (ie. commits that arrived before there - # were enough prepares), since there are now enough prepares we - # can process them - if "commit:"+str(prepare.blockhash) in self.dependencies: - for c in self.dependencies["commit:"+str(prepare.blockhash)]: - self.accept_commit(c) - del self.dependencies["commit:"+str(prepare.blockhash)] - # Broadcast a commit - if self.current_epoch == prepare.view: - self.network.broadcast(Commit(prepare.view, prepare.blockhash, self.id)) - print('Committing %d for epoch %d' % (prepare.blockhash, prepare.view)) - self.highest_committed_epoch = prepare.view - self.highest_committed_hash = prepare.blockhash - self.current_epoch = prepare.view + 0.5 - return True - - # Called on receiving a commit message - def accept_commit(self, commit): - if self.id == 0: - print('got a commmit', commit.view, commit.blockhash, commit.blockhash in self.received, commit.blockhash in self.committable) - # If the block has not yet been received, wait - if commit.blockhash not in self.received: - self.add_dependency(commit.blockhash, commit) - return False - # If the sender is not in the commit's dynasty, ignore the commit - if commit.sender not in self.received[commit.blockhash].current_dynasty.validators and \ - commit.sender not in self.received[commit.blockhash].prev_dynasty.validators: - return False - # If there have not yet been enough prepares, wait - if commit.blockhash not in self.committable: - self.add_dependency("commit:"+str(commit.blockhash), commit) - return False - # Add the commit by recording the sender - self.commits[commit.blockhash].append(commit.sender) - # Check if the block is finalized - current_dynasty_commits = list(set(self.received[commit.blockhash].current_dynasty.validators) & set(self.commits[commit.blockhash])) - prev_dynasty_commits = list(set(self.received[commit.blockhash].prev_dynasty.validators) & set(self.commits[commit.blockhash])) - if len(current_dynasty_commits) > (POOL_SIZE * 2) // 3 and len(prev_dynasty_commits) > (POOL_SIZE * 2) // 3: - # Because the block has been finalized let's record its dynasty as finalized - finalized_dynasty = self.received[commit.blockhash].current_dynasty - self.finalized_dynasties.add(finalized_dynasty) - print('Finalizing dynasty number %d for block number %d' % - (finalized_dynasty.number, self.received[commit.blockhash].number)) - # Update the checkpoints if needed - self.check_checkpoints(self.received[commit.blockhash]) - return True - - # Called on receiving any object - def on_receive(self, obj): - if obj.hash in self.received: - return False - if isinstance(obj, Block): - o = self.accept_block(obj) - elif isinstance(obj, Prepare): - o = self.accept_prepare(obj) - elif isinstance(obj, Commit): - o = self.accept_commit(obj) - # If the object was successfully processed - # (ie. not flagged as having unsatisfied dependencies) - if o: - self.received[obj.hash] = obj - if obj.hash in self.dependencies: - for d in self.dependencies[obj.hash]: - self.on_receive(d) - del self.dependencies[obj.hash] - - # Called every round - def tick(self, _time): - if self.id == (_time // BLOCK_TIME) % POOL_SIZE and _time % BLOCK_TIME == 0: - new_block = Block(self.head, self.finalized_dynasties) - self.network.broadcast(new_block) - self.on_receive(new_block) - -network = Network(poisson_latency(AVG_LATENCY)) -nodes = [Node(network, i) for i in VALIDATOR_IDS] -for t in range(25000): - network.tick() - if t % 1000 == 999: - print('Heads:', [n.head.number for n in nodes]) - print('Checkpoints:', nodes[0].checkpoints) - print('Commits:', [nodes[0].commits.get(c, 0) for c in nodes[0].checkpoints]) - print('Blocks Dynasties:', [(nodes[0].received[c].current_dynasty.number) for c in nodes[0].checkpoints]) - print('All Node Dynasties:', [(node.tails[node.checkpoints[-1]].current_dynasty.number) for node in nodes]) diff --git a/casper4/sqrt.se.py b/casper4/sqrt.se.py deleted file mode 100644 index fe4775a..0000000 --- a/casper4/sqrt.se.py +++ /dev/null @@ -1,12 +0,0 @@ -with inp = ~calldataload(0): - foo = inp - exp = 0 - while foo >= 256: - foo = ~div(foo, 256) - exp += 1 - with x = ~div(inp, 16 ** exp): - while 1: - y = ~div(x + ~div(inp, x) + 1, 2) - if x == y: - return x - x = y diff --git a/casper4/surround_checker.py b/casper4/surround_checker.py deleted file mode 100644 index 585e9ac..0000000 --- a/casper4/surround_checker.py +++ /dev/null @@ -1,52 +0,0 @@ -# NO_SURROUND validation checker. For any attestation, call `new_attestation(s, t)`. -# If there is a no surround validation, you will be notified. Requires 2*N*log(N) -# bits per validator in addition to the attestations themselves. - -class CollisionFound(Exception): - pass - -class Checker(): - def __init__(self, MAX=16): - self.array1 = [i for i in range(MAX)] - self.array2 = [MAX for i in range(MAX)] - self.attestations = [] - - def new_attestation(self, s, t): - assert s < t - if s > 0 and t < self.array1[s - 1]: - for os, ot in self.attestations: - if os < s < t < ot: - raise CollisionFound("Collision found: ({} {}) surrounds provided ({} {})".format(os, ot, s, t)) - raise Exception("panic, should never be here") - if t > self.array2[s + 1]: - for os, ot in self.attestations: - if s < os < ot < t: - raise CollisionFound("Collision found: ({} {}) is surrounded by provided ({} {})".format(os, ot, s, t)) - raise Exception("panic, should never be here") - _s = s - while self.array1[_s] < t and _s < t: - self.array1[_s] = t - _s += 1 - _s = s - while self.array2[_s] > t and _s >= 0: - self.array2[_s] = t - _s -= 1 - for os, ot in self.attestations: - assert not((os < s < t < ot) or (s < os < ot < t)) - self.attestations.append((s, t)) - -def test(): - c = Checker(16) - import random - for i in range(30): - x, y = random.randrange(16), random.randrange(16) - if x == y: - continue - try: - c.new_attestation(min(x, y), max(x, y)) - except CollisionFound as e: - print(e) - print("Test successful") - -if __name__ == '__main__': - test() diff --git a/clock_disparity/distributions.py b/clock_disparity/distributions.py deleted file mode 100644 index 6412e3d..0000000 --- a/clock_disparity/distributions.py +++ /dev/null @@ -1,37 +0,0 @@ -import random, sys - - -def normal_distribution(mean, standev): - def f(): - return int(random.normalvariate(mean, standev)) - - return f - - -def exponential_distribution(mean): - def f(): - total = 0 - while 1: - total += 1 - if not random.randrange(32): - break - return int(total * 0.03125 * mean) - - return f - - -def convolve(*args): - def f(): - total = 0 - for arg in args: - total += arg() - return total - - return f - - -def transform(dist, xformer): - def f(): - return xformer(dist()) - - return f diff --git a/clock_disparity/ghost_node.py b/clock_disparity/ghost_node.py deleted file mode 100644 index 0510219..0000000 --- a/clock_disparity/ghost_node.py +++ /dev/null @@ -1,278 +0,0 @@ -import os -from binascii import hexlify -from Crypto.Hash import keccak -import random - -def to_hex(s): - return hexlify(s).decode('utf-8') - -memo = {} - -def sha3(x): - if x not in memo: - memo[x] = keccak.new(digest_bits=256, data=x).digest() - return memo[x] - -def hash_to_int(h): - o = 0 - for c in h: - o = (o << 8) + c - return o - -NOTARIES = 100 -SLOT_SIZE = 6 -EPOCH_LENGTH = 25 - -# Not a full RANDAO; stub for now -class Block(): - def __init__(self, parent, slot, proposer): - self.contents = os.urandom(32) - self.parent_hash = parent.hash if parent else (b'\x00' * 32) - self.hash = sha3(self.parent_hash + self.contents) - self.height = parent.height + 1 if parent else 0 - assert slot % NOTARIES == proposer - self.proposer = proposer - self.slot = slot - - def min_timestamp(self): - return SLOT_SIZE * self.slot - -class Sig(): - def __init__(self, proposer, targets, slot, ts): - self.proposer = proposer - self.targets = targets - self.slot = slot - self.ts = ts - self.hash = os.urandom(32) - -genesis = Block(None, 0, 0) - -class Node(): - - def __init__(self, _id, network, sleepy=False, careless=False, ts=0): - self.blocks = { - genesis.hash: genesis, - } - self.sigs = {} - self.main_chain = [genesis.hash] - self.timequeue = [] - self.parentqueue = {} - self.children = {} - self.scores = {} - self.scores_at_height = {} - self.justified = {} - self.finalized = {} - self.ts = ts - self.id = _id - self.network = network - self.used_parents = {} - self.processed = {} - self.sleepy = sleepy - self.careless = careless - self.first_round = True - self.last_made_block = 0 - self.last_made_sig = 0 - - def broadcast(self, x): - if self.sleepy and self.ts: - return - self.network.broadcast(self, x) - self.on_receive(x) - - def log(self, words, lvl=3, all=False): - #if "Tick:" != words[:5] or self.id == 0: - if (self.id == 0 or all) and lvl >= 2: - print(self.id, words) - - def on_receive(self, obj, reprocess=False): - if obj.hash in self.processed and not reprocess: - return - self.processed[obj.hash] = obj - if isinstance(obj, Block): - return self.on_receive_beacon_block(obj) - elif isinstance(obj, Sig): - return self.on_receive_sig(obj) - - def add_to_timequeue(self, obj): - i = 0 - while i < len(self.timequeue) and self.timequeue[i].min_timestamp() < obj.min_timestamp(): - i += 1 - self.timequeue.insert(i, obj) - - def add_to_multiset(self, _set, k, v): - if k not in _set: - _set[k] = [] - _set[k].append(v) - - def change_head(self, chain, new_head): - chain.extend([None] * (new_head.height + 1 - len(chain))) - i, c = new_head.height, new_head.hash - while c != chain[i]: - chain[i] = c - c = self.blocks[c].parent_hash - i -= 1 - for i in range(len(chain)): - assert self.blocks[chain[i]].height == i - - def recalculate_head(self): - while 1: - descendant_queue = [self.main_chain[-1]] - new_head = None - max_count = 0 - while len(descendant_queue): - first = descendant_queue.pop(0) - if first in self.children: - for c in self.children[first]: - descendant_queue.append(c) - if self.scores.get(first, 0) > max_count and first != self.main_chain[-1]: - new_head = first - max_count = self.scores.get(first, 0) - if new_head: - self.change_head(self.main_chain, self.blocks[new_head]) - else: - return - - def process_children(self, h): - if h in self.parentqueue: - for b in self.parentqueue[h]: - self.on_receive(b, reprocess=True) - del self.parentqueue[h] - - def get_common_ancestor(self, a, b): - a, b = self.blocks[a], self.blocks[b] - while b.height > a.height: - b = self.blocks[b.parent_hash] - while a.height > b.height: - a = self.blocks[a.parent_hash] - while a.hash != b.hash: - a = self.blocks[a.parent_hash] - b = self.blocks[b.parent_hash] - return a - - def is_descendant(self, a, b): - a, b = self.blocks[a], self.blocks[b] - while b.height > a.height: - b = self.blocks[b.parent_hash] - return a.hash == b.hash - - def have_ancestry(self, h): - while h != genesis.hash: - if h not in self.processed: - return False - h = self.processed[h].parent_hash - return True - - def on_receive_beacon_block(self, block): - # Parent not yet received - if block.parent_hash not in self.blocks: - self.add_to_multiset(self.parentqueue, block.parent_hash, block) - return - # Too early - if block.min_timestamp() > self.ts: - self.add_to_timequeue(block) - return - # Add the block - self.log("Processing beacon block %s" % to_hex(block.hash[:4])) - self.blocks[block.hash] = block - # Is the block building on the head? Then add it to the head! - if block.parent_hash == self.main_chain[-1] or self.careless: - self.main_chain.append(block.hash) - # Add child record - self.add_to_multiset(self.children, block.parent_hash, block.hash) - # Final steps - self.process_children(block.hash) - self.network.broadcast(self, block) - - def on_receive_sig(self, sig): - if sig.targets[0] not in self.blocks: - self.add_to_multiset(self.parentqueue, sig.targets[0], sig) - return - # Get common ancestor - anc = self.get_common_ancestor(self.main_chain[-1], sig.targets[0]) - max_score = max([0] + [self.scores.get(self.main_chain[i], 0) for i in range(anc.height + 1, len(self.main_chain))]) - # Process scoring - max_newchain_score = 0 - for i, c in list(enumerate(sig.targets))[::-1]: - slot = sig.slot - 1 - i - slot_key = slot.to_bytes(4, 'big') - assert self.blocks[c].slot <= slot - - # If a parent and child block have non-consecutive slots, then the parent - # block is also considered to be the canonical block at all of the intermediate - # slot numbers. We store the scores for the block at each height separately - self.scores_at_height[slot_key + c] = self.scores_at_height.get(slot_key + c, 0) + 1 - - # For fork choice rule purposes, the score of a block is the highest score - # that it has at any height - self.scores[c] = max(self.scores.get(c, 0), self.scores_at_height[slot_key + c]) - - # If 2/3 of notaries vote for a block, it is justified - if self.scores_at_height[slot_key + c] == NOTARIES * 2 // 3: - self.justified[c] = True - c2 = c - self.log("Justified: %d %s" % (slot, hexlify(c).decode('utf-8')[:8])) - - # If EPOCH_LENGTH+1 blocks are justified in a row, the oldest is - # considered finalized - - finalize = True - for slot2 in range(slot - 1, max(slot - EPOCH_LENGTH * 2, 0) - 1, -1): - if slot2 < self.blocks[c2].slot: - c2 = self.blocks[c2].parent_hash - if self.scores_at_height.get(slot2.to_bytes(4, 'big') + c2, 0) < (NOTARIES * 2 // 3): - finalize = False - # self.log("Not quite finalized: stopped at %d needed %d" % (slot2, max(slot - EPOCH_LENGTH, 0))) - break - if slot2 < slot - EPOCH_LENGTH - 1 and finalize and c2 not in self.finalized: - self.log("Finalized: %d %s" % (self.blocks[c2].slot, hexlify(c).decode('utf-8')[:8])) - self.finalized[c2] = True - - # Find the maximum score of a block on the chain that this sig is weighing on - if self.blocks[c].slot > anc.slot: - max_newchain_score = max(max_newchain_score, self.scores[c]) - - # If it's higher, switch over the canonical chain - if max_newchain_score > max_score: - self.main_chain = self.main_chain[:anc.height+1] - self.recalculate_head() - - self.sigs[sig.hash] = sig - - # Rebroadcast - self.network.broadcast(self, sig) - - # Get the portion of the main chain that is within the last EPOCH_LENGTH - # slots, once again duplicating the parent in cases where the parent and - # child's slots are not consecutive - def get_sig_targets(self, start_slot): - o = [] - i = len(self.main_chain) - 1 - for slot in range(start_slot - 1, max(start_slot - EPOCH_LENGTH, 0) - 1, -1): - if slot < self.blocks[self.main_chain[i]].slot: - i -= 1 - o.append(self.main_chain[i]) - for i, x in enumerate(o): - assert self.blocks[x].slot <= start_slot - 1 - i - assert len(o) == min(EPOCH_LENGTH, start_slot) - return o - - def tick(self): - self.ts += 0.1 - self.log("Tick: %.1f" % self.ts, lvl=1) - # Make a block? - slot = int(self.ts // SLOT_SIZE) - if slot > self.last_made_block and (slot % NOTARIES) == self.id: - self.broadcast(Block(self.blocks[self.main_chain[-1]], slot, self.id)) - self.last_made_block = slot - # Make a sig? - if slot > self.last_made_sig and (slot % EPOCH_LENGTH) == self.id % EPOCH_LENGTH: - sig_from = len(self.main_chain) - 1 - while sig_from > 0 and self.blocks[self.main_chain[sig_from]].slot >= slot - EPOCH_LENGTH: - sig_from -= 1 - sig = Sig(self.id, self.get_sig_targets(slot), slot, self.ts) - # self.log('Sig:', self.id, sig.slot, ' '.join([hexlify(t).decode('utf-8')[:4] for t in sig.targets])) - self.broadcast(sig) - self.last_made_sig = slot - # Process time queue - while len(self.timequeue) and self.timequeue[0].min_timestamp() <= self.ts: - self.on_receive(self.timequeue.pop(0), reprocess=True) diff --git a/clock_disparity/ghost_test.py b/clock_disparity/ghost_test.py deleted file mode 100644 index d381d69..0000000 --- a/clock_disparity/ghost_test.py +++ /dev/null @@ -1,73 +0,0 @@ -from networksim import NetworkSimulator -from ghost_node import Node, NOTARIES, Block, Sig, genesis, SLOT_SIZE -from distributions import normal_distribution - -net = NetworkSimulator(latency=45) -notaries = [Node(i, net, ts=max(normal_distribution(5, 5)(), 0) * 0.1, sleepy=False) for i in range(NOTARIES)] -net.agents = notaries -net.generate_peers() -for i in range(12000): - net.tick() -for n in notaries: - print("Local timestamp: %.1f, timequeue len %d" % (n.ts, len(n.timequeue))) - print("Main chain head: %d" % n.blocks[n.main_chain[-1]].height) - print("Total main chain blocks received: %d" % (len([b for b in n.blocks.values() if isinstance(b, Block)]) - 1)) - -import matplotlib.pyplot as plt -import networkx as nx -import random - -G=nx.Graph() - -#positions = {genesis.hash: 0, beacon_genesis.hash: 0} -#queue = [ - -for b in n.blocks.values(): - if b.height > 0: - if isinstance(b, Block): - G.add_edge(b.hash, b.parent_hash, color='b') -for s in n.sigs.values(): - G.add_edge(s.hash, s.targets[0], color='0.75') - - -cache = {genesis.hash: 0} - -def mkoffset(b): - if b.hash not in cache: - cache[b.hash] = cache[b.parent_hash] + random.randrange(35) - return cache[b.hash] - -pos={b'\x00'*32: (0, 0)} -for b in sorted(n.blocks.values(), key=lambda b: b.height): - x,y = pos[b.parent_hash] - pos[b.hash] = (x + (random.randrange(5) if b.hash in n.main_chain else -random.randrange(5)), y+10) -for s in n.sigs.values(): - parent = n.blocks[s.targets[0]] - x,y = pos[parent.hash] - pos[s.hash] = (x - 2 + random.randrange(5), - y + 5) - -finalized = {k:v for k,v in pos.items() if k in n.finalized} -justified = {k:v for k,v in pos.items() if k in n.justified and k not in n.finalized} -unjustified = {k:v for k,v in pos.items() if k not in n.justified and k in n.blocks} -sigs = {k:v for k,v in pos.items() if k not in n.blocks} - -edges = G.edges() -colors = [G[u][v]['color'] for u,v in edges] - -nx.draw_networkx_nodes(G, pos, nodelist=sigs.keys(), node_size=5, node_shape='o',node_color='0.75') -nx.draw_networkx_nodes(G, pos, nodelist=unjustified.keys(), node_size=10, node_shape='o',node_color='0.75') -nx.draw_networkx_nodes(G, pos, nodelist=justified.keys(), node_size=16, node_shape='o',node_color='y') -nx.draw_networkx_nodes(G, pos, nodelist=finalized.keys(), node_size=25, node_shape='o',node_color='g') -# nx.draw_networkx_labels(G, pos, {h: n.scores.get(h, 0) for h in n.blocks.keys()}, font_size=5) - -blockedges = [(u,v) for (u,v) in edges if G[u][v]['color'] == 'b'] -otheredges = [(u,v) for (u,v) in edges if G[u][v]['color'] == '0.75'] -nx.draw_networkx_edges(G, pos, edgelist=otheredges, width=1, edge_color='0.75') -nx.draw_networkx_edges(G, pos, edgelist=blockedges, width=2, edge_color='b') - -print('Scores:', [n.scores.get(c, 0) for c in n.main_chain]) - -plt.axis('off') -# plt.savefig("degree.png", bbox_inches="tight") -plt.show() diff --git a/clock_disparity/lmd_node.py b/clock_disparity/lmd_node.py deleted file mode 100644 index 8921e06..0000000 --- a/clock_disparity/lmd_node.py +++ /dev/null @@ -1,367 +0,0 @@ -import os -from binascii import hexlify -from Crypto.Hash import keccak -import random - -def to_hex(s): - return hexlify(s).decode('utf-8') - -memo = {} - -def sha3(x): - if x not in memo: - memo[x] = keccak.new(digest_bits=256, data=x).digest() - return memo[x] - -def hash_to_int(h): - o = 0 - for c in h: - o = (o << 8) + c - return o - -def get_most_common_entry(lst): - counts = {} - for l in lst: - counts[l] = counts.get(l, 0) + 1 - maxcount, maxkey = max(zip(counts.values(), counts.keys())) - return maxkey, maxcount - -NOTARIES = 50 -SLOT_SIZE = 3 -EPOCH_LENGTH = 25 - -# Not a full RANDAO; stub for now -class Block(): - def __init__(self, parent, slot, proposer): - self.contents = os.urandom(32) - if parent: - self.ancestor_hashes = [None] * 16 - self.ancestor_slots = [0] * 16 - for i in range(16): - if (parent.slot // 2**i) > (parent.ancestor_slots[i] // 2**i): - self.ancestor_hashes[i] = parent.hash - self.ancestor_slots[i] = parent.slot - else: - self.ancestor_hashes[i] = parent.ancestor_hashes[i] - self.ancestor_slots[i] = parent.ancestor_slots[i] - else: - self.ancestor_hashes = [b'\x00' * 32 for i in range(16)] - self.ancestor_slots = [-1 for i in range(16)] - self.hash = sha3(self.parent_hash + self.contents) - self.height = parent.height + 1 if parent else 0 - assert slot % NOTARIES == proposer - self.proposer = proposer - self.slot = slot - - @property - def parent_hash(self): - return self.ancestor_hashes[0] - - def min_timestamp(self): - return SLOT_SIZE * self.slot - -class Sig(): - def __init__(self, proposer, targets, slot, ts): - self.proposer = proposer - self.targets = targets - self.slot = slot - self.ts = ts - self.hash = os.urandom(32) - -genesis = Block(None, 0, 0) - -class Node(): - - def __init__(self, _id, network, sleepy=False, careless=False, ts=0): - self.blocks = { - genesis.hash: genesis, - } - self.sigs = {} - self.main_chain = [genesis.hash] - self.lmd_head = genesis.hash - self.timequeue = [] - self.parentqueue = {} - self.children = {} - self.scores = {} - self.scores_at_height = {} - self.justified = {} - self.finalized = {} - self.ts = ts - self.id = _id - self.network = network - self.used_parents = {} - self.processed = {} - self.sleepy = sleepy - self.careless = careless - self.first_round = True - self.last_made_block = 0 - self.last_made_sig = 0 - self.most_recent_votes = {} - self.observed_ts_deltas = [0] * NOTARIES - - def broadcast(self, x): - if self.sleepy and self.ts: - return - self.network.broadcast(self, x) - self.on_receive(x) - - def log(self, words, lvl=3, all=False): - #if "Tick:" != words[:5] or self.id == 0: - if (self.id == 0 or all) and lvl >= 2: - print(self.id, words) - - def on_receive(self, obj, reprocess=False): - if obj.hash in self.processed and not reprocess: - return - self.processed[obj.hash] = obj - if isinstance(obj, Block): - return self.on_receive_beacon_block(obj) - elif isinstance(obj, Sig): - return self.on_receive_sig(obj) - - def add_to_timequeue(self, obj): - i = 0 - while i < len(self.timequeue) and self.timequeue[i].min_timestamp() < obj.min_timestamp(): - i += 1 - self.timequeue.insert(i, obj) - - def add_to_multiset(self, _set, k, v): - if k not in _set: - _set[k] = [] - _set[k].append(v) - - def get_ancestor_at_slot(self, block, slot): - if not isinstance(block, Block): - block = self.blocks[block] - if block.slot <= slot: - return block - d = 15 - while (block.slot - slot) < 2**d: - d -= 1 - anc = self.blocks[block.ancestor_hashes[d]] - return self.get_ancestor_at_slot(anc, slot) - - def change_head(self, chain, new_head): - chain.extend([None] * (new_head.height + 1 - len(chain))) - i, c = new_head.height, new_head.hash - while c != chain[i]: - chain[i] = c - c = self.blocks[c].parent_hash - i -= 1 - for i in range(len(chain)): - assert self.blocks[chain[i]].height == i - - def recalculate_head(self): - while 1: - descendant_queue = [self.main_chain[-1]] - new_head = None - max_count = 0 - while len(descendant_queue): - first = descendant_queue.pop(0) - if first in self.children: - for c in self.children[first]: - descendant_queue.append(c) - if self.scores.get(first, 0) > max_count and first != self.main_chain[-1]: - new_head = first - max_count = self.scores.get(first, 0) - if new_head: - self.change_head(self.main_chain, self.blocks[new_head]) - else: - return - - def process_children(self, h): - if h in self.parentqueue: - for b in self.parentqueue[h]: - self.on_receive(b, reprocess=True) - del self.parentqueue[h] - - def get_common_ancestor(self, a, b): - if not isinstance(a, Block): - a = self.blocks[a] - if not isinstance(b, Block): - b = self.blocks[b] - while b.height > a.height: - b = self.blocks[b.parent_hash] - while a.height > b.height: - a = self.blocks[a.parent_hash] - while a.hash != b.hash: - a = self.blocks[a.parent_hash] - b = self.blocks[b.parent_hash] - return a - - def is_descendant(self, a, b): - a, b = self.blocks[a], self.blocks[b] - while b.height > a.height: - b = self.blocks[b.parent_hash] - return a.hash == b.hash - - def have_ancestry(self, h): - while h != genesis.hash: - if h not in self.processed: - return False - h = self.processed[h].parent_hash - return True - - def on_receive_beacon_block(self, block): - # Parent not yet received - if block.parent_hash not in self.blocks: - self.add_to_multiset(self.parentqueue, block.parent_hash, block) - return - # Too early - if block.min_timestamp() > self.ts: - self.add_to_timequeue(block) - return - # Add the block - self.log("Processing beacon block %s" % to_hex(block.hash[:4])) - self.blocks[block.hash] = block - # Is the block building on the head? Then add it to the head! - if block.parent_hash == self.main_chain[-1] or self.careless: - self.main_chain.append(block.hash) - # Add child record - self.add_to_multiset(self.children, block.parent_hash, block.hash) - # head = self.compute_lmd_head() - # if head.hash == block.hash: - self.observed_ts_deltas[block.proposer] = block.min_timestamp() - self.ts - # Final steps - self.process_children(block.hash) - self.network.broadcast(self, block) - - def compute_lmd_head(self): - voters = list(range(NOTARIES)) - binary_search_anchor = 0 - skip = 1 - last_nonnull_maxkey = genesis.hash - print("Computing LMD head") - print('top_slots of votes', [self.blocks[v[0]].slot for v in self.most_recent_votes.values()]) - while 1: - slot_at = binary_search_anchor + skip - votes_at_slot = [] - voters_for_hash = {} - for voter in voters: - if voter in self.most_recent_votes and self.most_recent_votes[voter][1] >= slot_at: - votes_at_slot.append(self.get_ancestor_at_slot(self.most_recent_votes[voter][0], slot_at).hash) - maxkey, maxcount = get_most_common_entry(votes_at_slot) if votes_at_slot else (None, 0) - if maxkey: - last_nonnull_maxkey = maxkey - assert votes_at_slot.count(maxkey) == maxcount - print(slot_at, maxkey, maxcount) - if maxcount > len(voters) // 2: - binary_search_anchor += skip - skip *= 2 - else: - if skip == 1: - remaining_voters = [ - v for v in voters if \ - v in self.most_recent_votes and \ - self.most_recent_votes[v][1] >= slot_at and \ - self.get_ancestor_at_slot(self.most_recent_votes[v][0], slot_at).hash == maxkey - ] - assert maxcount == len(remaining_voters) - voters = remaining_voters - binary_search_anchor += skip - print("%d remaining_voters" % len(remaining_voters)) - print('top_slots', [self.blocks[self.most_recent_votes[v][0]].slot for v in voters]) - else: - skip //= 2 - if len(voters) == 0: - o = self.blocks[last_nonnull_maxkey] - while o.hash in self.children: - o = self.blocks[self.children[o.hash][0]] - return o - - def on_receive_sig(self, sig): - if sig.targets[0] not in self.blocks: - self.add_to_multiset(self.parentqueue, sig.targets[0], sig) - return - # Get common ancestor - anc = self.get_common_ancestor(self.main_chain[-1], sig.targets[0]) - max_score = max([0] + [self.scores.get(self.main_chain[i], 0) for i in range(anc.height + 1, len(self.main_chain))]) - # Process scoring - max_newchain_score = 0 - for i, c in list(enumerate(sig.targets))[::-1]: - slot = sig.slot - 1 - i - slot_key = slot.to_bytes(4, 'big') - assert self.blocks[c].slot <= slot - - # If a parent and child block have non-consecutive slots, then the parent - # block is also considered to be the canonical block at all of the intermediate - # slot numbers. We store the scores for the block at each height separately - self.scores_at_height[slot_key + c] = self.scores_at_height.get(slot_key + c, 0) + 1 - - # For fork choice rule purposes, the score of a block is the highest score - # that it has at any height - self.scores[c] = max(self.scores.get(c, 0), self.scores_at_height[slot_key + c]) - - # If 2/3 of notaries vote for a block, it is justified - if self.scores_at_height[slot_key + c] == NOTARIES * 2 // 3: - self.justified[c] = True - c2 = c - self.log("Justified: %d %s" % (slot, hexlify(c).decode('utf-8')[:8])) - - # If EPOCH_LENGTH+1 blocks are justified in a row, the oldest is - # considered finalized - - finalize = True - for slot2 in range(slot - 1, max(slot - EPOCH_LENGTH * 2, 0) - 1, -1): - if slot2 < self.blocks[c2].slot: - c2 = self.blocks[c2].parent_hash - if self.scores_at_height.get(slot2.to_bytes(4, 'big') + c2, 0) < (NOTARIES * 2 // 3): - finalize = False - # self.log("Not quite finalized: stopped at %d needed %d" % (slot2, max(slot - EPOCH_LENGTH, 0))) - break - if slot2 < slot - EPOCH_LENGTH - 1 and finalize and c2 not in self.finalized: - self.log("Finalized: %d %s" % (self.blocks[c2].slot, hexlify(c).decode('utf-8')[:8])) - self.finalized[c2] = True - - # Find the maximum score of a block on the chain that this sig is weighing on - if self.blocks[c].slot > anc.slot: - max_newchain_score = max(max_newchain_score, self.scores[c]) - - # If it's higher, switch over the canonical chain - if max_newchain_score > max_score: - self.main_chain = self.main_chain[:anc.height+1] - self.recalculate_head() - - # Adjust most recent votes array - existing_vote_slot = self.most_recent_votes.get(sig.proposer, (None, -1))[1] - if sig.slot > existing_vote_slot: - self.most_recent_votes[sig.proposer] = (sig.targets[0], sig.slot) - - self.sigs[sig.hash] = sig - - # Rebroadcast - self.network.broadcast(self, sig) - - # Get an EPOCH_LENGTH-chain starting from a given block and slot - # slots, once again duplicating the parent in cases where the parent and - # child's slots are not consecutive - def get_sig_targets(self, head, slot): - return [self.get_ancestor_at_slot(head, s).hash for s in range(slot - 1, max(slot - EPOCH_LENGTH, 0) - 1, -1)] - - def get_adjusted_timestamp(self): - pull_threshold = 0.50 - add_zeroes = int(NOTARIES * (pull_threshold * 2 -1)) - index = int(NOTARIES * pull_threshold) - return self.ts + sorted(self.observed_ts_deltas + [0] * add_zeroes)[index] - - def tick(self): - self.ts += 0.1 - self.log("Tick: %.1f" % self.ts, lvl=1) - # Make a block? - ts = self.get_adjusted_timestamp() - slot = int(ts // SLOT_SIZE) - if slot > self.last_made_block and (slot % NOTARIES) == self.id: - head = self.compute_lmd_head() - b = Block(head, slot, self.id) - self.broadcast(b) - self.last_made_block = slot - # Make a sig? - if slot > self.last_made_sig and (slot % EPOCH_LENGTH) == self.id % EPOCH_LENGTH: - head = self.compute_lmd_head() - sig = Sig(self.id, self.get_sig_targets(head, slot), slot, ts) - # self.log('Sig:', self.id, sig.slot, ' '.join([hexlify(t).decode('utf-8')[:4] for t in sig.targets])) - self.broadcast(sig) - self.last_made_sig = slot - # Process time queue - while len(self.timequeue) and self.timequeue[0].min_timestamp() <= ts: - self.on_receive(self.timequeue.pop(0), reprocess=True) diff --git a/clock_disparity/lmd_test.py b/clock_disparity/lmd_test.py deleted file mode 100644 index a39a748..0000000 --- a/clock_disparity/lmd_test.py +++ /dev/null @@ -1,74 +0,0 @@ -from networksim import NetworkSimulator -from lmd_node import Node, NOTARIES, Block, Sig, genesis, SLOT_SIZE -from distributions import normal_distribution - -net = NetworkSimulator(latency=20) -notaries = [Node(i, net, ts=max(normal_distribution(1000, 1000)(), 0) * 0.1, sleepy=False) for i in range(NOTARIES)] -net.agents = notaries -net.generate_peers() -for i in range(12000): - net.tick() -for n in notaries: - print("Local timestamp: %.1f, timequeue len %d" % (n.ts, len(n.timequeue))) - print("Main chain head: %d" % n.compute_lmd_head().height) - print("Total main chain blocks received: %d" % (len([b for b in n.blocks.values() if isinstance(b, Block)]) - 1)) - -import matplotlib.pyplot as plt -import networkx as nx -import random - -G=nx.Graph() - -#positions = {genesis.hash: 0, beacon_genesis.hash: 0} -#queue = [ - -for b in n.blocks.values(): - if b.height > 0: - if isinstance(b, Block): - G.add_edge(b.hash, b.parent_hash, color='b') -for s in n.sigs.values(): - G.add_edge(s.hash, s.targets[0], color='0.75') - - -cache = {genesis.hash: 0} - -def mkoffset(b): - if b.hash not in cache: - cache[b.hash] = cache[b.parent_hash] + random.randrange(35) - return cache[b.hash] - -pos={b'\x00'*32: (0, 0)} -for b in sorted(n.blocks.values(), key=lambda b: b.height): - x,y = pos[b.parent_hash] - pos[b.hash] = (x + (random.randrange(5) if b.hash in n.main_chain else -random.randrange(5)), y+10) -for s in n.sigs.values(): - parent = n.blocks[s.targets[0]] - x,y = pos[parent.hash] - pos[s.hash] = (x - 2 + random.randrange(5), - y + 5) - -finalized = {k:v for k,v in pos.items() if k in n.finalized} -justified = {k:v for k,v in pos.items() if k in n.justified and k not in n.finalized} -unjustified = {k:v for k,v in pos.items() if k not in n.justified and k in n.blocks} -sigs = {k:v for k,v in pos.items() if k not in n.blocks} - -edges = G.edges() -colors = [G[u][v]['color'] for u,v in edges] - -nx.draw_networkx_nodes(G, pos, nodelist=sigs.keys(), node_size=5, node_shape='o',node_color='0.75') -nx.draw_networkx_nodes(G, pos, nodelist=unjustified.keys(), node_size=10, node_shape='o',node_color='0.75') -nx.draw_networkx_nodes(G, pos, nodelist=justified.keys(), node_size=16, node_shape='o',node_color='y') -nx.draw_networkx_nodes(G, pos, nodelist=finalized.keys(), node_size=25, node_shape='o',node_color='g') -# nx.draw_networkx_labels(G, pos, {h: n.scores.get(h, 0) for h in n.blocks.keys()}, font_size=5) - -blockedges = [(u,v) for (u,v) in edges if G[u][v]['color'] == 'b'] -otheredges = [(u,v) for (u,v) in edges if G[u][v]['color'] == '0.75'] -nx.draw_networkx_edges(G, pos, edgelist=otheredges, width=1, edge_color='0.75') -nx.draw_networkx_edges(G, pos, edgelist=blockedges, width=2, edge_color='b') - -print('Scores:', [n.scores.get(c, 0) for c in n.main_chain]) -print('Timestamps:', [n.get_adjusted_timestamp() for n in notaries]) - -plt.axis('off') -# plt.savefig("degree.png", bbox_inches="tight") -plt.show() diff --git a/clock_disparity/networksim.py b/clock_disparity/networksim.py deleted file mode 100644 index 2415262..0000000 --- a/clock_disparity/networksim.py +++ /dev/null @@ -1,75 +0,0 @@ -from distributions import transform, normal_distribution -import random - - -class NetworkSimulator(): - - def __init__(self, latency=50): - self.agents = [] - self.latency_distribution_sample = transform(normal_distribution(latency, (latency * 2) // 5), lambda x: max(x, 0)) - self.time = 0 - self.objqueue = {} - self.peers = {} - self.reliability = 0.9 - - def generate_peers(self, num_peers=5): - self.peers = {} - for a in self.agents: - p = [] - while len(p) <= num_peers // 2: - p.append(random.choice(self.agents)) - if p[-1] == a: - p.pop() - self.peers[a.id] = self.peers.get(a.id, []) + p - for peer in p: - self.peers[peer.id] = self.peers.get(peer.id, []) + [a] - - def tick(self): - if self.time in self.objqueue: - for recipient, obj in self.objqueue[self.time]: - if random.random() < self.reliability: - recipient.on_receive(obj) - del self.objqueue[self.time] - for a in self.agents: - a.tick() - self.time += 1 - - def run(self, steps): - for i in range(steps): - self.tick() - - def broadcast(self, sender, obj): - for p in self.peers[sender.id]: - recv_time = self.time + self.latency_distribution_sample() - if recv_time not in self.objqueue: - self.objqueue[recv_time] = [] - self.objqueue[recv_time].append((p, obj)) - - def direct_send(self, to_id, obj): - for a in self.agents: - if a.id == to_id: - recv_time = self.time + self.latency_distribution_sample() - if recv_time not in self.objqueue: - self.objqueue[recv_time] = [] - self.objqueue[recv_time].append((a, obj)) - - def knock_offline_random(self, n): - ko = {} - while len(ko) < n: - c = random.choice(self.agents) - ko[c.id] = c - for c in ko.values(): - self.peers[c.id] = [] - for a in self.agents: - self.peers[a.id] = [x for x in self.peers[a.id] if x.id not in ko] - - def partition(self): - a = {} - while len(a) < len(self.agents) / 2: - c = random.choice(self.agents) - a[c.id] = c - for c in self.agents: - if c.id in a: - self.peers[c.id] = [x for x in self.peers[c.id] if x.id in a] - else: - self.peers[c.id] = [x for x in self.peers[c.id] if x.id not in a] diff --git a/clock_disparity/pos_node.py b/clock_disparity/pos_node.py deleted file mode 100644 index 7b59f88..0000000 --- a/clock_disparity/pos_node.py +++ /dev/null @@ -1,251 +0,0 @@ -import os -from binascii import hexlify -from Crypto.Hash import keccak -import random - -def to_hex(s): - return hexlify(s).decode('utf-8') - -memo = {} - -def sha3(x): - if x not in memo: - memo[x] = keccak.new(digest_bits=256, data=x).digest() - return memo[x] - -def hash_to_int(h): - o = 0 - for c in h: - o = (o << 8) + c - return o - -NOTARIES = 20 -BASE_TS_DIFF = 1 -SKIP_TS_DIFF = 6 -SAMPLE = 8 -MIN_SAMPLE = lambda x: [6, 4, 3, 2, 2][x] if x < 5 else 1 -POWDIFF = 50 * NOTARIES -SHARDS = 12 - -# Not a full RANDAO; stub for now -class Block(): - def __init__(self, parent, proposer, ts, sigs): - self.contents = os.urandom(32) - self.parent_hash = parent.hash if parent else (b'\x11' * 32) - self.hash = sha3(self.parent_hash + self.contents) - self.ts = ts - self.sigs = sigs - self.number = parent.number + 1 if parent else 0 - - if parent: - i = parent.child_proposers.index(proposer) - assert self.ts >= parent.ts + BASE_TS_DIFF + i * SKIP_TS_DIFF - assert len(sigs) >= parent.notary_req - for sig in sigs: - assert sig.target_hash == self.parent_hash - - # Calculate child proposers - v = hash_to_int(sha3(self.contents)) - self.child_proposers = [] - while v > 0: - self.child_proposers.append(v % NOTARIES) - v //= NOTARIES - - # Calculate notaries - if not parent: - index = 0 - elif proposer in parent.child_proposers: - index = parent.child_proposers.index(proposer) - else: - index = len(parent.child_proposers) - self.notary_req = MIN_SAMPLE(index) - v = hash_to_int(sha3(self.contents + b':n')) - self.notaries = [] - for i in range(SAMPLE): - self.notaries.append(v % NOTARIES) - v //= NOTARIES - - # Calculate shard proposers - v = hash_to_int(sha3(self.contents + b':s')) - self.shard_proposers = [] - for i in range(SHARDS): - self.shard_proposers.append(v % NOTARIES) - v //= NOTARIES - - -class Sig(): - def __init__(self, proposer, target): - self.proposer = proposer - self.target_hash = target.hash - self.hash = os.urandom(32) - assert self.proposer in target.notaries - -genesis = Block(None, 1, 0, []) - -class BlockMakingRequest(): - def __init__(self, parent, ts): - self.parent = parent - self.ts = ts - self.hash = os.urandom(32) - -class Node(): - - def __init__(self, _id, network, sleepy=False, careless=False, ts=0): - self.blocks = { - genesis.hash: genesis, - } - self.sigs = {} - self.main_chain = [genesis.hash] - self.timequeue = [] - self.parentqueue = {} - self.children = {} - self.ts = ts - self.id = _id - self.network = network - self.used_parents = {} - self.processed = {} - self.sleepy = sleepy - self.careless = careless - self.first_round = True - - def broadcast(self, x): - if self.sleepy and self.ts: - return - self.network.broadcast(self, x) - self.on_receive(x) - - def log(self, words, lvl=3, all=False): - #if "Tick:" != words[:5] or self.id == 0: - if (self.id == 0 or all) and lvl >= 2: - print(self.id, words) - - def on_receive(self, obj, reprocess=False): - if obj.hash in self.processed and not reprocess: - return - self.processed[obj.hash] = obj - if isinstance(obj, Block): - return self.on_receive_beacon_block(obj) - elif isinstance(obj, Sig): - return self.on_receive_sig(obj) - elif isinstance(obj, BlockMakingRequest): - if self.main_chain[-1] == obj.parent: - mc_ref = self.blocks[obj.parent] - for i in range(2): - if mc_ref.number == 0: - break - #mc_ref = self.blocks[mc_ref].parent_hash - x = Block(self.blocks[obj.parent], self.id, self.ts, - self.sigs[obj.parent] if obj.parent in self.sigs else []) - self.log("Broadcasting block %s" % to_hex(x.hash[:4])) - self.broadcast(x) - - def add_to_timequeue(self, obj): - i = 0 - while i < len(self.timequeue) and self.timequeue[i].ts < obj.ts: - i += 1 - self.timequeue.insert(i, obj) - - def add_to_multiset(self, _set, k, v): - if k not in _set: - _set[k] = [] - _set[k].append(v) - - def change_head(self, chain, new_head): - chain.extend([None] * (new_head.number + 1 - len(chain))) - i, c = new_head.number, new_head.hash - while c != chain[i]: - chain[i] = c - c = self.blocks[c].parent_hash - i -= 1 - for i in range(len(chain)): - assert self.blocks[chain[i]].number == i - - def recalculate_head(self, chain, condition): - while not condition(self.blocks[chain[-1]]): - chain.pop() - descendant_queue = [chain[-1]] - new_head = chain[-1] - while len(descendant_queue): - first = descendant_queue.pop(0) - if first in self.children: - for c in self.children[first]: - if condition(self.blocks[c]): - descendant_queue.append(c) - if self.blocks[first].number > self.blocks[new_head].number: - new_head = first - self.change_head(chain, self.blocks[new_head]) - for i in range(len(chain)): - assert condition(self.blocks[chain[i]]) - - def process_children(self, h): - if h in self.parentqueue: - for b in self.parentqueue[h]: - self.on_receive(b, reprocess=True) - del self.parentqueue[h] - - def is_descendant(self, a, b): - a, b = self.blocks[a], self.blocks[b] - while b.number > a.number: - b = self.blocks[b.parent_hash] - return a.hash == b.hash - - def have_ancestry(self, h): - while h != genesis.hash: - if h not in self.processed: - return False - h = self.processed[h].parent_hash - return True - - def is_notarized(self, b): - return len(self.sigs.get(b.hash, [])) >= b.notary_req - - def on_receive_beacon_block(self, block): - # Parent not yet received - if block.parent_hash not in self.blocks: - self.add_to_multiset(self.parentqueue, block.parent_hash, block) - return - # Too early - if block.ts > self.ts: - self.add_to_timequeue(block) - return - # Add the block - self.log("Processing beacon block %s" % to_hex(block.hash[:4])) - self.blocks[block.hash] = block - # Am I a notary, and is the block building on the head? Then broadcast a signature. - if block.parent_hash == self.main_chain[-1] or self.careless: - if self.id in block.notaries: - self.broadcast(Sig(self.id, block)) - # Add child record - self.add_to_multiset(self.children, block.parent_hash, block.hash) - # Final steps - self.process_children(block.hash) - self.network.broadcast(self, block) - - def on_receive_sig(self, sig): - if sig.target_hash not in self.blocks: - self.add_to_multiset(self.parentqueue, sig.target_hash, sig) - return - # Add to head? Make a block? - self.add_to_multiset(self.sigs, sig.target_hash, sig) - if len(self.sigs[sig.target_hash]) == self.blocks[sig.target_hash].notary_req: - block = self.blocks[sig.target_hash] - if block.number > self.blocks[self.main_chain[-1]].number: - self.change_head(self.main_chain, block) - if self.id in block.child_proposers: - my_index = block.child_proposers.index(self.id) - target_ts = block.ts + BASE_TS_DIFF + my_index * SKIP_TS_DIFF - self.log("Making block request for %.1f" % target_ts) - self.add_to_timequeue(BlockMakingRequest(block.hash, target_ts)) - # Rebroadcast - self.network.broadcast(self, sig) - - def tick(self): - if self.first_round: - if self.id in genesis.notaries: - self.broadcast(Sig(self.id, genesis)) - self.first_round = False - self.ts += 0.1 - self.log("Tick: %.1f" % self.ts, lvl=1) - # Process time queue - while len(self.timequeue) and self.timequeue[0].ts <= self.ts: - self.on_receive(self.timequeue.pop(0), reprocess=True) diff --git a/clock_disparity/pow_node.py b/clock_disparity/pow_node.py deleted file mode 100644 index 57d5573..0000000 --- a/clock_disparity/pow_node.py +++ /dev/null @@ -1,161 +0,0 @@ -import os -from binascii import hexlify -from Crypto.Hash import keccak -import random - -def to_hex(s): - return hexlify(s).decode('utf-8') - -memo = {} - -def sha3(x): - if x not in memo: - memo[x] = keccak.new(digest_bits=256, data=x).digest() - return memo[x] - -def hash_to_int(h): - o = 0 - for c in h: - o = (o << 8) + c - return o - -NOTARIES = 40 -BASE_TS_DIFF = 1 -SKIP_TS_DIFF = 6 -SAMPLE = 8 -MIN_SAMPLE = 7 -POWDIFF = 50 * NOTARIES -SHARDS = 12 - -def checkpow(work, nonce): - # Discrete log PoW, lolz - # Quadratic nonresidues only - return pow(work, nonce, 65537) * POWDIFF < 65537 * 2 and pow(nonce, 32768, 65537) == 65536 - -class Block(): - def __init__(self, parent, pownonce, ts): - self.parent_hash = parent.hash if parent else (b'\x00' * 32) - assert isinstance(self.parent_hash, bytes) - self.hash = sha3(self.parent_hash + str(pownonce).encode('utf-8')) - self.ts = ts - if parent: - assert checkpow(parent.pownonce, pownonce) - assert self.ts >= parent.ts - self.pownonce = pownonce - self.number = 0 if parent is None else parent.number + 1 - - -genesis = Block(None, 59049, 0) - -class Node(): - - def __init__(self, _id, network, sleepy=False, careless=False, ts=0): - self.blocks = { - genesis.hash: genesis - } - self.main_chain = [genesis.hash] - self.timequeue = [] - self.parentqueue = {} - self.children = {} - self.ts = ts - self.id = _id - self.network = network - self.used_parents = {} - self.processed = {} - self.sleepy = sleepy - self.careless = careless - - def broadcast(self, x): - if self.sleepy and self.ts: - return - self.network.broadcast(self, x) - self.on_receive(x) - - def log(self, words, lvl=3, all=False): - #if "Tick:" != words[:5] or self.id == 0: - if (self.id == 0 or all) and lvl >= 2: - print(self.id, words) - - def on_receive(self, obj, reprocess=False): - if obj.hash in self.processed and not reprocess: - return - self.processed[obj.hash] = obj - if isinstance(obj, Block): - return self.on_receive_main_block(obj) - - def add_to_timequeue(self, obj): - i = 0 - while i < len(self.timequeue) and self.timequeue[i].ts < obj.ts: - i += 1 - self.timequeue.insert(i, obj) - - def add_to_multiset(self, _set, k, v): - if k not in _set: - _set[k] = [] - _set[k].append(v) - - def change_head(self, chain, new_head): - chain.extend([None] * (new_head.number + 1 - len(chain))) - i, c = new_head.number, new_head.hash - while c != chain[i]: - chain[i] = c - c = self.blocks[c].parent_hash - i -= 1 - for i in range(len(chain)): - assert self.blocks[chain[i]].number == i - assert self.blocks[chain[i]].ts <= self.ts - - def process_children(self, h): - if h in self.parentqueue: - for b in self.parentqueue[h]: - self.on_receive(b, reprocess=True) - del self.parentqueue[h] - - def have_ancestry(self, h): - while h != genesis.hash: - if h not in self.processed: - return False - h = self.processed[h].parent_hash - return True - - def is_notarized(self, b): - return b.hash in self.children - - def on_receive_main_block(self, block): - # Parent not yet received - if block.parent_hash not in self.blocks: - self.add_to_multiset(self.parentqueue, block.parent_hash, block) - return None - if block.ts > self.ts: - self.add_to_timequeue(block) - return None - self.log("Processing main chain block %s" % to_hex(block.hash[:4])) - self.blocks[block.hash] = block - # Reorg the main chain if new head - if block.number > self.blocks[self.main_chain[-1]].number: - reorging = (block.parent_hash != self.main_chain[-1]) - self.change_head(self.main_chain, block) - # Add child record - self.add_to_multiset(self.children, block.parent_hash, block.hash) - # Final steps - self.process_children(block.hash) - self.network.broadcast(self, block) - - def is_descendant(self, a, b): - a, b = self.blocks[a], self.blocks[b] - while b.number > a.number: - b = self.blocks[b.parent_hash] - return a.hash == b.hash - - def tick(self): - self.ts += 0.1 - self.log("Tick: %.1f" % self.ts, lvl=1) - # Process time queue - while len(self.timequeue) and self.timequeue[0].ts <= self.ts: - self.on_receive(self.timequeue.pop(0), reprocess=True) - # Attempt to mine a main chain block - pownonce = random.randrange(65537) - mchead = self.blocks[self.main_chain[-1]] - if checkpow(mchead.pownonce, pownonce): - assert self.ts >= mchead.ts - self.broadcast(Block(mchead, pownonce, self.ts)) diff --git a/clock_disparity/test.py b/clock_disparity/test.py deleted file mode 100644 index 0e9d1e6..0000000 --- a/clock_disparity/test.py +++ /dev/null @@ -1,55 +0,0 @@ -from networksim import NetworkSimulator -from ghost_node import Node, NOTARIES, Block, genesis -from distributions import normal_distribution - -net = NetworkSimulator(latency=22) -notaries = [Node(i, net, ts=max(normal_distribution(300, 300)(), 0) * 0.1, sleepy=i%4==0) for i in range(NOTARIES)] -net.agents = notaries -net.generate_peers() -for i in range(100000): - net.tick() -for n in notaries: - print("Local timestamp: %.1f, timequeue len %d" % (n.ts, len(n.timequeue))) - print("Main chain head: %d" % n.blocks[n.main_chain[-1]].number) - print("Total main chain blocks received: %d" % (len([b for b in n.blocks.values() if isinstance(b, Block)]) - 1)) - print("Notarized main chain blocks received: %d" % (len([b for b in n.blocks.values() if isinstance(b, Block) and n.is_notarized(b)]) - 1)) - -import matplotlib.pyplot as plt -import networkx as nx -import random - -G=nx.Graph() - -#positions = {genesis.hash: 0, beacon_genesis.hash: 0} -#queue = [ - -for b in n.blocks.values(): - for en in notaries: - if isinstance(b, Block) and b.hash in en.processed and b.hash not in en.blocks: - assert (not en.have_ancestry(b.hash)) or b.ts > en.ts - if b.number > 0: - if isinstance(b, Block): - if n.is_notarized(b): - G.add_edge(b.hash, b.parent_hash, color='b') - else: - G.add_edge(b.hash, b.parent_hash, color='#dddddd') - - -cache = {genesis.hash: 0} - -def mkoffset(b): - if b.hash not in cache: - cache[b.hash] = cache[b.parent_hash] + random.randrange(35) - return cache[b.hash] - -pos={b.hash: (b.ts + mkoffset(b), b.ts) for b in n.blocks.values()} -edges = G.edges() -colors = [G[u][v]['color'] for u,v in edges] -nx.draw_networkx_nodes(G,pos,node_size=10,node_shape='o',node_color='0.75') - -nx.draw_networkx_edges(G,pos, - width=2,edge_color=colors) - -plt.axis('off') -# plt.savefig("degree.png", bbox_inches="tight") -plt.show() diff --git a/py_plonk/compiler.py b/compiler.py similarity index 100% rename from py_plonk/compiler.py rename to compiler.py diff --git a/cycle_finding_function_collision_generator.py b/cycle_finding_function_collision_generator.py deleted file mode 100644 index 4c5790f..0000000 --- a/cycle_finding_function_collision_generator.py +++ /dev/null @@ -1,49 +0,0 @@ -from ethereum.utils import sha3 -import sys - -STEPLENGTH = 100 - -dp = {} - -def step(inp): - return sha3('function_'+inp.encode('hex')+'()')[:4] - -def run_round(inp): - orig_inp = inp - for i in range(STEPLENGTH): - inp = step(inp) - if inp in dp.keys(): - print 'Found!', i + 1, repr(inp) - return(True, i + 1, inp) - dp[inp] = orig_inp - return(False, None, inp) - -y = '\xff' * 4 -orig_y = y -rounds = 0 -while 1: - print 'Running round', rounds - rounds += 1 - x, t, y2 = run_round(y) - if x: - prev1, prev2 = y, dp[y2] - assert prev1 != prev2 - # print '-----' - for i in range(STEPLENGTH - t): - # print repr(prev2) - prev2 = step(prev2) - # print '-----' - for i in range(t): - # print repr(prev1), repr(prev2) - next1 = step(prev1) - next2 = step(prev2) - if next1 == next2: - print 'Found!' - print 'function_'+prev1.encode('hex')+'()' - print 'function_'+prev2.encode('hex')+'()' - sys.exit() - prev1, prev2 = next1, next2 - # print repr(prev1), repr(prev2) - raise Exception("Something weird happened") - else: - y = y2 diff --git a/dao_tests/bytecode.txt b/dao_tests/bytecode.txt deleted file mode 100644 index bb0c79c..0000000 --- a/dao_tests/bytecode.txt +++ /dev/null @@ -1 +0,0 @@ -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 diff --git a/dao_tests/dao_dump.json b/dao_tests/dao_dump.json deleted file mode 100644 index 7eb921e..0000000 --- a/dao_tests/dao_dump.json +++ /dev/null @@ -1 +0,0 @@ -{"nonce": "3", "balance": "1", "storage": {"0xcfaec65381607776273b63cb03ef27a7e70b0eff4db247cea8074cfaeda64b12": "0x204fce5e1482de4619d40000", "0xa592fcd16f610309197e0ec7976511dea6c887093eb21bb74744190965584f31": "0x01", "0x8700da3c91829b30e19bf294f4615663dfe7de49a9247bade46a93252da4d075": "0xf7d9afd0a6bee7ff", "0x38ae389f936fe5e5d42f08a7ebec0999818e2012bcf513ab8ebaf3089d0db214": "0x06f05b59d3b20000", "0x11b8d3f0d7e1538c588f35283f0340a77fa0e9660b7c5ed55089b45799c2b2b5": "0x204fce5bbfc42e18fc080000", "0x3ad29e94b0856bad4a92f3d30780fbfc4bbd52bb73b0e4bb3adfd9d230e66657": "0x01", "0x2ba3cd510e182a7624fc66bed948edcf54835d4cc9e3d01e0ce22d0c4083c16a": "0x0fd3fedcc0403ac400", "0x9f7918895f82ad57ad4c13dec88f6abd3080120ce85c46d014c282dd8abaf657": "0xffffffffffffffffffffffffffffffffffffffffffffffff4c8a4dff90c6f7ff", 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diff --git a/dao_tests/fork_tester.py b/dao_tests/fork_tester.py deleted file mode 100644 index 1371a50..0000000 --- a/dao_tests/fork_tester.py +++ /dev/null @@ -1,196 +0,0 @@ -from ethereum.state import State -import json -from ethereum import abi -from ethereum.utils import normalize_address -from ethereum.state_transition import apply_transaction, apply_const_message -from ethereum.vm import Message, CallData -from ethereum.config import Env -from ethereum.parse_genesis_declaration import mk_basic_state -from ethereum.transactions import Transaction - -account_dict = json.load(open('dao_dump.json')) -withdrawer_code = '0x' + open('bytecode.txt').read().strip() -true, false = True, False -withdrawer_ct = abi.ContractTranslator([{"constant":false,"inputs":[],"name":"trusteeWithdraw","outputs":[],"type":"function"},{"constant":false,"inputs":[],"name":"withdraw","outputs":[],"type":"function"},{"constant":true,"inputs":[],"name":"mainDAO","outputs":[{"name":"","type":"address"}],"type":"function"},{"constant":true,"inputs":[],"name":"trustee","outputs":[{"name":"","type":"address"}],"type":"function"}]) -dao_ct = abi.ContractTranslator([{"constant":true,"inputs":[],"name":"name","outputs":[{"name":"","type":"string"}],"type":"function"},{"constant":false,"inputs":[{"name":"_spender","type":"address"},{"name":"_amount","type":"uint256"}],"name":"approve","outputs":[{"name":"success","type":"bool"}],"type":"function"},{"constant":true,"inputs":[],"name":"totalSupply","outputs":[{"name":"","type":"uint256"}],"type":"function"},{"constant":false,"inputs":[{"name":"_from","type":"address"},{"name":"_to","type":"address"},{"name":"_amount","type":"uint256"}],"name":"transferFrom","outputs":[{"name":"success","type":"bool"}],"type":"function"},{"constant":true,"inputs":[],"name":"decimals","outputs":[{"name":"","type":"uint8"}],"type":"function"},{"constant":true,"inputs":[],"name":"standard","outputs":[{"name":"","type":"string"}],"type":"function"},{"constant":true,"inputs":[{"name":"_owner","type":"address"}],"name":"balanceOf","outputs":[{"name":"balance","type":"uint256"}],"type":"function"},{"constant":true,"inputs":[],"name":"symbol","outputs":[{"name":"","type":"string"}],"type":"function"},{"constant":false,"inputs":[{"name":"_to","type":"address"},{"name":"_amount","type":"uint256"}],"name":"transfer","outputs":[{"name":"success","type":"bool"}],"type":"function"},{"constant":true,"inputs":[{"name":"_owner","type":"address"},{"name":"_spender","type":"address"}],"name":"allowance","outputs":[{"name":"remaining","type":"uint256"}],"type":"function"},{"anonymous":false,"inputs":[{"indexed":true,"name":"_from","type":"address"},{"indexed":true,"name":"_to","type":"address"},{"indexed":false,"name":"_amount","type":"uint256"}],"name":"Transfer","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"name":"_owner","type":"address"},{"indexed":true,"name":"_spender","type":"address"},{"indexed":false,"name":"_amount","type":"uint256"}],"name":"Approval","type":"event"}]) - -# Initialize state - -dao = "0xbb9bc244d798123fde783fcc1c72d3bb8c189413" -withdrawer = "0xbf4ed7b27f1d666546e30d74d50d173d20bca754" -my_account = "0x1db3439a222c519ab44bb1144fc28167b4fa6ee6" -my_other_account = "0xd8da6bf26964af9d7eed9e03e53415d37aa96045" -curator = "0xda4a4626d3e16e094de3225a751aab7128e96526" - -state = mk_basic_state({ - dao: account_dict, - withdrawer: { - "code": withdrawer_code, - "balance": "12072877497524777000000000", - "storage": { - "0x": "0xda4a4626d3e16e094de3225a751aab7128e96526" - } - }, -}, { - "number": 1920001, - "gas_limit": 4712388, - "gas_used": 0, - "timestamp": 1467446877, - "difficulty": 2**25, - "hash": '00' * 32, - "uncles_hash": '00' * 32 -}, Env()) - -def get_dao_balance(state, address): - msg_data = CallData([ord(x) for x in dao_ct.encode('balanceOf', [address])]) - msg = Message(normalize_address(address), normalize_address(dao), 0, 1000000, msg_data, code_address=normalize_address(dao)) - output = ''.join(map(chr, apply_const_message(state, msg))) - return dao_ct.decode('balanceOf', output)[0] - -import sys -state.log_listeners.append(lambda x: sys.stdout.write(str(dao_ct.listen(x))+'\n')) -state.log_listeners.append(lambda x: sys.stdout.write(str(withdrawer_ct.listen(x))+'\n')) - -print 'State created' - -# Check pre-balance - -pre_balance = state.get_balance(my_account) -pre_dao_tokens = get_dao_balance(state, my_account) -pre_withdrawer_balance = state.get_balance(withdrawer) - -print 'Pre ETH (wei) balance: %d' % pre_balance -print 'Pre DAO (base unit) balance: %d' % pre_dao_tokens - -# Attempt to claim the ETH without approving (should fail) - -tx0 = Transaction(state.get_nonce(my_account), 0, 1000000, withdrawer, 0, withdrawer_ct.encode('withdraw', [])).sign('\x33' * 32) -tx0._sender = normalize_address(my_account) -apply_transaction(state, tx0) - -med_balance = state.get_balance(my_account) -med_dao_tokens = get_dao_balance(state, my_account) -med_withdrawer_balance = state.get_balance(withdrawer) - -assert med_balance == pre_balance -assert med_dao_tokens == pre_dao_tokens -assert med_withdrawer_balance == pre_withdrawer_balance > 0 - -print 'ETH claim without approving failed, as expected' - -# Approve the withdrawal - -tx1 = Transaction(state.get_nonce(my_account), 0, 1000000, dao, 0, dao_ct.encode('approve', [withdrawer, 100000 * 10**18])).sign('\x33' * 32) -tx1._sender = normalize_address(my_account) -apply_transaction(state, tx1) - -# Check allowance - -allowance = dao_ct.decode('allowance', ''.join(map(chr, apply_const_message(state, Message(normalize_address(my_account), normalize_address(dao), 0, 1000000, CallData([ord(x) for x in dao_ct.encode('allowance', [my_account, withdrawer])]), code_address=dao)))))[0] -assert allowance == 100000 * 10**18, allowance -print 'Allowance verified' - -# Claim the ETH - -tx2 = Transaction(state.get_nonce(my_account), 0, 1000000, withdrawer, 0, withdrawer_ct.encode('withdraw', [])).sign('\x33' * 32) -tx2._sender = normalize_address(my_account) -apply_transaction(state, tx2) - -# Compare post_balance - -post_balance = state.get_balance(my_account) -post_dao_tokens = get_dao_balance(state, my_account) - -print 'Post ETH (wei) balance: %d' % post_balance -print 'Post DAO (base unit) balance: %d' % post_dao_tokens - -assert post_dao_tokens == 0 -assert post_balance - pre_balance == pre_dao_tokens - -print 'Withdrawing once works' - -# Try to claim post_balance again, should have no effect - -tx3 = Transaction(state.get_nonce(my_account), 0, 1000000, withdrawer, 0, withdrawer_ct.encode('withdraw', [])).sign('\x33' * 32) -tx3._sender = normalize_address(my_account) -apply_transaction(state, tx3) - -post_balance2 = state.get_balance(my_account) -post_dao_tokens2 = get_dao_balance(state, my_account) - -assert post_balance2 == post_balance -assert post_dao_tokens2 == post_dao_tokens - -# Curator withdraw - -pre_curator_balance = state.get_balance(curator) -pre_withdrawer_balance = state.get_balance(withdrawer) - -# from ethereum.slogging import LogRecorder, configure_logging, set_level -# config_string = ':info,eth.vm.log:trace,eth.vm.op:trace,eth.vm.stack:trace,eth.vm.exit:trace,eth.pb.msg:trace,eth.pb.tx:debug' -# configure_logging(config_string=config_string) - -tx4 = Transaction(0, 0, 1000000, withdrawer, 0, withdrawer_ct.encode('trusteeWithdraw', [])).sign('\x33' * 32) -apply_transaction(state, tx4) - -post_curator_balance = state.get_balance(curator) -post_withdrawer_balance = state.get_balance(withdrawer) -print 'Curator withdrawn', post_curator_balance - pre_curator_balance - -assert 500000 * 10**18 < post_curator_balance - pre_curator_balance < 600000 * 10**18 -assert pre_curator_balance + pre_withdrawer_balance == post_curator_balance + post_withdrawer_balance - -tx5 = Transaction(1, 0, 1000000, withdrawer, 0, withdrawer_ct.encode('trusteeWithdraw', [])).sign('\x33' * 32) -apply_transaction(state, tx5) - -post_curator_balance2 = state.get_balance(curator) -post_withdrawer_balance2 = state.get_balance(withdrawer) -assert post_curator_balance2 == post_curator_balance -assert post_withdrawer_balance2 == post_withdrawer_balance - -print 'Second withdrawal has no effect as expected' - -# Withdraw again, and try curator withdrawing again - -tx6 = Transaction(state.get_nonce(my_other_account), 0, 1000000, dao, 0, dao_ct.encode('approve', [withdrawer, 100000 * 10**18])).sign('\x33' * 32) -tx6._sender = normalize_address(my_other_account) -apply_transaction(state, tx6) - -tx7 = Transaction(state.get_nonce(my_other_account), 0, 1000000, withdrawer, 0, withdrawer_ct.encode('withdraw', [])).sign('\x33' * 32) -tx7._sender = normalize_address(my_other_account) -apply_transaction(state, tx7) - -post_withdrawer_balance3 = state.get_balance(withdrawer) -print 'Another %d wei withdrawn' % (post_withdrawer_balance2 - post_withdrawer_balance3) -assert post_withdrawer_balance3 < post_withdrawer_balance2 - -tx8 = Transaction(2, 0, 1000000, withdrawer, 0, withdrawer_ct.encode('trusteeWithdraw', [])).sign('\x33' * 32) -apply_transaction(state, tx8) - -post_curator_balance3 = state.get_balance(curator) -assert post_curator_balance2 == post_curator_balance - -print 'Third withdrawal has no effect as expected' - -# Withdraw from an account with no DAO - -no_dao_account = '\x35' * 20 - -pre_balance = state.get_balance(no_dao_account) -pre_dao_tokens = get_dao_balance(state, no_dao_account) - -tx9 = Transaction(state.get_nonce(no_dao_account), 0, 1000000, dao, 0, dao_ct.encode('approve', [withdrawer, 100000 * 10**18])).sign('\x33' * 32) -tx9._sender = no_dao_account -apply_transaction(state, tx9) - -tx10 = Transaction(state.get_nonce(no_dao_account), 0, 1000000, withdrawer, 0, withdrawer_ct.encode('withdraw', [])).sign('\x33' * 32) -tx10._sender = no_dao_account -apply_transaction(state, tx10) - -post_balance = state.get_balance(no_dao_account) -post_dao_tokens = get_dao_balance(state, no_dao_account) - -assert pre_balance == post_balance == 0 -assert pre_dao_tokens == post_dao_tokens - -print 'Withdrawal from a non-DAO-holding account has no effect' diff --git a/defrag/defrag_sim.py b/defrag/defrag_sim.py deleted file mode 100644 index 87dd979..0000000 --- a/defrag/defrag_sim.py +++ /dev/null @@ -1,83 +0,0 @@ -import random, math - -def mk_initial_balances(accts, coins): - o = [] - for i in range(accts): - o.extend([i] * random.randrange((coins - len(o)) * 2 // (accts - i))) - o.extend([accts-1] * (coins - len(o))) - return o - -def fragments(coins): - o = 0 - for i in range(1, len(coins)): - if coins[i] != coins[i-1]: - o += 1 - return o - -def xfer(coins, frm, to, value): - coins = coins[::] - pos = 0 - while pos < len(coins) and value > 0: - if coins[pos] == frm: - coins[pos] = to - value -= 1 - pos += 1 - return coins - -def unscramble(coins, c1, c2): - coins = coins[::] - k1 = coins.count(c1) - pos = 0 - while pos < len(coins): - if coins[pos] in (c1, c2): - coins[pos] = c1 if k1 > 0 else c2 - if coins[pos] == c1: - k1 -= 1 - pos += 1 - return coins - -def multi_unscramble(coins, addrs): - coins = coins[::] - ks = [coins.count(c) for c in addrs] - pos = 0 - at = 0 - while pos < len(coins): - if coins[pos] in addrs: - coins[pos] = addrs[at] - ks[at] -= 1 - if ks[at] == 0: - at += 1 - pos += 1 - return coins - -def unscramble_swap_strategy(coins, rounds): - for i in range(rounds): - c1, c2 = sorted([random.randrange(max(coins)+1) for _ in range(2)]) - coins = unscramble(coins, c1, c2) - return coins - -def run_with_unscrambling(coins, rounds): - M = max(coins) + 1 - for i in range(rounds): - c1, c2 = [random.randrange(M) for _ in range(2)] - value = int(coins.count(c1) ** random.random()) - coins = xfer(coins, c1, c2, value) - coins = unscramble(coins, min(c1, c2), max(c1, c2)) - return coins - -def run_with_unscramble_online(coins, rounds): - M = max(coins) + 1 - for i in range(rounds): - c1, c2 = [random.randrange(M) for _ in range(2)] - value = int(coins.count(c1) ** random.random()) - coins = xfer(coins, c1, c2, value) - if random.random() < 1: - cx = sorted([random.randrange(M) for _ in range(5)]) - coins = multi_unscramble(coins, cx) - return coins - -c = mk_initial_balances(200, 10000) -# random.shuffle(c) -# c = unscramble_swap_strategy(c, 20000) -c = run_with_unscramble_online(c, 10000) -print(fragments(c)) diff --git a/defrag/permutation2.py b/defrag/permutation2.py deleted file mode 100644 index ca71c0f..0000000 --- a/defrag/permutation2.py +++ /dev/null @@ -1,49 +0,0 @@ -import random - -def mk_shuffle(n): - L = list(range(n)) - random.shuffle(L) - return L - -def mk_fragmented_shuffle(n, shuffs): - L = list(range(n)) - for i in range(shuffs): - x1 = random.randrange(n) - x2 = random.randrange(n) - value = int(min(n - x1, n - x2, abs(x2 - x1)) ** random.random()) - L[x1:x1+value], L[x2:x2+value] = L[x2:x2+value], L[x1:x1+value] - return L - -def fragments(vals): - tot = 1 - for i in range(1, len(vals)): - if vals[i] != vals[i-1] + 1: - tot += 1 - return tot - -def apply_perm(vals, perm): - o = [0 for x in vals] - for i in range(len(perm)): - o[i] = vals[perm[i]] - return o - -def attempt_fix(vals): - perm = list(range(len(vals))) - indices = {} - for i, x in enumerate(vals): - indices[x] = i - for i in range(len(vals)): - if perm[i] == i and vals[i] != i: - poz = indices[i] - if perm[poz] == poz: - perm[i], perm[poz] = perm[poz], perm[i] - assert apply_perm(perm, perm) == list(range(len(vals))) - return perm - -def fix(vals): - goal = list(range(len(vals))) - path = [] - while vals != goal: - vals = apply_perm(vals, attempt_fix(vals)) - path.append(vals) - return path diff --git a/defrag/permutation_bfs.py b/defrag/permutation_bfs.py deleted file mode 100644 index 1391c2e..0000000 --- a/defrag/permutation_bfs.py +++ /dev/null @@ -1,65 +0,0 @@ -import heapq, random - -def distance_score(state): - state = [int(x) for x in state.split(',')] - tot = 0 - for i, s in enumerate(state): - xorval = (i+1) ^ s - indexmask = 1 - while indexmask < len(state): - if xorval & indexmask: - tot += 1 - indexmask <<= 1 - return tot - -def generate_legal_moves_for_bit(state, bit): - o = set() - xormask = 2**bit - state = [int(x) for x in state.split(',')] - for i in range(2**(len(state)-1)): - new_state = state[::] - indexmask = 1 - for j in range(len(state)): - if j > (j ^ xormask): - if i & indexmask: - new_state[j], new_state[j ^ xormask] = new_state[j ^ xormask], new_state[j] - indexmask <<= 1 - o.add(','.join([str(x) for x in new_state])) - return o - -def generate_legal_moves(state): - o = set() - b = 0 - while 2**b < len(state): - o = o.union(generate_legal_moves_for_bit(state, b)) - b += 1 - return o - -def mk_shuffle(n): - L = list(range(1, n+1)) - random.shuffle(L) - return ','.join([str(x) for x in L]) - -def find_path(start): - parents = {} - scores = {start: 0} - queue = [(distance_score(start), start)] - goal = ','.join([str(x) for x in sorted([int(x) for x in start.split(',')])]) - totvs = 0 - while len(queue): - qval = heapq.heappop(queue)[1] - newvals = [x for x in generate_legal_moves(qval) if x not in scores] - for v in newvals: - if scores.get(v, 99999) > scores[qval] + 1: - scores[v] = scores[qval] + 1 - parents[v] = qval - totvs += 1 - if v == goal: - path = [v] - while path[-1] != start: - parent = parents[path[-1]] - path.append(parent) - return path - for v in newvals: - heapq.heappush(queue, (distance_score(v), v)) - raise Exception("huh") diff --git a/defrag/send_bfs.py b/defrag/send_bfs.py deleted file mode 100644 index 45f4d53..0000000 --- a/defrag/send_bfs.py +++ /dev/null @@ -1,146 +0,0 @@ -import random, heapq - -# Assuming `online` is the set of users that is online, find a path to -# send `amount` coins from `frm` to `to` through `coins` where each -# step along the path is between users that have adjacent fragments. -# A transfer done in this way does not contribute to fragmentation. -def find_path(coins, frm, to, amount, online): - # Determine who is whose neighbor - neighbor_map = {} - for i in range(amount, len(coins) - amount + 1): - if coins[i-1] != coins[i]: - if coins[i-1] in online and coins[i] in online: - if coins[i-amount:i] == [coins[i-1]] * amount: - neighbor_map[coins[i-1]] = list(set(neighbor_map.get(coins[i-1], []) + [coins[i]])) - if coins[i:i+amount] == [coins[i]] * amount: - neighbor_map[coins[i]] = list(set(neighbor_map.get(coins[i], []) + [coins[i-1]])) - # Search for the path - parents = {frm: None} - q = [(0, frm)] - while q: - dist, sender = heapq.heappop(q) - neighbors = neighbor_map.get(sender, []) - for n in neighbors: - if n not in parents: - heapq.heappush(q, (dist+1, n)) - parents[n] = sender - if n == to: - o = [n] - while o[0] != frm: - o.insert(0, parents[o[0]]) - return o - return False - -# How many fragments are in this set of coins? -def fragments(vals): - tot = 1 - for i in range(1, len(vals)): - if vals[i] != vals[i-1]: - tot += 1 - return tot - -# Send `amt` coins from `frm` to `to`. Increases fragmentation by -# maximum 1 -def send_coins(coins, frm, to, amt): - coins_to_send = amt - for i in range(len(coins)): - if coins[i] == frm: - coins[i] = to - coins_to_send -= 1 - if coins_to_send == 0: - return True - return False - -# Get the concrete range to transfer if we are transfering `amt` -# coins from `frm` to `to` (must be neighboring fragments) -def get_coin_shunt(coins, frm, to, amt): - i = 1 - L = len(coins) - while i < L: - while i < L and coins[i] not in (frm, to): - i += 1 - if not((coins[i-1] == frm and coins[i] == to) or (coins[i-1] == to and coins[i] == frm)): - i += 1 - continue - if coins[i-amt:i] == [frm] * amt and coins[i] == to: - coins[i-amt:i] = [to] * amt - return (i-amt, i, to) - if coins[i:i+amt] == [frm] * amt and coins[i-1] == to: - coins[i:i+amt] = [to] * amt - return (i, i+amt, to) - i += 1 - return False - -# Find the largest slice controlled by `acct` -def maxslice(coins, acct): - maxsz = 0 - sz = 0 - for i in range(len(coins)): - if coins[i] == acct: - sz += 1 - maxsz = max(sz, maxsz) - else: - sz = 0 - return maxsz - -# Count the number of coins and the number of fragments -# held by each user -def count_coins_and_fragments(coins): - user_count = max(coins) + 1 - coin_count = [0] * user_count - frag_count = [0] * user_count - for i in range(len(coins)): - coin_count[coins[i]] += 1 - if i > 0 and coins[i] != coins[i-1]: - frag_count[coins[i]] += 1 - return coin_count, frag_count - -userz = 25 -coinz = 50000 -part_online = 0.1 -initial_fragments_per_user = 100 -ordering = list(range(userz)) * initial_fragments_per_user -random.shuffle(ordering) -c = [ordering[i * len(ordering) //coinz] for i in range(coinz)] -balances = count_coins_and_fragments(c)[0] -for i in range(250000): - if i%100 == 0: - print(i, fragments(c)) - # if i%2000 == 0: - # coin_count, frag_count = count_coins_and_fragments(c) - # print(sorted(zip(coin_count, frag_count))) - - # Randomly select sender, recipient and amount - frm = random.randrange(userz) - to = random.randrange(userz) - if frm == to: - continue - pre_balance = balances[frm] - amount = random.randrange(1, 1 + int(pre_balance ** random.random())) if pre_balance >= 2 else pre_balance - full_amount = amount - # print("Paying %d coins from %d to %d" % (amount, frm, to)) - # Randomly select the users that are online - online = [i for i in range(userz) if random.random() < part_online or i in (frm, to)] - while amount > 0: - maxpay = maxslice(c, frm) - pay_this_round = min(amount, maxpay) - path = find_path(c, frm, to, pay_this_round, online) - if path: - #print("Found path for %d coins (%d hops)" % (pay_this_round, len(path)-1)) - assert path[0] == frm - assert path[-1] == to - shunts = [] - for i in range(1, len(path)): - shunts.append(get_coin_shunt(c, path[i-1], path[i], pay_this_round)) - assert shunts[-1] - for shunt in shunts: - start, end, to = shunt - c[start:end] = [to] * (end-start) - amount -= pay_this_round - else: - # print('No path, paying remaining amount %d via fragmentation' % amount) - # print('%d fragments' % fragments(c)) - assert send_coins(c, frm, to, amount) - break - balances[frm] -= full_amount - balances[to] += full_amount diff --git a/diffadjust/blkdiff.py b/diffadjust/blkdiff.py deleted file mode 100644 index 5046c91..0000000 --- a/diffadjust/blkdiff.py +++ /dev/null @@ -1,150 +0,0 @@ -import math, random - -hashpower = [float(x) for x in open('hashpower.csv').readlines()] - -# Target block time -TARGET = 12 -# Should be 86400, but can reduce for a quicker sim -SECONDS_IN_DAY = 86400 -# Look at the 1/x day exponential moving average -EMA_FACTOR = 0.01 -# Damping factor for simple difficulty adjustment -SIMPLE_ADJUST_DAMPING_FACTOR = 20 -# Maximum per-block diff adjustment (as fraction of current diff) -SIMPLE_ADJUST_MAX = 0.5 -# Damping factor for quadratic difficulty adjustment -QUADRATIC_ADJUST_DAMPING_FACTOR = 3 -# Maximum per-block diff adjustment (as fraction of current diff) -QUADRATIC_ADJUST_MAX = 0.5 -# Threshold for bounded adjustor -BOUNDED_ADJUST_THRESHOLD = 1.3 -# Bounded adjustment factor -BOUNDED_ADJUST_FACTOR = 0.01 -# How many blocks back to look -BLKS_BACK = 10 -# Naive difficulty adjustment factor -NAIVE_ADJUST_FACTOR = 1/1024. - - -# Produces a value according to the exponential distribution; used -# to determine the time until the next block given an average block -# time of t -def expdiff(t): - return -math.log(random.random()) * t - - -# abs_sqr(3) = 9, abs_sqr(-7) = -49, etc -def abs_sqr(x): - return -(x**2) if x < 0 else x**2 - - -# Given an array of the most recent timestamps, and the most recent -# difficulties, compute the next difficulty -def simple_adjust(timestamps, diffs): - if len(timestamps) < BLKS_BACK + 2: - return diffs[-1] - # Total interval between previous block and block a bit further back - delta = timestamps[-2] - timestamps[-2-BLKS_BACK] + 0.0 - # Expected interval - expected = TARGET * BLKS_BACK - # Compute adjustment factor - fac = 1 - (delta / expected - 1) / SIMPLE_ADJUST_DAMPING_FACTOR - fac = max(min(fac, 1 + SIMPLE_ADJUST_MAX), 1 - SIMPLE_ADJUST_MAX) - return diffs[-1] * fac - - -# Alternative adjustment algorithm -def quadratic_adjust(timestamps, diffs): - if len(timestamps) < BLKS_BACK + 2: - return diffs[-1] - # Total interval between previous block and block a bit further back - delta = timestamps[-2] - timestamps[-2-BLKS_BACK] + 0.0 - # Expected interval - expected = TARGET * BLKS_BACK - # Compute adjustment factor - fac = 1 - abs_sqr(delta / expected - 1) / QUADRATIC_ADJUST_DAMPING_FACTOR - fac = max(min(fac, 1 + QUADRATIC_ADJUST_MAX), 1 - QUADRATIC_ADJUST_MAX) - return diffs[-1] * fac - - -# Alternative adjustment algorithm -def bounded_adjust(timestamps, diffs): - if len(timestamps) < BLKS_BACK + 2: - return diffs[-1] - # Total interval between previous block and block a bit further back - delta = timestamps[-2] - timestamps[-2-BLKS_BACK] + 0.0 - # Expected interval - expected = TARGET * BLKS_BACK - if delta / expected > BOUNDED_ADJUST_THRESHOLD: - fac = (1 - BOUNDED_ADJUST_FACTOR) - elif delta / expected < 1 / BOUNDED_ADJUST_THRESHOLD: - fac = (1 + BOUNDED_ADJUST_FACTOR) ** (delta / expected) - else: - fac = 1 - return diffs[-1] * fac - - -# Old Ethereum algorithm -def old_adjust(timestamps, diffs): - if len(timestamps) < 2: - return diffs[-1] - delta = timestamps[-1] - timestamps[-2] - expected = TARGET * 0.693 - if delta > expected: - fac = 1 - NAIVE_ADJUST_FACTOR - else: - fac = 1 + NAIVE_ADJUST_FACTOR - return diffs[-1] * fac - - -def test(source, adjust): - # Variables to keep track of for stats purposes - ema = maxema = minema = TARGET - lthalf, gtdouble, lttq, gtft = 0, 0, 0, 0 - count = 0 - # Block times - times = [0] - # Block difficulty values - diffs = [source[0]] - # Next time to print status update - nextprint = 10**6 - # Main loop - while times[-1] < len(source) * SECONDS_IN_DAY: - # Print status update every 10**6 seconds - if times[-1] > nextprint: - print '%d out of %d processed, ema %f' % \ - (times[-1], len(source) * SECONDS_IN_DAY, ema) - nextprint += 10**6 - # Grab hashpower from data source - hashpower = source[int(times[-1] // SECONDS_IN_DAY)] - # Calculate new difficulty - diffs.append(adjust(times, diffs)) - # Calculate next block time - times.append(times[-1] + expdiff(diffs[-1] / hashpower)) - # Calculate min and max ema - ema = ema * (1 - EMA_FACTOR) + (times[-1] - times[-2]) * EMA_FACTOR - minema = min(minema, ema) - maxema = max(maxema, ema) - count += 1 - # Keep track of number of blocks we are below 75/50% or above - # 133/200% of target - if ema < TARGET * 0.75: - lttq += 1 - if ema < TARGET * 0.5: - lthalf += 1 - elif ema > TARGET * 1.33333: - gtft += 1 - if ema > TARGET * 2: - gtdouble += 1 - # Pop items to save memory - if len(times) > 2000: - times.pop(0) - diffs.pop(0) - print 'min', minema, 'max', maxema, 'avg', times[-1] / count, \ - 'ema < half', lthalf * 1.0 / count, \ - 'ema > double', gtdouble * 1.0 / 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b/economic_analysis/censorship_sim.py deleted file mode 100644 index d1bf4fa..0000000 --- a/economic_analysis/censorship_sim.py +++ /dev/null @@ -1,68 +0,0 @@ -# Total ETH supply -total_supply = 10**8 - -# Returns to online validators, based on perceived fraction online -def R(p): - return p**1.53 - -# Returns to offline validators, based on perceived fraction online -def P(p): - return 0 - -# What interest rate are `deposits` ETH worth of validators willing to accept? -def demand_curve(deposits): - return deposits / total_supply / 10 - -# Given a total deposit size, and a fraction online, compute the interest -# paid to each online and offline validator -def get_rewards(deposits, p_online): - # Total txfees - fees = 50000 - # Portion of fees that get "reclaimed" by the protocol - reclaimed = 0.5 - # The un-reclaimed fees, which are necessarily distributed among - # the online validators - uncontrolled_reward = fees * (1 - reclaimed) / deposits / p_online - # The reclaimed fees, minus a portion that gets held back based on - # the portion of ETH holders staking - max_controlled_rewards = fees * reclaimed * \ - (deposits / total_supply) ** 0.8 - # In the best possible case (100% online), everyone gets R(1) interest. - # Rescale interest based on this. - controlled_rewards_multiplier = max_controlled_rewards / deposits / R(1) - # Return computed interest - return uncontrolled_reward + controlled_rewards_multiplier * R(p_online), \ - controlled_rewards_multiplier * P(p_online) - -# Total deposits in the validator set -deposits = 1000000 - -# Find the pre-attack equilibrium -for i in range(100): - interest, _ = get_rewards(deposits, 1) - if interest < demand_curve(deposits): - deposits -= 10000 - else: - deposits += 10000 - -attacker = deposits * 0.501 -print('Baseline total deposits:', deposits) -print('Baseline interest:', get_rewards(deposits, 1)[0]) -print('Baseline attacker revenue:', get_rewards(deposits, 1)[0] * attacker) -print('Baseline victim revenue:', get_rewards(deposits, 1)[0] * (deposits - attacker)) - -# Start the attack. Find the post-attack equilibrium. -for i in range(1000): - attacker_share = attacker / deposits - atk_interest, vic_interest = get_rewards(deposits, attacker_share) - if vic_interest < demand_curve(deposits): - deposits -= min(10000, deposits - attacker) - else: - deposits += 10000 - -print('New total deposits:', deposits) -print('Attacker share:', attacker_share) -print('Victim interest:', vic_interest) -print('Attacker interest:', atk_interest) -print('Attacker revenue:', atk_interest * attacker) -print('Possible non-attacking revenue:', get_rewards(deposits, 1)[0]) diff --git a/eip86/eip_86_basic_account.se b/eip86/eip_86_basic_account.se deleted file mode 100644 index 573e460..0000000 --- a/eip86/eip_86_basic_account.se +++ /dev/null @@ -1,28 +0,0 @@ -# Expects input 224+x bytes: v, r, s, nonce, gasprice, to, value, data -with zero = ~mload(0): - # Anti re-entrancy - ~jumpi(~pc(), msg.sender != ~sub(zero, 1)) - # Copy calldata - ~calldatacopy(32, zero, ~calldatasize()) - # Compute sighash - ~mstore(zero, ~sha3(32, 32 + ~calldatasize())) - # Do elliptic curve verification - ~call(3000, 1, zero, zero, 128, zero, 32) - # Memory: hash, v, r, s, nonce, gasprice, to, value, data - # Check sig is correct - ~jumpi(~pc(), ~mload(zero) != 0xfe2ec957647679d210034b65e9c7db2452910b0c) - with s = ~sload(zero): - # Check nonce is correct - ~jumpi(~pc(), s != ~mload(128)) - # Increment nonce - ~sstore(zero, s + 1) - with gasprice = ~mload(160): - # Check balance - ~jumpi(~pc(), self.balance < gasprice * msg.gas) - with g1 = msg.gas: - # Make the main call - ~call(msg.gas - 25000, ~mload(192), ~mload(224), 256, ~calldatasize() - 224, zero, 10000) - # Pay the miner - ~call(zero, block.coinbase, (g1 - msg.gas + 5000) * gasprice, zero, zero, zero, zero) - # Log to establish that the tx passed through successfully - ~log0(zero, zero) diff --git a/eip96/eip_96_blockhash_getter.se.py b/eip96/eip_96_blockhash_getter.se.py deleted file mode 100644 index 0376e1a..0000000 --- a/eip96/eip_96_blockhash_getter.se.py +++ /dev/null @@ -1,25 +0,0 @@ -# Setting the block hash -if msg.sender == 2**160 - 2: - with prev_block_number = block.number - 1: - # Use storage fields 0..255 to store the last 256 hashes - ~sstore(prev_block_number % 256, ~calldataload(0)) - # Use storage fields 256..511 to store the hashes of the last 256 - # blocks with block.number % 256 == 0 - if not (prev_block_number % 256): - ~sstore(256 + (prev_block_number / 256) % 256, ~calldataload(0)) - # Use storage fields 512..767 to store the hashes of the last 256 - # blocks with block.number % 65536 == 0 - if not (prev_block_number % 65536): - ~sstore(512 + (prev_block_number / 65536) % 256, ~calldataload(0)) -# Getting the block hash -else: - if ~calldataload(0) >= block.number: - return(0) - elif block.number - ~calldataload(0) <= 256: - return(~sload(~calldataload(0) % 256)) - elif (not (~calldataload(0) % 256) and block.number - ~calldataload(0) <= 65536): - return(~sload(256 + (~calldataload(0) / 256) % 256)) - elif (not (~calldataload(0) % 65536) and block.number - ~calldataload(0) <= 16777216): - return(~sload(512 + (~calldataload(0) / 65536) % 256)) - else: - return(0) diff --git a/eip96/eip_96_test_script.py b/eip96/eip_96_test_script.py deleted file mode 100644 index bffa21b..0000000 --- a/eip96/eip_96_test_script.py +++ /dev/null @@ -1,34 +0,0 @@ -from ethereum import tester, vm -from ethereum.utils import sha3, encode_int32, safe_ord, encode_hex -from ethereum.state_transition import apply_message -s = tester.state() -c = s.contract('eip_96_blockhash_getter.se.py') -blockhash_addr = b'\x00' * 19 + b'\x10' -system_addr = b'\xff' * 19 + b'\xfe' -s.state.set_code(blockhash_addr, s.state.get_code(c)) - -def mk_hash_setting_message(data): - return vm.Message(sender=system_addr, to=blockhash_addr, value=0, gas=1000000, data=data) - -print("Setting block hashes") -for i in range(1, 1000): - s.state.block_number = i + 1 - o = apply_message(s.state, mk_hash_setting_message(sha3(str(i)))) - if i % 100 == 0: - print("Set %d" % i) - -print("Testing reads") -s.state.block_number = 1000 -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(999)) == sha3(str(999)) -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(998)) == sha3(str(998)) -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(744)) == sha3(str(744)) -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(743)) == b'\x00' * 32 -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(1000)) == b'\x00' * 32 -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(1001)) == b'\x00' * 32 -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(513)) == b'\x00' * 32 -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(512)) == sha3(str(512)) -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(511)) == b'\x00' * 32 -assert s.send(tester.k0, blockhash_addr, 0, encode_int32(256)) == sha3(str(256)) -print("Tests passed!") - -print("EVM code: 0x%s" % encode_hex(s.state.get_code(blockhash_addr))) diff --git a/elasticity/analyzer.py b/elasticity/analyzer.py deleted file mode 100644 index c10e942..0000000 --- a/elasticity/analyzer.py +++ /dev/null @@ -1,36 +0,0 @@ -lines = open('data.csv').read().split('\n') -data = [(int(x[:x.find(',')]), float(x[x.find(',')+1:])) for x in lines if x] - -REPORT_THRESHOLD = 0.23 - -def get_error(scale, elasticity, growth): - err = 0 - bs_fac, fee_fac = 1 / (1 + elasticity), elasticity / (1 + elasticity) - for i, (block_size, avg_fee) in enumerate(data): - expected = scale * (1 + growth) ** i - actual = block_size ** bs_fac * avg_fee ** fee_fac - # if i >= len(data) - 6: - # err += ((expected / actual - 1) ** 2) * 2 - err += (expected / actual - 1) ** 2 - return err - -best = (0, 0, 0, 9999999999999999999999999.0) - -for scale in [1 * 1.05 ** x for x in range(300)]: - for elasticity in [x*0.025 for x in range(120)]: - for growth in [x*0.001 for x in range(120)]: - err = get_error(scale, elasticity, growth) - if err <= REPORT_THRESHOLD: - print('%d %.3f %.3f: %.3f' % (scale, elasticity, growth, err)) - if err < best[-1]: - best = scale, elasticity, growth, err - -print('Best params: %d %.3f %.3f (err %.3f)' % best) - -scale, elasticity, growth, err = best -bs_fac, fee_fac = 1 / (1 + elasticity), elasticity / (1 + elasticity) - -for i, (block_size, avg_fee) in enumerate(data): - expected = scale * (1 + growth) ** i - actual = block_size ** bs_fac * avg_fee ** fee_fac - print(i, actual, expected) diff --git a/elasticity/data.csv b/elasticity/data.csv deleted file mode 100644 index 1b2eb35..0000000 --- a/elasticity/data.csv +++ /dev/null @@ -1,28 +0,0 @@ -358373,0.0001556 -373527,0.00014486 -387199,0.00014816 -404860,0.00017626 -392748,0.00015425 -454844,0.00016187 -594453,0.0002212 -463351,0.00021871 -555749,0.00019946 -543490,0.00019368 -566810,0.00017566 -623697,0.00017407 -662227,0.00019356 -732706,0.00020016 -715370,0.00022996 -743867,0.00025096 -769594,0.00022846 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constexpr std::uint8_t tpl(std::uint8_t a) { - return a ^ (a<<1) // a * (x+1) - ^ ((a & (1<<7)) != 0 - ? // would overflow (have an x^8 term); reduce by the AES polynomial, - // x^8 + x^4 + x^3 + x + 1 - 0b00011011u - : 0 - ); -} - -// constexpr functions to compute exp/log -// these are not intended to be fast, but they must be constexpr to populate a -// table at compile time -static constexpr std::uint8_t gexp(unsigned k) { - return k > 0 ? tpl(gexp(k-1)) : 1; -} -static constexpr std::uint8_t glog(unsigned k, unsigned i = 0, unsigned v = 1) { - return k == v ? i : glog(k, i+1, tpl(v)); -} - -// insane hack (courtesy of Xeo on stackoverflow): gen_seq expands to a -// struct that derives from seq<0, 1, ..., N-1> -template struct seq{}; -template -struct gen_seq : gen_seq{}; -template -struct gen_seq<0, I...> : seq{}; - -// produce the actual tables in array form... -template -constexpr std::array exptbl(seq) { - return { { Galois(gexp(I))... } }; -} -template -constexpr std::array logtbl(seq) { - // manually populate entry zero, for two reasons: - // - it makes glog simpler - // - it avoids clang++'s default template instantiation depth limit of 256 - return { { 0, glog(I+1)... } }; -} - -// and initialize the static variables -const std::array Galois::exptable = exptbl(gen_seq<255>{}); -const std::array Galois::logtable = logtbl(gen_seq<255>{}); - -// by populating everything at compile-time, we avoid a static initialization -// step and any possible associated static initialization "races" diff --git a/erasure_code/ec256/share.go b/erasure_code/ec256/share.go deleted file mode 100644 index 6ae8b8e..0000000 --- a/erasure_code/ec256/share.go +++ /dev/null @@ -1,559 +0,0 @@ -package erasure_code - -import "fmt" - -func init() { - galoisInit() -} - -// Finite fields -// ============= - -type ZeroDivisionError struct { -} - -func (e *ZeroDivisionError) Error() string { - return "division by zero" -} - -// should panic with ZeroDivisionError when dividing by zero -type Field interface { - Add(b Field) Field - Sub(b Field) Field - Mul(b Field) Field - Div(b Field) Field - Value() int - Factory() FieldFactory -} -type FieldFactory interface { - Construct(v int) Field -} - -// per-byte 2^8 Galois field -// Note that this imposes a hard limit that the number of extended chunks can -// be at most 256 along each dimension -type Galois struct { - v uint8 -} - -var gexptable [255]uint8 -var glogtable [256]uint8 - -func galoisTpl(a uint8) uint8 { - r := a ^ (a << 1) // a * (x+1) - if (a & (1 << 7)) != 0 { - // would overflow (have an x^8 term); reduce by the AES polynomial, - // x^8 + x^4 + x^3 + x + 1 - return r ^ 0x1b - } else { - return r - } -} - -func galoisInit() { - var v uint8 = 1 - for i := uint8(0); i < 255; i++ { - glogtable[v] = i - gexptable[i] = v - v = galoisTpl(v) - } -} - -func (a *Galois) Add(_b Field) Field { - b := _b.(*Galois) - return &Galois{a.v ^ b.v} -} -func (a *Galois) Sub(_b Field) Field { - b := _b.(*Galois) - return &Galois{a.v ^ b.v} -} -func (a *Galois) Mul(_b Field) Field { - b := _b.(*Galois) - if a.v == 0 || b.v == 0 { - return &Galois{0} - } - return &Galois{gexptable[(int(glogtable[a.v])+ - int(glogtable[b.v]))%255]} -} -func (a *Galois) Div(_b Field) Field { - b := _b.(*Galois) - if b.v == 0 { - panic(ZeroDivisionError{}) - } - if a.v == 0 { - return &Galois{0} - } - return &Galois{gexptable[(int(glogtable[a.v])+255- - int(glogtable[b.v]))%255]} -} -func (a *Galois) Value() int { - return int(a.v) -} -func (a *Galois) String() string { - return fmt.Sprintf("%d",a.v) -} - -type galoisFactory struct { -} - -func GaloisFactory() FieldFactory { - return &galoisFactory{} -} -func (self *Galois) Factory() FieldFactory { - return GaloisFactory() -} -func (self *galoisFactory) Construct(v int) Field { - return &Galois{uint8(v)} -} - -// Modular arithmetic class -type modulo struct { - v uint - n uint // the modulus -} - -func (a *modulo) Add(_b Field) Field { - b := _b.(*modulo) - return &modulo{(a.v + b.v) % a.n, a.n} -} - -func (a *modulo) Sub(_b Field) Field { - b := _b.(*modulo) - return &modulo{(a.v + a.n - b.v) % a.n, a.n} -} - -func (a *modulo) Mul(_b Field) Field { - b := _b.(*modulo) - return &modulo{(a.v * b.v) % a.n, a.n} -} - -func powmod(b uint, e uint, m uint) uint { - var r uint = 1 - for e > 0 { - if (e & 1) == 1 { - r = (r * b) % m - } - b = (b * b) % m - e >>= 1 - } - return r -} - -func (a *modulo) Div(_b Field) Field { - b := _b.(*modulo) - return &modulo{(a.v * powmod(b.v, a.n-2, a.n)) % a.n, a.n} -} - -func (self *modulo) Value() int { - return int(self.v) -} - -type moduloFactory struct { - n uint -} - -func (self *modulo) Factory() FieldFactory { - return &moduloFactory{self.n} -} - -func (self *moduloFactory) Construct(v int) Field { - return &modulo{uint(v), self.n} -} - -func MakeModuloFactory(n uint) FieldFactory { - return &moduloFactory{n} -} - -func zero(f FieldFactory) Field { - return f.Construct(0) -} -func one(f FieldFactory) Field { - return f.Construct(1) -} - -// Helper functions -// ================ - -// Evaluates a polynomial p in little-endian form (e.g. x^2 + 3x + 2 is -// represented as [2, 3, 1]) at coordinate x, -func EvalPolyAt(poly []Field, x Field) Field { - arithmetic := x.Factory() - r, xi := zero(arithmetic), one(arithmetic) - for _, ci := range poly { - r = r.Add(xi.Mul(ci)) - xi = xi.Mul(x) - } - return r -} - -// Given p+1 y values and x values with no errors, recovers the original -// p+1 degree polynomial. For example, -// LagrangeInterp({51.0, 59.0, 66.0}, {1, 3, 4}) = {50.0, 0, 1.0} -// (or it would be, if floats were Fields) -func LagrangeInterp(pieces []Field, xs []Field) []Field { - arithmetic := pieces[0].Factory() - zero, one := zero(arithmetic), one(arithmetic) - - // `size` is the number of datapoints; the degree of the result polynomial - // is then `size-1` - size := len(pieces) - - root := []Field{one} // initially just the polynomial "1" - // build up the numerator polynomial, `root`, by taking the product of (x-v) - // (implemented as convolving repeatedly with [-v, 1]) - for _, v := range xs { - // iterate backward since new root[i] depends on old root[i-1] - for i := len(root) - 1; i >= 0; i-- { - root[i] = root[i].Mul(zero.Sub(v)) - if i > 0 { - root[i] = root[i].Add(root[i-1]) - } - } - // polynomial is always monic so save an extra multiply by doing this - // after - root = append(root, one) - } - - // generate per-value numerator polynomials by dividing the master - // polynomial back by each x coordinate - nums := make([][]Field, size) - for i, v := range xs { - // divide `root` by (x-v) to get a degree size-1 polynomial - // (i.e. with `size` coefficients) - num := make([]Field, size) - // compute the x^0, x^1, ..., x^(p-2) coefficients by long division - last := one - num[len(num)-1] = last // still always a monic polynomial - for j := size - 2; j >= 0; j-- { - last = root[j+1].Add(last.Mul(v)) - num[j] = last - } - nums[i] = num - } - - // generate denominators by evaluating numerator polys at their x - denoms := make([]Field, size) - for i, x := range xs { - denoms[i] = EvalPolyAt(nums[i], x) - } - - // generate output polynomial by taking the sum over i of - // (nums[i] * pieces[i] / denoms[i]) - sum := make([]Field, size) - for i := range sum { - sum[i] = zero - } - for i, y := range pieces { - factor := y.Div(denoms[i]) - // add nums[i] * factor to sum, as a vector - for j := 0; j < size; j++ { - sum[j] = sum[j].Add(nums[i][j].Mul(factor)) - } - } - return sum -} - -// Given two linear equations, eliminates the first variable and returns -// the resulting equation. -// -// An equation of the form a_1 x_1 + ... + a_n x_n + b = 0 -// is represented as the array [a_1, ..., a_n, b]. -func elim(a []Field, b []Field) []Field { - result := make([]Field, len(a)-1) - for i := range result { - result[i] = a[i+1].Mul(b[0]).Sub(b[i+1].Mul(a[0])) - } - return result -} - -// Given one homogeneous linear equation and the values of all but the first -// variable, solve for the value of the first variable. -// -// For an equation of the form -// a_1 x_1 + ... + a_n x_n = 0 -// pass two arrays, [a_1, ..., a_n] and [x_2, ..., x_n]. -func evaluate(coeffs []Field, vals []Field) Field { - total := zero(coeffs[0].Factory()) - for i, val := range vals { - total = total.Sub(coeffs[i+1].Mul(val)) - } - return total.Div(coeffs[0]) -} - -// Given an n*n system of inhomogeneous linear equations, solve for the value of -// every variable. -// -// For equations of the form -// a_1,1 x_1 + ... + a_1,n x_n + b_1 = 0 -// a_2,1 x_1 + ... + a_2,n x_n + b_2 = 0 -// ... -// a_n,1 x_1 + ... + a_n,n x_n + b_n = 0 -// pass a two-dimensional array -// [[a_1,1, ..., a_1,n, b_1], ..., [a_n,1, ..., a_n,n, b_n]]. -// -// Returns the values of [x_1, ..., x_n]. -func SysSolve(eqs [][]Field) []Field { - arithmetic := eqs[0][0].Factory() - backEqs := make([][]Field, 1, len(eqs)) - backEqs[0] = eqs[0] - - for len(eqs) > 1 { - neweqs := make([][]Field, len(eqs)-1) - for i := 0; i < len(eqs)-1; i++ { - neweqs[i] = elim(eqs[i], eqs[i+1]) - } - eqs = neweqs - // find a row with a nonzero first entry - i := 0 - for i+1 < len(eqs) && eqs[i][0].Value() == 0 { - i++ - } - backEqs = append(backEqs, eqs[i]) - } - - kvals := make([]Field, len(backEqs)+1) - kvals[len(backEqs)] = one(arithmetic) - // back-substitute in reverse order - // (smallest to largest equation) - for i := len(backEqs) - 1; i >= 0; i-- { - kvals[i] = evaluate(backEqs[i], kvals[i+1:]) - } - - return kvals[:len(kvals)-1] -} - -// Divide two polynomials with nonzero leading terms. -// T should be a field. -func PolyDiv(Q []Field, E []Field) []Field { - if len(Q) < len(E) { - return []Field{} - } - div := make([]Field, len(Q)-len(E)+1) - for i := len(div) - 1; i >= 0; i-- { - factor := Q[len(Q)-1].Div(E[len(E)-1]) - div[i] = factor - // subtract factor * E * x^i from Q - Q = Q[:len(Q)-1] // the highest term should cancel - for j := 0; j < len(E)-1; j++ { - Q[i+j] = Q[i+j].Sub(factor.Mul(E[j])) - } - } - return div -} - -func trySysSolve(eqs [][]Field) (ret []Field, ok bool) { - defer func() { - err := recover() - if err == nil { - return - } - switch err := err.(type) { - case ZeroDivisionError: - ret = nil - ok = false - default: - panic(err) - } - }() - return SysSolve(eqs), true -} - -type NotEnoughData struct { } -func (self *NotEnoughData) Error() string { - return "Not enough data!" -} -type TooManyErrors struct { } -func (self *TooManyErrors) Error() string { - return "Answer doesn't match (too many errors)!" -} - -// Given a set of y coordinates and x coordinates, and the degree of the -// original polynomial, determines the original polynomial even if some of the y -// coordinates are wrong. If m is the minimal number of pieces (ie. degree + -// 1), t is the total number of pieces provided, then the algo can handle up to -// (t-m)/2 errors. -func BerlekampWelchAttempt(pieces []Field, xs []Field, masterDegree int) ([]Field, error) { - errorLocatorDegree := (len(pieces) - masterDegree - 1) / 2 - arithmetic := pieces[0].Factory() - zero, one := zero(arithmetic), one(arithmetic) - // Set up the equations for y[i]E(x[i]) = Q(x[i]) - // degree(E) = errorLocatorDegree - // degree(Q) = masterDegree + errorLocatorDegree - 1 - eqs := make([][]Field, 2*errorLocatorDegree+masterDegree+1) - for i := range eqs { - eq := []Field{} - x := xs[i] - piece := pieces[i] - neg_x_j := zero.Sub(one) - for j := 0; j < errorLocatorDegree+masterDegree+1; j++ { - eq = append(eq, neg_x_j) - neg_x_j = neg_x_j.Mul(x) - } - x_j := one - for j := 0; j < errorLocatorDegree+1; j++ { - eq = append(eq, x_j.Mul(piece)) - x_j = x_j.Mul(x) - } - eqs[i] = eq - } - // Solve the equations - // Assume the top error polynomial term to be one - errors := errorLocatorDegree - ones := 1 - var polys []Field - for errors >= 0 { - if p, ok := trySysSolve(eqs); ok { - for i := 0; i < ones; i++ { - p = append(p, one) - } - polys = p - break - } - // caught ZeroDivisionError - eqs = eqs[:len(eqs)-1] - for i, eq := range eqs { - eq[len(eq)-2] = eq[len(eq)-2].Add(eq[len(eq)-1]) - eqs[i] = eq[:len(eq)-1] - } - errors-- - ones++ - } - if errors < 0 { - return nil, &NotEnoughData{} - } - // divide the polynomials... - split := errorLocatorDegree + masterDegree + 1 - div := PolyDiv(polys[:split], polys[split:]) - corrects := 0 - for i := 0; i < len(xs); i++ { - if EvalPolyAt(div, xs[i]).Value() == pieces[i].Value() { - corrects++ - } - } - if corrects < masterDegree+errors { - return nil, &TooManyErrors{} - } - return div, nil -} - -// Extends a list of integers in [0 ... 255] (if using Galois arithmetic) by -// adding n redundant error-correction values -func Extend(data []int, n int, arithmetic FieldFactory) ([]int, error) { - size := len(data) - - dataF := make([]Field, size) - for i, d := range data { - dataF[i] = arithmetic.Construct(d) - } - - xs := make([]Field, size) - for i := range xs { - xs[i] = arithmetic.Construct(i) - } - - poly, err := BerlekampWelchAttempt(dataF, xs, size-1) - if err != nil { - return nil, err - } - - for i := 0; i < n; i++ { - data = append(data, - int(EvalPolyAt(poly, arithmetic.Construct(size+i)).Value())) - } - return data, nil -} - -// Repairs a list of integers in [0 ... 255]. Some integers can be erroneous, -// and you can put -1 in place of an integer if you know that a certain -// value is defective or missing. Uses the Berlekamp-Welch algorithm to -// do error-correction -func Repair(data []int, datasize int, arithmetic FieldFactory) ([]int, error) { - vs := make([]Field, 0, len(data)) - xs := make([]Field, 0, len(data)) - for i, d := range data { - if d >= 0 { - vs = append(vs, arithmetic.Construct(d)) - xs = append(xs, arithmetic.Construct(i)) - } - } - - poly, err := BerlekampWelchAttempt(vs, xs, datasize-1) - if err != nil { - return nil, err - } - - result := make([]int, len(data)) - for i := range result { - result[i] = int(EvalPolyAt(poly, arithmetic.Construct(i)).Value()) - } - return result, nil -} - -func transpose(d [][]int) [][]int { - width := len(d[0]) - result := make([][]int, width) - for i := range result { - col := make([]int, len(d)) - for j := range col { - col[j] = d[j][i] - } - result[i] = col - } - return result -} - -func extractColumn(d [][]int, j int) []int { - result := make([]int, len(d)) - for i, row := range d { - result[i] = row[j] - } - return result -} - -// Extends a list of bytearrays -// eg. ExtendChunks([map(ord, 'hello'), map(ord, 'world')], 2) -// n is the number of redundant error-correction chunks to add -func ExtendChunks(data [][]int, n int, arithmetic FieldFactory) ([][]int, error) { - width := len(data[0]) - o := make([][]int, width) - for i := 0; i < width; i++ { - row, err := Extend(extractColumn(data, i), n, arithmetic) - if err != nil { - return nil, err - } - o[i] = row - } - return transpose(o), nil -} - -// Repairs a list of bytearrays. Use an empty array in place of a missing array. -// Individual arrays can contain some missing or erroneous data. -func RepairChunks(data [][]int, datasize int, arithmetic FieldFactory) ([][]int, error) { - var width int - for _, row := range data { - if len(row) > 0 { - width = len(row) - break - } - } - filledData := make([][]int, len(data)) - for i, row := range data { - if len(row) == 0 { - filledData[i] = make([]int, width) - for j := range filledData[i] { - filledData[i][j] = -1 - } - } else { - filledData[i] = row - } - } - o := make([][]int, width) - for i := range o { - row, err := Repair(extractColumn(data, i), datasize, arithmetic) - if err != nil { - return nil, err - } - o[i] = row - } - return transpose(o), nil -} diff --git a/erasure_code/ec256/share.h b/erasure_code/ec256/share.h deleted file mode 100644 index cd1c2e5..0000000 --- a/erasure_code/ec256/share.h +++ /dev/null @@ -1,549 +0,0 @@ -#include -#include -#include -#include -#include -#include - -#include "utils.h" - -class ZeroDivisionError : std::domain_error { -public: - ZeroDivisionError() : domain_error("division by zero") { } -}; - -// GF(2^8) in the form (Z/2Z)[x]/(x^8+x^4+x^3+x+1) -// (the AES polynomial) -class Galois { - // the coefficients of the polynomial, where the ith bit of `val` is the x^i - // coefficient - std::uint8_t v; - - // precomputed data: log and exp tables - static const std::array exptable; - static const std::array logtable; - -public: - explicit constexpr Galois(unsigned char val) : v(val) { } - - Galois operator+(Galois b) const { - return Galois(v ^ b.v); - } - Galois operator-(Galois b) const { - return Galois(v ^ b.v); - } - Galois operator*(Galois b) const { - return v == 0 || b.v == 0 - ? Galois(0) - : exptable[(unsigned(logtable[v]) + logtable[b.v]) % 255]; - } - Galois operator/(Galois b) const { - if (b.v == 0) { - throw ZeroDivisionError(); - } - return v == 0 || b.v == 0 - ? Galois(0) - : exptable[(unsigned(logtable[v]) + 255u - logtable[b.v]) % 255]; - } - Galois operator-() const { - return *this; - } - - Galois& operator+=(Galois b) { - return *this = *this + b; - } - Galois& operator-=(Galois b) { - return *this = *this - b; - } - Galois& operator*=(Galois b) { - return *this = *this * b; - } - Galois& operator/=(Galois b) { - return *this = *this / b; - } - - bool operator==(Galois b) { - return v == b.v; - } - - // back door - std::uint8_t val() const { - return v; - } -}; - -// Z/pZ, for an odd prime p -template -class Modulo { - // check that p is prime by trial division - static constexpr bool is_prime(unsigned x, unsigned divisor = 2) { - return divisor * divisor > x - ? true - : x % divisor != 0 && is_prime(x, divisor + 1); - } - static_assert(p > 2 && is_prime(p, 2), "p must be an odd prime!"); - - unsigned v; - -public: - explicit Modulo(unsigned val) : v(val) { - assert(v >= 0 && v < p); - } - - - Modulo inv() const { - if (v == 0) { - throw ZeroDivisionError(); - } - unsigned r = 1, base = v, exp = p-2; - while (exp > 0) { - if (exp & 1) r = (r * base) % p; - base = (base * base) % p; - exp >>= 1; - } - return Modulo(r); - } - Modulo operator+(Modulo b) const { - return Modulo((v + b.v) % p); - } - Modulo operator-(Modulo b) const { - return Modulo((v + p - b.v) % p); - } - Modulo operator*(Modulo b) const { - return Modulo((v * b.v) % p); - } - Modulo operator/(Modulo b) const { - return *this * b.inv(); - } - - Modulo& operator+=(Modulo b) { - return *this = *this + b; - } - Modulo& operator-=(Modulo b) { - return *this = *this - b; - } - Modulo& operator*=(Modulo b) { - return *this = *this * b; - } - Modulo& operator/=(Modulo b) { - return *this = *this / b; - } - - bool operator==(Modulo b) { - return v == b.v; - } - - // back door - unsigned val() const { - return v; - } -}; - -// Evaluates a polynomial p in little-endian form (e.g. x^2 + 3x + 2 is -// represented as {2, 3, 1}) at coordinate x, -// e.g. eval_poly_at((int[]){2, 3, 1}, 5) = 42. -// -// T should be a type supporting ring arithmetic and T(0) and T(1) should be the -// appropriate identities. -// -// Range should be a type that can be iterated to get const T& elements. -template -T eval_poly_at(const Range& p, T x) { - T r(0), xi(1); - for (const T& c_i : p) { - r += c_i * xi; - xi *= x; - } - return r; -} - -// Given p+1 y values and x values with no errors, recovers the original -// degree-p polynomial. For example, -// lagrange_interp((double[]){51.0, 59.0, 66.0}, -// (double[]){1.0, 3.0, 4.0}) -// = {50.0, 0.0, 1.0}. -// -// T should be a field and Range should be a sized range type with values of -// type T. T(0) and T(1) should be the appropriate field identities. -template -std::vector lagrange_interp(const Range& pieces, const Range& xs) { - // `size` is the number of datapoints; the degree of the result polynomial - // is then `size-1` - const unsigned size = pieces.size(); - assert(size == xs.size()); - - std::vector root{T(1)}; // initially just the polynomial "1" - // build up the numerator polynomial, `root`, by taking the product of (x-v) - // (implemented as convolving repeatedly with [-v, 1]) - for (const T& v : xs) { - // iterate backward since new root[i] depends on old root[i-1] - for (unsigned i = root.size(); i--; ) { - root[i] *= -v; - if (i > 0) root[i] += root[i-1]; - } - // polynomial is always monic so save an extra multiply by doing this - // after - root.emplace_back(1); - } - // should have degree `size` - assert(root.size() == size + 1); - - // generate per-value numerator polynomials by dividing the master - // polynomial back by each x coordinate - std::vector > nums; - nums.reserve(size); - for (const T& v : xs) { - // divide `root` by (x-v) to get a degree size-1 polynomial - // (i.e. with `size` coefficients) - std::vector num(size, T(0)); - // compute the x^0, x^1, ..., x^(p-2) coefficients by long division - T last = num.back() = T(1); // still always a monic polynomial - for (int i = int(size)-2; i >= 0; --i) { - num[i] = last = root[i+1] + last * v; - } - nums.emplace_back(std::move(num)); - } - assert(nums.size() == size); - - // generate denominators by evaluating numerator polys at their x - std::vector denoms; - denoms.reserve(size); - { - unsigned i = 0; - for (const T& v : xs) { - denoms.push_back(eval_poly_at(nums[i], v)); - ++i; - } - } - assert(denoms.size() == size); - - // generate output polynomial by taking the sum over i of - // (nums[i] * pieces[i] / denoms[i]) - std::vector sum(size, T(0)); - { - unsigned i = 0; - for (const T& y : pieces) { - T factor = y / denoms[i]; - // add nums[i] * factor to sum, as a vector - for (unsigned j = 0; j < size; ++j) { - sum[j] += nums[i][j] * factor; - } - ++i; - } - } - return sum; -} - -// Given two linear equations, eliminates the first variable and returns -// the resulting equation. -// -// An equation of the form a_1 x_1 + ... + a_n x_n + b = 0 -// is represented as the array [a_1, ..., a_n, b]. -// -// T should be a ring and Range should be an indexable, sized range of T. -template -std::vector elim(const Range& a, const Range& b) { - assert(a.size() == b.size()); - std::vector result; - const unsigned size = a.size(); - for (unsigned i = 1; i < size; ++i) { - result.push_back(a[i] * b[0] - b[i] * a[0]); - } - return result; -} - -// Given one homogeneous linear equation and the values of all but the first -// variable, solve for the value of the first variable. -// -// For an equation of the form -// a_1 x_1 + ... + a_n x_n = 0 -// pass two arrays, [a_1, ..., a_n] and [x_2, ..., x_n]. -// -// T should be a field; and R1 and R2 should be indexable, sized ranges of T. -template -T evaluate(const R1& coeffs, const R2& vals) { - assert(coeffs.size() == vals.size() + 1); - T total(0); - const unsigned size = vals.size(); - for (unsigned i = 0; i < size; ++i) { - total -= coeffs[i+1] * vals[i]; - } - return total / coeffs[0]; -} - -// Given an n*n system of inhomogeneous linear equations, solve for the value of -// every variable. -// -// For equations of the form -// a_1,1 x_1 + ... + a_1,n x_n + b_1 = 0 -// a_2,1 x_1 + ... + a_2,n x_n + b_2 = 0 -// ... -// a_n,1 x_1 + ... + a_n,n x_n + b_n = 0 -// pass a two-dimensional array -// [[a_1,1, ..., a_1,n, b_1], ..., [a_n,1, ..., a_n,n, b_n]]. -// -// Returns the values of [x_1, ..., x_n]. -// -// T should be a field. -template -std::vector sys_solve(std::vector> eqs) { - assert(eqs.size() > 0); - std::vector> back_eqs{eqs[0]}; - - while (eqs.size() > 1) { - std::vector> neweqs; - neweqs.reserve(eqs.size()-1); - for (unsigned i = 0; i < eqs.size()-1; ++i) { - neweqs.push_back(elim(eqs[i], eqs[i+1])); - } - eqs = std::move(neweqs); - // find a row with a nonzero first entry - unsigned i = 0; - while (i + 1 < eqs.size() && eqs[i][0] == T(0)) { - ++i; - } - back_eqs.push_back(eqs[i]); - } - - std::vector kvals(back_eqs.size()+1, T(0)); - kvals.back() = T(1); - // back-substitute in reverse order - // (smallest to largest equation) - for (unsigned i = back_eqs.size(); i--; ) { - kvals[i] = evaluate(back_eqs[i], - // use the already-computed values + the 1 at the end - make_iter_pair(kvals.begin()+i+1, kvals.end())); - } - - kvals.pop_back(); - - return kvals; -} - -// Divide two polynomials with nonzero leading terms. -// T should be a field. -template -std::vector polydiv(std::vector Q, const std::vector& E) { - if (Q.size() < E.size()) return {}; - std::vector div(Q.size() - E.size() + 1, T(0)); - unsigned i = div.size(); - while (i--) { - T factor = Q.back() / E.back(); - div[i] = factor; - // subtract factor * E * x^i from Q - Q.pop_back(); // the highest term should cancel - for (unsigned j = 0; j < E.size() - 1; ++j) { - Q[i+j] -= factor * E[j]; - } - assert(Q.size() == i + E.size() - 1); - } - return div; -} - -// Given a set of y coordinates and x coordinates, and the degree of the -// original polynomial, determines the original polynomial even if some of the y -// coordinates are wrong. If m is the minimal number of pieces (ie. degree + -// 1), t is the total number of pieces provided, then the algo can handle up to -// (t-m)/2 errors. -// -// T should be a field. In particular, division by zero over T should throw -// ZeroDivisionError. -template -std::vector berlekamp_welch_attempt(const std::vector& pieces, - const std::vector& xs, unsigned master_degree) { - const unsigned error_locator_degree = (pieces.size() - master_degree - 1) / 2; - // Set up the equations for y[i]E(x[i]) = Q(x[i]) - // degree(E) = error_locator_degree - // degree(Q) = master_degree + error_locator_degree - 1 - std::vector> eqs(2*error_locator_degree + master_degree + 1); - for (unsigned i = 0; i < eqs.size(); ++i) { - std::vector& eq = eqs[i]; - const T& x = xs[i]; - const T& piece = pieces[i]; - T neg_x_j = T(0) - T(1); - for (unsigned j = 0; j < error_locator_degree + master_degree + 1; ++j) { - eq.push_back(neg_x_j); - neg_x_j *= x; - } - T x_j = T(1); - for (unsigned j = 0; j < error_locator_degree + 1; ++j) { - eq.push_back(x_j * piece); - x_j *= x; - } - } - // Solve the equations - // Assume the top error polynomial term to be one - int errors = error_locator_degree; - unsigned ones = 1; - std::vector polys; - while (errors >= 0) { - try { - polys = sys_solve(eqs); - } catch (const ZeroDivisionError&) { - eqs.pop_back(); - for (auto& eq : eqs) { - eq[eq.size()-2] += eq.back(); - eq.pop_back(); - } - --errors; - ++ones; - continue; - } - for (unsigned i = 0; i < ones; ++i) polys.emplace_back(1); - break; - } - if (errors < 0) { - throw std::logic_error("Not enough data!"); - } - // divide the polynomials... - const unsigned split = error_locator_degree + master_degree + 1; - std::vector div = polydiv(std::vector(polys.begin(), polys.begin() + split), - std::vector(polys.begin() + split, polys.end())); - unsigned corrects = 0; - for (unsigned i = 0; i < xs.size(); ++i) { - if (eval_poly_at(div, xs[i]) == pieces[i]) { - ++corrects; - } - } - if (corrects < master_degree + errors) { - throw std::logic_error("Answer doesn't match (too many errors)!"); - } - return div; -} - -// Extends a list of integers in [0 ... 255] (if using Galois arithmetic) by -// adding n redundant error-correction values -template -std::vector extend(std::vector data, unsigned n) { - const unsigned size = data.size(); - - std::vector data_f; - data_f.reserve(size); - for (T d : data) data_f.emplace_back(d); - - std::vector xs; - for (unsigned i = 0; i < size; ++i) xs.emplace_back(i); - - std::vector poly = berlekamp_welch_attempt(data_f, xs, size-1); - - data.reserve(size+n); - for (unsigned i = 0; i < n; ++i) { - data.push_back(eval_poly_at(poly, F(T(size + i))).val()); - } - return data; -} - -// Repairs a list of integers in [0 ... 255]. Some integers can be erroneous, -// and you can put -1 in place of an integer if you know that a certain -// value is defective or missing. Uses the Berlekamp-Welch algorithm to -// do error-correction -template -std::vector repair(const std::vector& data, unsigned datasize) { - std::vector vs, xs; - for (unsigned i = 0; i < data.size(); ++i) { - if (data[i] >= 0) { - vs.emplace_back(data[i]); - xs.emplace_back(T(i)); - } - } - std::vector poly = berlekamp_welch_attempt(vs, xs, datasize - 1); - std::vector result; - for (unsigned i = 0; i < data.size(); ++i) { - result.push_back(eval_poly_at(poly, F(T(i))).val()); - } - return result; -} - - -template -std::vector> transpose(const std::vector>& d) { - assert(d.size() > 0); - unsigned width = d[0].size(); - std::vector> result(width); - for (unsigned i = 0; i < width; ++i) { - for (unsigned j = 0; j < d.size(); ++j) { - result[i].push_back(d[j][i]); - } - } - return result; -} - -template -std::vector extract_column(const std::vector>& d, unsigned i) { - std::vector result; - for (unsigned j = 0; j < d.size(); ++j) { - result.push_back(d[j][i]); - } - return result; -} - -// Extends a list of bytearrays -// eg. extend_chunks([map(ord, 'hello'), map(ord, 'world')], 2) -// n is the number of redundant error-correction chunks to add -template -std::vector> extend_chunks( - const std::vector>& data, - unsigned n) { - std::vector> o; - const unsigned height = data.size(); - assert(height > 0); - const unsigned width = data[0].size(); - for (unsigned i = 0; i < width; ++i) { - o.push_back(extend(extract_column(data, i), n)); - } - return transpose(o); -} - -// Repairs a list of bytearrays. Use an empty array in place of a missing array. -// Individual arrays can contain some missing or erroneous data. -template -std::vector> repair_chunks( - std::vector> data, - unsigned datasize) { - unsigned width = 0; - for (const std::vector& row : data) { - if (row.size() > 0) { - width = row.size(); - break; - } - } - assert(width > 0); - for (std::vector& row : data) { - if (row.size() == 0) { - row.assign(width, -1); - } else { - assert(row.size() == width); - } - } - std::vector> o; - for (unsigned i = 0; i < width; ++i) { - o.push_back(repair(extract_column(data, i), datasize)); - } - return transpose(o); -} - -// Extends either a bytearray or a list of bytearrays or a list of lists... -// Used in the cubify method to expand a cube in all dimensions -template -struct deep_extend_chunks_helper { - static std::vector go(const std::vector& data, unsigned n) { - return extend(data, n); - } -}; -template -struct deep_extend_chunks_helper, F> { - static std::vector> go(const std::vector>& data, unsigned n) { - std::vector> o; - const unsigned height = data.size(); - assert(height > 0); - const unsigned width = data[0].size(); - for (unsigned i = 0; i < width; ++i) { - o.push_back(deep_extend_chunks_helper::go(extract_column(data, i), n)); - } - return transpose(o); - } -}; -template -std::vector deep_extend_chunks(const std::vector& data, unsigned n) { - return deep_extend_chunks_helper::go(data, n); -} diff --git a/erasure_code/ec256/share.js b/erasure_code/ec256/share.js deleted file mode 100644 index 638fcb1..0000000 --- a/erasure_code/ec256/share.js +++ /dev/null @@ -1,478 +0,0 @@ -(function() { - var me = {}; - - function ZeroDivisionError() { - if (!this) return new ZeroDivisionError(); - this.message = "division by zero"; - this.name = "ZeroDivisionError"; - } - me.ZeroDivisionError = ZeroDivisionError; - - // per-byte 2^8 Galois field - // Note that this imposes a hard limit that the number of extended chunks can - // be at most 256 along each dimension - function galoistpl(a) { - // 2 is not a primitive root, so we have to use 3 as our logarithm base - var r = a ^ (a<<1); // a * (x+1) - if (r > 0xff) { // overflow? - r = r ^ 0x11b; - } - return r; - } - - // Precomputing a multiplication and XOR table for increased speed - var glogtable = new Array(256); - var gexptable = []; - (function() { - var v = 1; - for (var i = 0; i < 255; i++) { - glogtable[v] = i; - gexptable.push(v); - v = galoistpl(v); - } - })(); - me.glogtable = glogtable; - me.gexptable = gexptable; - - function Galois(val) { - if (!(this instanceof Galois)) return new Galois(val); - if (val instanceof Galois) { - this.val = val.val; - } else { - this.val = val; - } - if (typeof Object.freeze == 'function') { - Object.freeze(this); - } - } - me.Galois = Galois; - Galois.prototype.add = Galois.prototype.sub = function(other) { - return new Galois(this.val ^ other.val); - }; - Galois.prototype.mul = function(other) { - if (this.val == 0 || other.val == 0) { - return new Galois(0); - } - return new Galois(gexptable[(glogtable[this.val] + - glogtable[other.val]) % 255]); - }; - Galois.prototype.div = function(other) { - if (other.val == 0) { - throw new ZeroDivisionError(); - } - if (this.val == 0) { - return new Galois(0); - } - return new Galois(gexptable[(glogtable[this.val] + 255 - - glogtable[other.val]) % 255]); - }; - Galois.prototype.inspect = function() { - return ""+this.val; - }; - - function powmod(b, e, m) { - var r = 1; - while (e > 0) { - if (e & 1) r = (r * b) % m; - b = (b * b) % m; - e = e >> 1; - } - return r; - } - - - // Modular division class - function mkModuloClass(n) { - if (n <= 2) throw new Error("n must be prime!"); - for (var divisor = 2; divisor * divisor <= n; divisor++) { - if (n % divisor == 0) { - throw new Error("n must be prime!"); - } - } - - function Mod(val) { - if (!(this instanceof Mod)) return new Mod(val); - if (val instanceof Mod) { - this.val = val.val; - } else { - this.val = val; - } - if (typeof Object.freeze == 'function') { - Object.freeze(this); - } - } - Mod.modulo = n; - Mod.prototype.add = function(other) { - return new Mod((this.val + other.val) % n); - }; - Mod.prototype.sub = function(other) { - return new Mod((this.val + n - other.val) % n); - }; - Mod.prototype.mul = function(other) { - return new Mod((this.val * other.val) % n); - }; - Mod.prototype.div = function(other) { - return new Mod((this.val * powmod(other.val, n-2, n)) % n); - }; - Mod.prototype.inspect = function() { - return ""+this.val; - }; - - return Mod; - } - me.mkModuloClass = mkModuloClass; - - // Evaluates a polynomial in little-endian form, eg. x^2 + 3x + 2 = [2, 3, 1] - // (normally I hate little-endian, but in this case dealing with polynomials - // it's justified, since you get the nice property that p[n] is the nth degree - // term of p) at coordinate x, eg. eval_poly_at([2, 3, 1], 5) = 42 if you are - // using float as your arithmetic - function eval_poly_at(p, x) { - var arithmetic = p[0].constructor; - var y = new arithmetic(0); - var x_to_the_i = new arithmetic(1); - for (var i = 0; i < p.length; i++) { - y = y.add(x_to_the_i.mul(p[i])) - x_to_the_i = x_to_the_i.mul(x); - } - return y; - } - me.eval_poly_at = eval_poly_at; - - // Given p+1 y values and x values with no errors, recovers the original - // p+1 degree polynomial. For example, - // lagrange_interp([51.0, 59.0, 66.0], [1, 3, 4]) = [50.0, 0, 1.0] - // if you are using float as your arithmetic - function lagrange_interp(pieces, xs) { - var arithmetic = pieces[0].constructor; - var zero = new arithmetic(0); - var one = new arithmetic(1); - // Generate master numerator polynomial - var root = [one]; - var i, j; - for (i = 0; i < xs.length; i++) { - root.unshift(zero); - for (j = 0; j < root.length - 1; j++) { - root[j] = root[j].sub(root[j+1].mul(xs[i])); - } - } - // Generate per-value numerator polynomials by dividing the master - // polynomial back by each x coordinate - var nums = []; - for (i = 0; i < xs.length; i++) { - var output = []; - var last = one; - for (j = 2; j < root.length+1; j++) { - output.unshift(last); - if (j != root.length) { - last = root[root.length-j].add(last.mul(xs[i])); - } - } - nums.push(output); - } - // Generate denominators by evaluating numerator polys at their x - var denoms = []; - for (i = 0; i < xs.length; i++) { - var denom = zero; - var x_to_the_j = one; - for (j = 0; j < nums[i].length; j++) { - denom = denom.add(x_to_the_j.mul(nums[i][j])); - x_to_the_j = x_to_the_j.mul(xs[i]); - } - denoms.push(denom); - } - // Generate output polynomial - var b = []; - for (i = 0; i < pieces.length; i++) { - b[i] = zero; - } - for (i = 0; i < xs.length; i++) { - var yslice = pieces[i].div(denoms[i]); - for (j = 0; j < pieces.length; j++) { - b[j] = b[j].add(nums[i][j].mul(yslice)); - } - } - return b; - } - me.lagrange_interp = lagrange_interp; - - // Compresses two linear equations of length n into one - // equation of length n-1 - // Format: - // 3x + 4y = 80 (ie. 3x + 4y - 80 = 0) -> a = [3,4,-80] - // 5x + 2y = 70 (ie. 5x + 2y - 70 = 0) -> b = [5,2,-70] - function elim(a, b) { - var c = []; - for (var i = 1; i < a.length; i++) { - c[i-1] = a[i].mul(b[0]).sub(b[i].mul(a[0])); - } - return c; - } - - // Linear equation solver - // Format: - // 3x + 4y = 80, y = 5 (ie. 3x + 4y - 80z = 0, y = 5, z = 1) - // -> coeffs = [3,4,-80], vals = [5,1] - function evaluate(coeffs, vals) { - var arithmetic = coeffs[0].constructor; - var tot = new arithmetic(0); - for (var i = 0; i < vals.length; i++) { - tot = tot.sub(coeffs[i+1].mul(vals[i])); - } - if (coeffs[0].val == 0) { - throw new ZeroDivisionError(); - } - return tot.div(coeffs[0]); - } - - // Linear equation system solver - // Format: - // ax + by + c = 0, dx + ey + f = 0 - // -> [[a, b, c], [d, e, f]] - // eg. - // [[3.0, 5.0, -13.0], [9.0, 1.0, -11.0]] -> [1.0, 2.0] - function sys_solve(eqs) { - var arithmetic = eqs[0][0].constructor; - var one = new arithmetic(1); - var back_eqs = [eqs[0]]; - var i; - while (eqs.length > 1) { - var neweqs = []; - for (i = 0; i < eqs.length - 1; i++) { - neweqs.push(elim(eqs[i], eqs[i+1])); - } - eqs = neweqs; - i = 0; - while (i < eqs.length - 1 && eqs[i][0].val == 0) { - i++; - } - back_eqs.unshift(eqs[i]); - } - var kvals = [one]; - for (i = 0; i < back_eqs.length; i++) { - kvals.unshift(evaluate(back_eqs[i], kvals)); - } - return kvals.slice(0, -1); - } - me.sys_solve = sys_solve; - - function polydiv(Q, E) { - var qpoly = Q.slice(); - var epoly = E.slice(); - var div = []; - while (qpoly.length >= epoly.length) { - div.unshift(qpoly[qpoly.length-1].div(epoly[epoly.length-1])); - for (var i = 2; i < epoly.length + 1; i++) { - qpoly[qpoly.length-i] = - qpoly[qpoly.length-i].sub(div[0].mul(epoly[epoly.length-i])); - } - qpoly.pop(); - } - return div; - } - me.polydiv = polydiv; - - // Given a set of y coordinates and x coordinates, and the degree of the - // original polynomial, determines the original polynomial even if some of - // the y coordinates are wrong. If m is the minimal number of pieces (ie. - // degree + 1), t is the total number of pieces provided, then the algo can - // handle up to (t-m)/2 errors. See: - // http://en.wikipedia.org/wiki/Berlekamp%E2%80%93Welch_algorithm#Example - // (just skip to my example, the rest of the article sucks imo) - function berlekamp_welch_attempt(pieces, xs, master_degree) { - var error_locator_degree = Math.floor((pieces.length - master_degree - 1) / 2); - var arithmetic = pieces[0].constructor; - var zero = new arithmetic(0); - var one = new arithmetic(1); - // Set up the equations for y[i]E(x[i]) = Q(x[i]) - // degree(E) = error_locator_degree - // degree(Q) = master_degree + error_locator_degree - 1 - var eqs = []; - var i,j; - for (i = 0; i < 2 * error_locator_degree + master_degree + 1; i++) { - eqs.push([]); - } - for (i = 0; i < 2 * error_locator_degree + master_degree + 1; i++) { - var neg_x_to_the_j = zero.sub(one); - for (j = 0; j < error_locator_degree + master_degree + 1; j++) { - eqs[i].push(neg_x_to_the_j); - neg_x_to_the_j = neg_x_to_the_j.mul(xs[i]); - } - var x_to_the_j = one; - for (j = 0; j < error_locator_degree + 1; j++) { - eqs[i].push(x_to_the_j.mul(pieces[i])); - x_to_the_j = x_to_the_j.mul(xs[i]); - } - } - // Solve 'em - // Assume the top error polynomial term to be one - var errors = error_locator_degree; - var ones = 1; - var polys; - while (errors >= 0) { - try { - polys = sys_solve(eqs); - for (i = 0; i < ones; i++) polys.push(one); - break; - } catch (e) { - if (e instanceof ZeroDivisionError) { - eqs.pop(); - for (i = 0; i < eqs.length; i++) { - var eq = eqs[i]; - eq[eq.length-2] = eq[eq.length-2].add(eq[eq.length-1]); - eq.pop(); - } - errors--; - ones++; - } else { - throw e; - } - } - } - if (errors < 0) { - throw new Error("Not enough data!"); - } - // Divide the polynomials - var qpoly = polys.slice(0, error_locator_degree + master_degree + 1); - var epoly = polys.slice(error_locator_degree + master_degree + 1); - var div = polydiv(qpoly, epoly); - // Check - var corrects = 0; - for (i = 0; i < xs.length; i++) { - if (eval_poly_at(div, xs[i]).val == pieces[i].val) { - corrects++; - } - } - if (corrects < master_degree + errors) { - throw new Error("Answer doesn't match (too many errors)!"); - } - return div; - } - me.berlekamp_welch_attempt = berlekamp_welch_attempt; - - // Extends a list of integers in [0 ... 255] (if using Galois arithmetic) by - // adding n redundant error-correction values - function extend(data, n, arithmetic) { - arithmetic = arithmetic || Galois; - function mk(x) { return new arithmetic(x); } - var data2 = data.map(mk); - var data3 = data.slice(); - var xs = []; - var i; - for (i = 0; i < data.length; i++) { - xs.push(new arithmetic(i)); - } - var poly = berlekamp_welch_attempt(data2, xs, data.length - 1); - for (i = 0; i < n; i++) { - data3.push(eval_poly_at(poly, new arithmetic(data.length + i)).val); - } - return data3; - } - me.extend = extend; - - // Repairs a list of integers in [0 ... 255]. Some integers can be - // erroneous, and you can put null (or undefined) in place of an integer if - // you know that a certain value is defective or missing. Uses the - // Berlekamp-Welch algorithm to do error-correction - function repair(data, datasize, arithmetic) { - arithmetic = arithmetic || Galois; - var vs = []; - var xs = []; - var i; - for (var i = 0; i < data.length; i++) { - if (data[i] != null) { - vs.push(new arithmetic(data[i])); - xs.push(new arithmetic(i)); - } - } - var poly = berlekamp_welch_attempt(vs, xs, datasize - 1); - var result = []; - for (i = 0; i < data.length; i++) { - result.push(eval_poly_at(poly, new arithmetic(i)).val); - } - return result; - } - me.repair = repair; - - function transpose(xs) { - var ys = []; - for (var i = 0; i < xs[0].length; i++) { - var y = []; - for (var j = 0; j < xs.length; j++) { - y.push(xs[j][i]); - } - ys.push(y); - } - return ys; - } - - // Extends a list of bytearrays - // eg. extend_chunks([map(ord, 'hello'), map(ord, 'world')], 2) - // n is the number of redundant error-correction chunks to add - function extend_chunks(data, n, arithmetic) { - arithmetic = arithmetic || Galois; - var o = []; - for (var i = 0; i < data[0].length; i++) { - o.push(extend(data.map(function(x) { return x[i]; }), n, arithmetic)); - } - return transpose(o); - } - me.extend_chunks = extend_chunks; - - // Repairs a list of bytearrays. Use null in place of a missing array. - // Individual arrays can contain some missing or erroneous data. - function repair_chunks(data, datasize, arithmetic) { - arithmetic = arithmetic || Galois; - var first_nonzero = 0; - while (data[first_nonzero] == null) { - first_nonzero++; - } - var i; - for (i = 0; i < data.length; i++) { - if (data[i] == null) { - data[i] = new Array(data[first_nonzero].length); - } - } - var o = []; - for (i = 0; i < data[0].length; i++) { - o.push(repair(data.map(function(x) { return x[i]; }), datasize, arithmetic)); - } - return transpose(o); - } - me.repair_chunks = repair_chunks; - - // Extends either a bytearray or a list of bytearrays or a list of lists... - // Used in the cubify method to expand a cube in all dimensions - function deep_extend_chunks(data, n, arithmetic) { - arithmetic = arithmetic || Galois; - if (!(data[0] instanceof Array)) { - return extend(data, n, arithmetic) - } else { - var o = []; - for (var i = 0; i < data[0].length; i++) { - o.push(deep_extend_chunks( - data.map(function(x) { return x[i]; }), n, arithmetic)); - } - return transpose(o); - } - } - me.deep_extend_chunks = deep_extend_chunks; - - function isObject(o) { - return typeof o == 'object' || typeof o == 'function'; - } - if (typeof define == 'function' && typeof define.amd == 'object' && define.amd) { - define(function() { - return me; - }); - } else { - done = 0 - try { - if (isObject(module)) { module.exports = me; } - else (isObject(window) ? window : this).Erasure = me; - } - catch(e) { - (isObject(window) ? window : this).Erasure = me; - } - } -}.call(this)); diff --git a/erasure_code/ec256/test.py b/erasure_code/ec256/test.py deleted file mode 100644 index f97aa5b..0000000 --- a/erasure_code/ec256/test.py +++ /dev/null @@ -1,75 +0,0 @@ -import random -import share - -fsz = 200 - -f = ''.join([ - random.choice('1234567890qwetyuiopasdfghjklzxcvbnm') for x in range(fsz)]) - -c = share.split_file(f, 5, 4) - -print 'File split successfully.' -print ' ' -print 'Chunks: ' -print ' ' -for chunk in c: - print chunk -print ' ' - -g = ''.join([ - random.choice('1234567890qwetyuiopasdfghjklzxcvbnm') for x in range(fsz)]) - -c2 = share.split_file(g, 5, 4) - -assert share.recombine_file( - [c[0], c2[1], c[2], c[3], c2[4], c[5], c[6], c[7], c[8]]) == f - -print '5 of 9 with 7 legit, 2 errors passed' - -assert share.recombine_file( - [c[0], c[2], c[3], c2[4], c[6], c[7], c[8]]) == f - -print '5 of 9 with 6 legit, 1 error passed' - -assert share.recombine_file( - [c[0], c[3], c[6], c[7], c[8]]) == f - -print '5 of 9 with 5 legit, 0 errors passed' - -chunks3 = share.serialize_cubify(f, 3, 3, 2) - -print ' ' -print 'Chunks: ' -print ' ' -for chunk in chunks3: - print chunk -print ' ' - -for i in range(26): - pos = random.randrange(len(chunks3)) - print 'Removing cell %d' % pos - chunks3.pop(pos) - -assert share.full_heal_set(chunks3) == f - -print ' ' -print 'Cube reconstruction test passed' -print ' ' - -chunks4 = share.serialize_cubify(g, 3, 3, 2) - -for i in range(7): - pos = random.randrange(len(chunks3)) - chunk = chunks3.pop(pos) - print 'Damaging cell %d' % pos - print 'Prior: %s' % chunk - metadata, content = share.deserialize_chunk(chunk) - for j in range(len(content)): - content[j] = random.randrange(256) - chunks3.append(share.serialize_chunk(content, *metadata)) - print 'Post: %s' % chunks3[-1] - -assert share.full_heal_set(chunks4) == g - -print ' ' -print 'Byzantine cube reconstruction test passed' diff --git a/erasure_code/ec256/utils.h b/erasure_code/ec256/utils.h deleted file mode 100644 index 2b979ea..0000000 --- a/erasure_code/ec256/utils.h +++ /dev/null @@ -1,34 +0,0 @@ -#ifndef UTILS_H_ -#define UTILS_H_ - -#include -#include -#include - -// turn a pair of iterators into a range -template -class iter_pair { - T a, b; - typedef typename std::remove_reference(nullptr))>::type value_type; -public: - iter_pair(const T& _a, const T& _b) : a(_a), b(_b) { } - iter_pair(T&& _a, T&& _b) : a(std::move(_a)), b(std::move(_b)) { } - T begin() const { return a; } - T end() const { return b; } - - // for random access iterators - value_type& operator[](std::size_t ix) { return *(a + ix); } - const value_type& operator[](std::size_t ix) const { return *(a + ix); } - std::size_t size() const { return b - a; } -}; - -template -iter_pair make_iter_pair(const T& a, const T& b) { - return iter_pair(a, b); -} -template -iter_pair make_iter_pair(T&& a, T&& b) { - return iter_pair(std::move(a), std::move(b)); -} - -#endif diff --git a/erasure_code/ec65536/LICENSE b/erasure_code/ec65536/LICENSE deleted file mode 100644 index e69de29..0000000 diff --git a/erasure_code/ec65536/README.md b/erasure_code/ec65536/README.md deleted file mode 100644 index e69de29..0000000 diff --git a/erasure_code/ec65536/ec65536/__init__.py b/erasure_code/ec65536/ec65536/__init__.py deleted file mode 100644 index 8dc9b7a..0000000 --- a/erasure_code/ec65536/ec65536/__init__.py +++ /dev/null @@ -1 +0,0 @@ -from .poly_utils import lagrange_interp, eval_poly_at, mul_polys, div_polys, add_polys, galois_add, galois_mul, galois_div, compose_polys diff --git a/erasure_code/ec65536/ec65536/ec65536.py b/erasure_code/ec65536/ec65536/ec65536.py deleted file mode 100644 index b93a307..0000000 --- a/erasure_code/ec65536/ec65536/ec65536.py +++ /dev/null @@ -1,152 +0,0 @@ -import copy -import poly_utils -import rlp - -try: - from Crypto.Hash import keccak - sha3 = lambda x: keccak.new(digest_bits=256, data=x).digest() -except ImportError: - import sha3 as _sha3 - sha3 = lambda x: _sha3.sha3_256(x).digest() - -# Every point is an element of GF(2**16), so represents two bytes -POINT_SIZE = 2 -# Every chunk contains 128 points -POINTS_IN_CHUNK = 128 -# A chunk is 256 bytes -CHUNK_SIZE = POINT_SIZE * POINTS_IN_CHUNK - -def bytes_to_num(bytez): - o = 0 - for b in bytez: - o = (o * 256) + b - return o - -def num_to_bytes(inp, n): - o = b'' - for i in range(n): - o = bytes([inp % 256]) + o - inp //= 256 - return o - -assert bytes_to_num(num_to_bytes(31337, 2)) == 31337 - -# Returns the smallest power of 2 equal to or greater than a number -def higher_power_of_2(x): - higher_power_of_2 = 1 - while higher_power_of_2 < x: - higher_power_of_2 *= 2 - return higher_power_of_2 - -# Unfortunately, most padding schemes standardized in cryptography seem to only work for -# block sizes strictly less than 256 bytes. So we'll use RLP plus zero byte padding -# instead (pre-RLP-encode because the RLP encoding adds length data, so the padding -# becomes reversible even in cases where the original data ends in zero bytes) -def pad(data): - med = rlp.encode(data) - return med + b'\x00' * (higher_power_of_2(len(med)) - len(med)) - -def unpad(data): - c, l1, l2 = rlp.codec.consume_length_prefix(data) - assert c == str - return data[:l1 + l2] - -# Deserialize a chunk into a list of points in GF2**16 -def chunk_to_points(chunk): - return [bytes_to_num(chunk[i: i + POINT_SIZE]) for i in range(0, CHUNK_SIZE, POINT_SIZE)] - -# Serialize a list of points into a chunk -def points_to_chunk(points): - return b''.join([num_to_bytes(p, POINT_SIZE) for p in points]) - -testdata = sha3(b'cow') * (CHUNK_SIZE // 32) -assert points_to_chunk(chunk_to_points(testdata)) == testdata - -# Make a Merkle tree out of a set of chunks -def merklize(chunks): - # Only accept a list of size which is exactly a power of two - assert higher_power_of_2(len(chunks)) == len(chunks) - merkle_nodes = [sha3(x) for x in chunks] - lower_tier = merkle_nodes[::] - higher_tier = [] - while len(higher_tier) != 1: - higher_tier = [sha3(lower_tier[i] + lower_tier[i + 1]) for i in range(0, len(lower_tier), 2)] - merkle_nodes = higher_tier + merkle_nodes - lower_tier = higher_tier - merkle_nodes.insert(0, b'\x00' * 32) - return merkle_nodes - - -class Prover(): - def __init__(self, data): - # Pad data - pdata = pad(data) - byte_chunks = [pdata[i: i + CHUNK_SIZE] for i in range(0, len(pdata), CHUNK_SIZE)] - # Decompose it into chunks, where each chunk is a collection of numbers - chunks = [] - for byte_chunk in byte_chunks: - chunks.append(chunk_to_points(byte_chunk)) - # Compute the polynomials representing the ith number in each chunk - polys = [poly_utils.lagrange_interp([chunk[i] for chunk in chunks], list(range(len(chunks)))) for i in range(POINTS_IN_CHUNK)] - # Use the polynomials to extend the chunks - new_chunks = [] - for x in range(len(chunks), len(chunks) * 2): - new_chunks.append(points_to_chunk([poly_utils.eval_poly_at(poly, x) for poly in polys])) - # Total length of data including new points - self.length = len(byte_chunks + new_chunks) - self.extended_data = byte_chunks + new_chunks - # Build up the Merkle tree - self.merkle_nodes = merklize(self.extended_data) - assert len(self.merkle_nodes) == 2 * self.length - self.merkle_root = self.merkle_nodes[1] - - # Make a Merkle proof for some index - def prove(self, index): - assert 0 <= index < self.length - adjusted_index = self.length + index - o = [self.extended_data[index]] - while adjusted_index > 1: - o.append(self.merkle_nodes[adjusted_index ^ 1]) - adjusted_index >>= 1 - return o - -# Verify a merkle proof of some index (light client friendly) -def verify_proof(merkle_root, proof, index): - h = sha3(proof[0]) - for p in proof[1:]: - if index % 2: - h = sha3(p + h) - else: - h = sha3(h + p) - index //= 2 - return h == merkle_root - -# Fill data from partially available proofs -# This method returning False can also be used as a verifier for fraud proofs -def fill(merkle_root, orig_data_length, proofs, indices): - if len(proofs) < orig_data_length: - raise Exception("Not enough proofs") - if len(proofs) > orig_data_length: - raise Exception("Too many proofs; if original data has n chunks, n chunks suffice") - for proof, index in zip(proofs, indices): - if not verify_proof(merkle_root, proof, index): - raise Exception("Merkle proof for index %d invalid" % index) - # Convert to points - coords = [chunk_to_points(p[0]) for p in proofs] - # Extract polynomials - polys = [poly_utils.lagrange_interp([c[i] for c in coords], indices) for i in range(POINTS_IN_CHUNK)] - # Fill in the remaining values - full_coords = [None] * orig_data_length * 2 - for points, index in zip(coords, indices): - full_coords[index] = points - for i in range(len(full_coords)): - if full_coords[i] is None: - full_coords[i] = [poly_utils.eval_poly_at(poly, i) for poly in polys] - # Serialize - full_chunks = [points_to_chunk(points) for points in full_coords] - # Merklize - merkle_nodes = merklize(full_chunks) - # Check equality of the Merkle root - if merkle_root != merkle_nodes[1]: - return False - return full_chunks diff --git a/erasure_code/ec65536/ec65536/poly_utils.py b/erasure_code/ec65536/ec65536/poly_utils.py deleted file mode 100644 index e657cca..0000000 --- a/erasure_code/ec65536/ec65536/poly_utils.py +++ /dev/null @@ -1,142 +0,0 @@ -modulus_poly = [1, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 1, 0, 1, 0, 0, 1, - 1] -modulus_poly_as_int = sum([(v << i) for i, v in enumerate(modulus_poly)]) -degree = len(modulus_poly) - 1 - -two_to_the_degree = 2**degree -two_to_the_degree_m1 = 2**degree - 1 - -def galoistpl(a): - # 2 is not a primitive root, so we have to use 3 as our logarithm base - if a * 2 < two_to_the_degree: - return (a * 2) ^ a - else: - return (a * 2) ^ a ^ modulus_poly_as_int - -# Precomputing a log table for increased speed of addition and multiplication -glogtable = [0] * (two_to_the_degree) -gexptable = [] -v = 1 -for i in range(two_to_the_degree_m1): - glogtable[v] = i - gexptable.append(v) - v = galoistpl(v) - -gexptable += gexptable + gexptable + [0] * two_to_the_degree * 4 -glogtable[0] = two_to_the_degree_m1 * 3 - -# Add two values in the Galois field -def galois_add(x, y): - return x ^ y - -# In binary fields, addition and subtraction are the same thing -galois_sub = galois_add - -# Multiply two values in the Galois field -def galois_mul(x, y): - return gexptable[glogtable[x] + glogtable[y]] - -# Divide two values in the Galois field -def galois_div(x, y): - return gexptable[glogtable[x] - glogtable[y] + two_to_the_degree_m1] - -# Evaluate a polynomial at a point -def eval_poly_at(p, x): - if x == 0: - return p[0] - y = 0 - logx = glogtable[x] - for i, p_coeff in enumerate(p): - if p_coeff: - # Add x**i * coeff - y ^= gexptable[(logx * i + glogtable[p_coeff]) % two_to_the_degree_m1] - return y - - -# Given p+1 y values and x values with no errors, recovers the original -# p+1 degree polynomial. -# Lagrange interpolation works roughly in the following way. -# 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] -# 2. For each x, generate a polynomial which equals its corresponding -# y coordinate at that point and 0 at all other points provided. -# 3. Add these polynomials together. - -def lagrange_interp(pieces, xs): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - root = [1] - for x in xs: - logx = glogtable[x] - root.insert(0, 0) - for j in range(len(root)-1): - if root[j+1] and x: - root[j] ^= gexptable[glogtable[root[j+1]] + logx] - #print(root) - assert len(root) == len(pieces) + 1 - # print(root) - # Generate per-value numerator polynomials, eg. for x=x2, - # (x - x1) * (x - x3) * ... * (x - xn), by dividing the master - # polynomial back by each x coordinate - nums = [] - for x in xs: - output = [0] * (len(root) - 2) + [1] - logx = glogtable[x] - for j in range(len(root) - 2, 0, -1): - if output[j] and x: - output[j-1] = root[j] ^ gexptable[glogtable[output[j]] + logx] - else: - output[j-1] = root[j] - assert len(output) == len(pieces) - nums.append(output) - #print(nums) - # Generate denominators by evaluating numerator polys at each x - denoms = [eval_poly_at(nums[i], xs[i]) for i in range(len(xs))] - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - b = [0 for p in pieces] - for i in range(len(xs)): - log_yslice = glogtable[pieces[i]] - glogtable[denoms[i]] + two_to_the_degree_m1 - for j in range(len(pieces)): - if nums[i][j] and pieces[i]: - b[j] ^= gexptable[glogtable[nums[i][j]] + log_yslice] - return b - -def add_polys(a, b): - return [(a[i] if i < len(a) else 0) ^ (b[i] if i < len(b) else 0) - for i in range(max(len(a), len(b)))] - -def mul_by_const(a, c): - logc = glogtable[c] - return [gexptable[glogtable[x] + logc] for x in a] - -def mul_polys(a, b): - o = [0] * (len(a) + len(b) - 1) - for i, aval in enumerate(a): - for j, bval in enumerate(b): - o[i+j] ^= gexptable[glogtable[a[i]] + glogtable[b[j]]] - return o - -def div_polys(a, b): - assert len(a) >= len(b) - a = [x for x in a] - o = [] - apos = len(a) - 1 - bpos = len(b) - 1 - diff = apos - bpos - while diff >= 0: - quot = gexptable[glogtable[a[apos]] - glogtable[b[bpos]] + two_to_the_degree_m1] - o.insert(0, quot) - for i in range(bpos, -1, -1): - a[diff+i] ^= gexptable[glogtable[b[i]] + glogtable[quot]] - apos -= 1 - diff -= 1 - return o - -def compose_polys(a, b): - o = [] - p = [1] - for c in a: - o = add_polys(o, mul_by_const(p, c)) - p = mul_polys(p, b) - return o - diff --git a/erasure_code/ec65536/ec65536/subquadratic_poly_utils.py b/erasure_code/ec65536/ec65536/subquadratic_poly_utils.py deleted file mode 100644 index c069678..0000000 --- a/erasure_code/ec65536/ec65536/subquadratic_poly_utils.py +++ /dev/null @@ -1,198 +0,0 @@ -modulus_poly = [1, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 1, 0, 1, 0, 0, 1, - 1] -modulus_poly_as_int = sum([(v << i) for i, v in enumerate(modulus_poly)]) -degree = len(modulus_poly) - 1 - -two_to_the_degree = 2**degree -two_to_the_degree_m1 = 2**degree - 1 - -def galoistpl(a): - # 2 is not a primitive root, so we have to use 3 as our logarithm base - if a * 2 < two_to_the_degree: - return (a * 2) ^ a - else: - return (a * 2) ^ a ^ modulus_poly_as_int - -# Precomputing a log table for increased speed of addition and multiplication -glogtable = [0] * (two_to_the_degree) -gexptable = [] -v = 1 -for i in range(two_to_the_degree_m1): - glogtable[v] = i - gexptable.append(v) - v = galoistpl(v) - -gexptable += gexptable + gexptable - -# Add two values in the Galois field -def galois_add(x, y): - return x ^ y - -# In binary fields, addition and subtraction are the same thing -galois_sub = galois_add - -# Multiply two values in the Galois field -def galois_mul(x, y): - return 0 if x*y == 0 else gexptable[glogtable[x] + glogtable[y]] - -# Divide two values in the Galois field -def galois_div(x, y): - return 0 if x == 0 else gexptable[(glogtable[x] - glogtable[y]) % two_to_the_degree_m1] - -# Evaluate a polynomial at a point -def eval_poly_at(p, x): - if x == 0: - return p[0] - y = 0 - logx = glogtable[x] - for i, p_coeff in enumerate(p): - if p_coeff: - # Add x**i * coeff - y ^= gexptable[(logx * i + glogtable[p_coeff]) % two_to_the_degree_m1] - return y - - -# Given p+1 y values and x values with no errors, recovers the original -# p+1 degree polynomial. -# Lagrange interpolation works roughly in the following way. -# 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] -# 2. For each x, generate a polynomial which equals its corresponding -# y coordinate at that point and 0 at all other points provided. -# 3. Add these polynomials together. - -def lagrange_interp(pieces, xs): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - root = mk_root_2(xs) - #print(root) - assert len(root) == len(pieces) + 1 - # print(root) - # Generate the derivative - d = derivative(root) - # Generate denominators by evaluating numerator polys at each x - denoms = multi_eval_2(d, xs) - print(denoms) - # denoms = [eval_poly_at(d, xs[i]) for i in range(len(xs))] - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - factors = [galois_div(p, d) for p, d in zip(pieces, denoms)] - o = multi_root_derive(xs, factors) - # print(o) - return o - -def multi_root_derive(xs, muls): - if len(xs) == 1: - return [muls[0]] - R1 = mk_root_2(xs[:len(xs) // 2]) - R2 = mk_root_2(xs[len(xs) // 2:]) - x1 = karatsuba_mul(R1, multi_root_derive(xs[len(xs) // 2:], muls[len(muls) // 2:]) + [0]) - x2 = karatsuba_mul(R2, multi_root_derive(xs[:len(xs) // 2], muls[:len(muls) // 2]) + [0]) - o = [v1 ^ v2 for v1, v2 in zip(x1, x2)][:len(xs)] - # print(len(R1), len(x1), len(xs), len(o)) - return o - -def multi_root_derive_1(xs, muls): - o = [0] * len(xs) - for i in range(len(xs)): - _xs = xs[:i] + xs[(i+1):] - root = mk_root_2(_xs) - for j in range(len(root)): - o[j] ^= galois_mul(root[j], muls[i]) - return o - -a = 124 -b = 8932 -c = 12415 - -assert galois_mul(galois_add(a, b), c) == galois_add(galois_mul(a, c), galois_mul(b, c)) - -def karatsuba_mul(p1, p2): - L = len(p1) - # assert L == len(p2) - if L <= 16: - o = [0] * (L * 2) - for i, v1 in enumerate(p1): - for j, v2 in enumerate(p2): - if v1 and v2: - o[i + j] ^= gexptable[glogtable[v1] + glogtable[v2]] - return o - if L % 2: - p1 = p1 + [0] - p2 = p2 + [0] - L += 1 - halflen = L // 2 - low1 = p1[:halflen] - high1 = p1[halflen:] - sum1 = [l ^ h for l, h in zip(low1, high1)] - low2 = p2[:halflen] - high2 = p2[halflen:] - sum2 = [l ^ h for l, h in zip(low2, high2)] - z2 = karatsuba_mul(high1, high2) - z0 = karatsuba_mul(low1, low2) - z1 = [m ^ _z0 ^ _z2 for m, _z0, _z2 in zip(karatsuba_mul(sum1, sum2), z0, z2)] - o = z0[:halflen] + \ - [a ^ b for a, b in zip(z0[halflen:], z1[:halflen])] + \ - [a ^ b for a, b in zip(z2[:halflen], z1[halflen:])] + \ - z2[halflen:] - return o - -def mk_root_1(xs): - root = [1] - for x in xs: - logx = glogtable[x] - root.insert(0, 0) - for j in range(len(root)-1): - if root[j+1] and x: - root[j] ^= gexptable[glogtable[root[j+1]] + logx] - return root - -def mk_root_2(xs): - if len(xs) >= 128: - return karatsuba_mul(mk_root_2(xs[:len(xs) // 2]), mk_root_2(xs[len(xs) // 2:]))[:len(xs) + 1] - root = [1] - for x in xs: - logx = glogtable[x] - root.insert(0, 0) - for j in range(len(root)-1): - if root[j+1] and x: - root[j] ^= gexptable[glogtable[root[j+1]] + logx] - return root - -def derivative(root): - return [0 if i % 2 else r for i, r in enumerate(root[1:])] - -# Credit to http://people.csail.mit.edu/madhu/ST12/scribe/lect06.pdf for the algorithm -def xn_mod_poly(p): - if len(p) == 1: - return [galois_div(1, p[0])] - halflen = len(p) // 2 - lowinv = xn_mod_poly(p[:halflen]) - submod_high = karatsuba_mul(lowinv, p[:halflen])[halflen:] - med = karatsuba_mul(p[halflen:], lowinv)[:halflen] - med_plus_high = [x ^ y for x, y in zip(med, submod_high)] - highinv = karatsuba_mul(med_plus_high, lowinv) - o = (lowinv + highinv)[:len(p)] - print(halflen, lowinv, submod_high, med, highinv) - # assert karatsuba_mul(o, p)[:len(p)] == [1] + [0] * (len(p) - 1) - return o - -def mod(a, b): - assert len(a) == 2 * (len(b) - 1) - L = len(b) - inv_rev_b = xn_mod_poly(b[::-1] + [0] * (len(a) - L))[:L] - quot = karatsuba_mul(inv_rev_b, a[::-1][:L])[:L-1][::-1] - subt = karatsuba_mul(b, quot + [0])[:-1] - o = [x ^ y for x, y in zip(a[:L-1], subt[:L-1])] - # assert [x^y for x, y in zip(karatsuba_mul(quot + [0], b), o)] == a - return o - -def multi_eval_1(poly, xs): - return [eval_poly_at(poly, x) for x in xs] - -def multi_eval_2(poly, xs): - if len(xs) <= 1024: - return [eval_poly_at(poly, x) for x in xs] - halflen = len(xs) // 2 - return multi_eval_2(mod(poly, mk_root_2(xs[:halflen])), xs[:halflen]) + \ - multi_eval_2(mod(poly, mk_root_2(xs[halflen:])), xs[halflen:]) - # [eval_poly_at(poly, xs[-2]), eval_poly_at(poly, xs[-1])] diff --git a/erasure_code/ec65536/faster_poly_utils.cpp b/erasure_code/ec65536/faster_poly_utils.cpp deleted file mode 100644 index 409af7d..0000000 --- a/erasure_code/ec65536/faster_poly_utils.cpp +++ /dev/null @@ -1,340 +0,0 @@ -#include "stdlib.h" -#include "stdio.h" -#include -#include -#include - -using namespace std; - -vector glogtable(65536, 0); -vector gexptable(196608, 0); - -const int ROOT_CUTOFF = 32; - -void initialize_tables() { - int v = 1; - for (int i = 0; i < 65536; i++) { - glogtable[v] = i; - gexptable[i] = v; - gexptable[i + 65535] = v; - gexptable[i + 131070] = v; - if (v & 32768) - v = (v * 2) ^ v ^ 103425; - else - v = (v * 2) ^ v; - } -} - -int eval_poly_at(vector poly, int x) { - if (x == 0) - return poly[0]; - int logx = glogtable[x]; - int y = 0; - for (int i = 0; i < poly.size(); i++) { - if (poly[i]) - y ^= gexptable[(logx * i + glogtable[poly[i]]) % 65535]; - } - return y; -} - -int eval_log_poly_at(vector poly, int x) { - if (x == 0) - return poly[0] == 65537 ? 0 : gexptable[poly[0]]; - int logx = glogtable[x]; - int y = 0; - for (int i = 0; i < poly.size(); i++) { - if (poly[i] != 65537) - y ^= gexptable[(logx * i + poly[i]) % 65535]; - } - return y; -} - -// Compute the product of two (equal length) polynomials. Takes ~O(N ** 1.59) time. -vector karatsuba_mul(vector p, vector q) { - int L = p.size(); - if (L <= 64) { - vector o(L * 2); - vector logq(L); - for (int i = 0; i < L; i++) logq[i] = glogtable[q[i]]; - for (int i = 0; i < L; i++) { - int log_pi = glogtable[p[i]]; - for (int j = 0; j < L; j++) { - if (p[i] && q[j]) - o[i + j] ^= gexptable[log_pi + logq[j]]; - } - } - return o; - } - if (L % 2) { - L += 1; - p.push_back(0); - q.push_back(0); - } - int halflen = L / 2; - vector low1 = vector(p.begin(), p.begin() + halflen); - vector low2 = vector(q.begin(), q.begin() + halflen); - vector high1 = vector(p.begin() + halflen, p.end()); - vector high2 = vector(q.begin() + halflen, q.end()); - vector sum1(halflen); - vector sum2(halflen); - for (int i = 0; i < halflen; i++) { - sum1[i] = low1[i] ^ high1[i]; - sum2[i] = low2[i] ^ high2[i]; - } - vector z0 = karatsuba_mul(low1, low2); - vector z2 = karatsuba_mul(high1, high2); - vector m = karatsuba_mul(sum1, sum2); - vector o(L * 2); - for (int i = 0; i < L; i++) { - o[i] ^= z0[i]; - o[i + halflen] ^= (m[i] ^ z0[i] ^ z2[i]); - o[i + L] ^= z2[i]; - } - return o; -} - -vector mk_root(vector xs) { - int L = xs.size(); - if (L >= ROOT_CUTOFF) { - int halflen = L / 2; - vector left = vector(xs.begin(), xs.begin() + halflen); - vector right = vector(xs.begin() + halflen, xs.end()); - vector o = karatsuba_mul(mk_root(left), mk_root(right)); - o.resize(L + 1); - return o; - } - vector root(L + 1); - root[L] = 1; - for (int i = 0; i < L; i++) { - int logx = glogtable[xs[i]]; - int offset = L - i - 1; - root[offset] = 0; - for (int j = offset; j < i + 1 + offset; j++) { - if (root[j + 1] and xs[i]) - root[j] ^= gexptable[glogtable[root[j+1]] + logx]; - } - } - return root; -} - -vector subroot_linear_combination(vector xs, vector factors) { - int L = xs.size(); - /*if (L <= ROOT_CUTOFF) { - vector out(L + 1); - vector root = mk_root(xs); - for (int i = 0; i < L; i++) { - vector output(L + 1); - output[root.size() - 2] = 1; - int logx = glogtable[xs[i]]; - if (factors[i]) { - int log_fac = glogtable[factors[i]]; - for (int j = root.size() - 2; j > 0; j--) { - if (output[j] and xs[i]) - output[j - 1] = root[j] ^ gexptable[glogtable[output[j]] + logx]; - else - output[j - 1] = root[j]; - out[j] ^= gexptable[glogtable[output[j]] + log_fac]; - } - out[0] ^= gexptable[glogtable[output[0]] + log_fac]; - } - } - return out; - }*/ - if (L == 1) { - vector o(2); - o[0] = factors[0]; - return o; - } - int halflen = L / 2; - vector xs_left = vector(xs.begin(), xs.begin() + halflen); - vector xs_right = vector(xs.begin() + halflen, xs.end()); - vector factors_left = vector(factors.begin(), factors.begin() + halflen); - vector factors_right = vector(factors.begin() + halflen, factors.end()); - vector R1 = mk_root(xs_left); - vector R2 = mk_root(xs_right); - vector o1 = karatsuba_mul(R1, subroot_linear_combination(xs_right, factors_right)); - vector o2 = karatsuba_mul(R2, subroot_linear_combination(xs_left, factors_left)); - vector o(L + 1); - for (int i = 0; i < L; i++) { - o[i] = o1[i] ^ o2[i]; - } - return o; -} - - -vector derivative_and_square_base(vector p) { - vector o((p.size() - 1) / 2); - for (int i = 0; i < o.size(); i+= 1) { - o[i] = p[i * 2 + 1]; - } - return o; -} - -vector poly_to_logs(vector p) { - vector o(p.size()); - for (int i = 0; i < p.size(); i++) { - if (p[i]) - o[i] = glogtable[p[i]]; - else - o[i] = 65537; - } - return o; -} - -vector xn_mod_poly(vector inp) { - if (inp.size() == 1) { - vector o(1); - o[0] = gexptable[65535 - glogtable[inp[0]]]; - return o; - } - int halflen = inp.size() / 2; - int highlen = inp.size() - (inp.size() / 2); - vector low(inp.begin(), inp.begin() + halflen); - vector high(inp.begin() + halflen, inp.end()); - vector lowinv = xn_mod_poly(low); - vector submod = karatsuba_mul(lowinv, low); - vector submod_high(submod.begin() + halflen, submod.end()); - lowinv.resize(highlen); - vector med = karatsuba_mul(high, lowinv); - vector med_plus_high(halflen); - for (int i = 0; i < halflen; i++) { - med_plus_high[i] = med[i] ^ submod_high[i]; - } - vector highinv = karatsuba_mul(med_plus_high, lowinv); - vector o(inp.size()); - for (int i = 0; i < halflen; i++) { - o[i] = lowinv[i]; - o[i + halflen] = highinv[i]; - } - return o; -} - -vector reverse(vector inp) { - vector o(inp.size()); - for (int i = 0; i < inp.size(); i++) { - o[inp.size() - 1 - i] = inp[i]; - } - return o; -} - -vector mod(vector a, vector b) { - int L = b.size(); - vector rev_b = reverse(b); - rev_b.resize((L - 1) * 2); - vector inv_rev_b = xn_mod_poly(reverse(b)); - inv_rev_b.resize(L); - vector rev_a = reverse(a); - rev_a.resize(L); - vector rev_quotient = karatsuba_mul(inv_rev_b, rev_a); - rev_quotient.resize(L - 1); - vector quotient = reverse(rev_quotient); - quotient.resize(L); - vector diff = karatsuba_mul(b, quotient); - vector o(L-1); - for (int i = 0; i < L-1; i++) { - o[i] = a[i] ^ diff[i]; - } - return o; -} - -vector multi_eval(vector poly, vector xs) { - int L = xs.size(); - if (L <= 1024) { - vector o(L); - vector logz = poly_to_logs(poly); - for (int i = 0; i < L; i++) { - o[i] = eval_log_poly_at(logz, xs[i]); - } - return o; - } - int halflen = L / 2; - vector left(xs.begin(), xs.begin() + halflen); - vector right(xs.begin() + halflen, xs.end()); - vector o1; - vector o2; - if (poly.size() < xs.size()) { - o1 = multi_eval(poly, left); - o2 = multi_eval(poly, right); - } - else { - o1 = multi_eval(mod(poly, mk_root(left)), left); - o2 = multi_eval(mod(poly, mk_root(right)), right); - } - o1.resize(L); - for (int i = 0; i < halflen; i++) { - o1[halflen + i] = o2[i]; - } - return o1; -} - -vector lagrange_interp(vector ys, vector xs) { - int xs_size = xs.size(); - vector root = mk_root(xs); - vector rootprime = derivative_and_square_base(root); - vector xsquares(xs_size); - for (int i = 0; i < xs_size; i++) - xsquares[i] = xs[i] ? gexptable[glogtable[xs[i]] * 2] : 0; - vector denoms = multi_eval(rootprime, xsquares); - vector factors(xs_size); - for (int i = 0; i < xs_size; i++) { - if (ys[i]) - factors[i] = gexptable[glogtable[ys[i]] + 65535 - glogtable[denoms[i]]]; - } - vector o = subroot_linear_combination(xs, factors); - o.resize(xs_size); - return o; -} - -const int SIZE = 4096; - - -int main() { - initialize_tables(); - /*int myxs[] = {1, 2, 3, 4, 5}; - std::vector test (myxs, myxs + sizeof(myxs) / sizeof(int) ); - int myxs2[] = {6, 7, 8, 9, 10, 11, 12, 13}; - std::vector test2 (myxs2, myxs2 + sizeof(myxs2) / sizeof(int) );*/ - /*std::vector test(257); - for (int i = 0; i < 257; i++) test[i] = i; - std::vector test2(512); - for (int i = 0; i < 512; i++) test2[i] = 1000 + i; - vector moose = mod(test2, test); - for (int i = 0; i < 256; i++) cout << moose[i] << " "; - cout << "\n";*/ - - vector xs(SIZE); - vector ys(SIZE); - for (int v = 0; v < SIZE; v++) { - ys[v] = v * 3; - xs[v] = 1000 + v * 7; - } - //vector d = derivative(mk_root(xs)); - //for (int i = 0; i < d.size(); i++) cout << d[i] << " "; - //cout << "\n"; - /*vector prod = mk_root(xs); - vector prod = karatsuba_mul(xs, ys); - for (int i = 0; i < SIZE + 1; i++) - cout << prod[i] << " "; - cout << "\n"; - cout << eval_poly_at(prod, 189) << " " << gexptable[glogtable[eval_poly_at(xs, 189)] + glogtable[eval_poly_at(ys, 189)]] << "\n";*/ - for (int a = 0; a < 10; a++) { - ys[0] = a; - vector poly = lagrange_interp(ys, xs); - vector new_xs(SIZE); - for (int i = 0; i < SIZE; i++) new_xs[i] = SIZE + i; - vector results = multi_eval(poly, new_xs); - cout << eval_poly_at(poly, 1700) << "\n"; - unsigned int o = 0; - for (int i = 0; i < SIZE; i++) { - o += results[i]; - } - cout << o << "\n"; - } - //cout << eval_poly_at(poly, 0) << " " << ys[0] << "\n"; - //cout << eval_poly_at(poly, 134) << " " << ys[134] << "\n"; - //cout << eval_poly_at(poly, 375) << " " << ys[375] << "\n"; - //int o; - //for (int i = 0; i < 524288; i ++) - // o += eval_poly_at(poly, i % 65536); - //std::cout << o; -} diff --git a/erasure_code/ec65536/poly_utils.cpp b/erasure_code/ec65536/poly_utils.cpp deleted file mode 100644 index 03b058c..0000000 --- a/erasure_code/ec65536/poly_utils.cpp +++ /dev/null @@ -1,238 +0,0 @@ -#include "stdlib.h" -#include "stdio.h" -#include -#include -#include - -using namespace std; - -vector glogtable(65536, 0); -vector gexptable(196608, 0); - -const int ROOT_CUTOFF = 32; - -void initialize_tables() { - int v = 1; - for (int i = 0; i < 65536; i++) { - glogtable[v] = i; - gexptable[i] = v; - gexptable[i + 65535] = v; - gexptable[i + 131070] = v; - if (v & 32768) - v = (v * 2) ^ v ^ 103425; - else - v = (v * 2) ^ v; - } -} - -int eval_poly_at(vector poly, int x) { - if (x == 0) - return poly[0]; - int logx = glogtable[x]; - int y = 0; - for (int i = 0; i < poly.size(); i++) { - if (poly[i]) - y ^= gexptable[(logx * i + glogtable[poly[i]]) % 65535]; - } - return y; -} - -int eval_log_poly_at(vector poly, int x) { - if (x == 0) - return poly[0] == 65537 ? 0 : gexptable[poly[0]]; - int logx = glogtable[x]; - int y = 0; - for (int i = 0; i < poly.size(); i++) { - if (poly[i] != 65537) - y ^= gexptable[(logx * i + poly[i]) % 65535]; - } - return y; -} - -// Compute the product of two (equal length) polynomials. Takes ~O(N ** 1.59) time. -vector karatsuba_mul(vector p, vector q) { - int L = p.size(); - if (L <= 64) { - vector o(L * 2); - vector logq(L); - for (int i = 0; i < L; i++) logq[i] = glogtable[q[i]]; - for (int i = 0; i < L; i++) { - int log_pi = glogtable[p[i]]; - for (int j = 0; j < L; j++) { - if (p[i] && q[j]) - o[i + j] ^= gexptable[log_pi + logq[j]]; - } - } - return o; - } - if (L % 2) { - L += 1; - p.push_back(0); - q.push_back(0); - } - int halflen = L / 2; - vector low1 = vector(p.begin(), p.begin() + halflen); - vector low2 = vector(q.begin(), q.begin() + halflen); - vector high1 = vector(p.begin() + halflen, p.end()); - vector high2 = vector(q.begin() + halflen, q.end()); - vector sum1(halflen); - vector sum2(halflen); - for (int i = 0; i < halflen; i++) { - sum1[i] = low1[i] ^ high1[i]; - sum2[i] = low2[i] ^ high2[i]; - } - vector z0 = karatsuba_mul(low1, low2); - vector z2 = karatsuba_mul(high1, high2); - vector m = karatsuba_mul(sum1, sum2); - vector o(L * 2); - for (int i = 0; i < L; i++) { - o[i] ^= z0[i]; - o[i + halflen] ^= (m[i] ^ z0[i] ^ z2[i]); - o[i + L] ^= z2[i]; - } - return o; -} - -vector mk_root(vector xs) { - int L = xs.size(); - if (L >= ROOT_CUTOFF) { - int halflen = L / 2; - vector left = vector(xs.begin(), xs.begin() + halflen); - vector right = vector(xs.begin() + halflen, xs.end()); - vector o = karatsuba_mul(mk_root(left), mk_root(right)); - o.resize(L + 1); - return o; - } - vector root(L + 1); - root[L] = 1; - for (int i = 0; i < L; i++) { - int logx = glogtable[xs[i]]; - int offset = L - i - 1; - root[offset] = 0; - for (int j = offset; j < i + 1 + offset; j++) { - if (root[j + 1] and xs[i]) - root[j] ^= gexptable[glogtable[root[j+1]] + logx]; - } - } - return root; -} - -vector subroot_linear_combination(vector xs, vector factors) { - int L = xs.size(); - /*if (L <= ROOT_CUTOFF) { - vector out(L + 1); - vector root = mk_root(xs); - for (int i = 0; i < L; i++) { - vector output(L + 1); - output[root.size() - 2] = 1; - int logx = glogtable[xs[i]]; - if (factors[i]) { - int log_fac = glogtable[factors[i]]; - for (int j = root.size() - 2; j > 0; j--) { - if (output[j] and xs[i]) - output[j - 1] = root[j] ^ gexptable[glogtable[output[j]] + logx]; - else - output[j - 1] = root[j]; - out[j] ^= gexptable[glogtable[output[j]] + log_fac]; - } - out[0] ^= gexptable[glogtable[output[0]] + log_fac]; - } - } - return out; - }*/ - if (L == 1) { - vector o(2); - o[0] = factors[0]; - return o; - } - int halflen = L / 2; - vector xs_left = vector(xs.begin(), xs.begin() + halflen); - vector xs_right = vector(xs.begin() + halflen, xs.end()); - vector factors_left = vector(factors.begin(), factors.begin() + halflen); - vector factors_right = vector(factors.begin() + halflen, factors.end()); - vector R1 = mk_root(xs_left); - vector R2 = mk_root(xs_right); - vector o1 = karatsuba_mul(R1, subroot_linear_combination(xs_right, factors_right)); - vector o2 = karatsuba_mul(R2, subroot_linear_combination(xs_left, factors_left)); - vector o(L + 1); - for (int i = 0; i < L; i++) { - o[i] = o1[i] ^ o2[i]; - } - return o; -} - - -vector derivative_and_square_base(vector p) { - vector o((p.size() - 1) / 2); - for (int i = 0; i < o.size(); i+= 1) { - o[i] = p[i * 2 + 1]; - } - return o; -} - -vector poly_to_logs(vector p) { - vector o(p.size()); - for (int i = 0; i < p.size(); i++) { - if (p[i]) - o[i] = glogtable[p[i]]; - else - o[i] = 65537; - } - return o; -} - -vector lagrange_interp(vector ys, vector xs) { - int xs_size = xs.size(); - vector root = mk_root(xs); - vector log_rootprime = poly_to_logs(derivative_and_square_base(root)); - vector factors(xs_size); - for (int i = 0; i < xs_size; i++) { - int x_square = xs[i] ? gexptable[glogtable[xs[i]] * 2] : 0; - int denom = eval_log_poly_at(log_rootprime, x_square); - if (ys[i]) - factors[i] = gexptable[glogtable[ys[i]] + 65535 - glogtable[denom]]; - } - return subroot_linear_combination(xs, factors); -} - -const int SIZE = 4096; - - -int main() { - initialize_tables(); - //int myxs[] = {1, 2, 3, 4}; - //std::vector xs (myxs, myxs + sizeof(myxs) / sizeof(int) ); - vector xs(SIZE); - vector ys(SIZE); - for (int v = 0; v < SIZE; v++) { - ys[v] = v * 3; - xs[v] = 1000 + v * 7; - } - //vector d = derivative(mk_root(xs)); - //for (int i = 0; i < d.size(); i++) cout << d[i] << " "; - //cout << "\n"; - /*vector prod = mk_root(xs); - vector prod = karatsuba_mul(xs, ys); - for (int i = 0; i < SIZE + 1; i++) - cout << prod[i] << " "; - cout << "\n"; - cout << eval_poly_at(prod, 189) << " " << gexptable[glogtable[eval_poly_at(xs, 189)] + glogtable[eval_poly_at(ys, 189)]] << "\n";*/ - for (int a = 0; a < 10; a++) { - ys[0] = a; - vector poly = lagrange_interp(ys, xs); - vector logpoly = poly_to_logs(poly); - cout << eval_poly_at(poly, 1700) << "\n"; - unsigned int o = 0; - for (int i = SIZE; i < SIZE * 2; i++) { - o += eval_log_poly_at(logpoly, i); - } - cout << o << "\n"; - } - //cout << eval_poly_at(poly, 0) << " " << ys[0] << "\n"; - //cout << eval_poly_at(poly, 134) << " " << ys[134] << "\n"; - //cout << eval_poly_at(poly, 375) << " " << ys[375] << "\n"; - //int o; - //for (int i = 0; i < 524288; i ++) - // o += eval_poly_at(poly, i % 65536); - //std::cout << o; -} diff --git a/erasure_code/ec65536/setup.py b/erasure_code/ec65536/setup.py deleted file mode 100644 index 12b42d1..0000000 --- a/erasure_code/ec65536/setup.py +++ /dev/null @@ -1,24 +0,0 @@ -# -*- coding: utf-8 -*- - -from setuptools import setup, find_packages - - -with open('README.md') as f: - readme = f.read() - -with open('LICENSE') as f: - license = f.read() - -setup( - name='ec65536', - version='1.0.0', - description='Erasure code utilities for GF16', - long_description=readme, - author='Vitalik Buterin', - author_email='', - url='https://github.com/ethereum/research/tree/master/erasure_code/ec65536', - license=license, - packages=find_packages(exclude=('tests', 'docs')), - install_requires=[ - ], -) diff --git a/erasure_code/ec65536/tests/test_basic_ops.py b/erasure_code/ec65536/tests/test_basic_ops.py deleted file mode 100644 index ad207f4..0000000 --- a/erasure_code/ec65536/tests/test_basic_ops.py +++ /dev/null @@ -1,17 +0,0 @@ -from ec65536 import * - -a = 124 -b = 8932 -c = 12415 - -assert galois_mul(galois_add(a, b), c) == galois_add(galois_mul(a, c), galois_mul(b, c)) - -k1 = list(range(10)) -k2 = list(range(100, 200)) -k3 = mul_polys(k1, k2) -assert div_polys(k3, k1) == k2 -assert div_polys(k3, k2) == k1 -assert galois_mul(eval_poly_at(k1, 9999), eval_poly_at(k2, 9999)) == \ - eval_poly_at(k3, 9999) -k4 = compose_polys(k1, k2) -assert eval_poly_at(k4, 9998) == eval_poly_at(k1, eval_poly_at(k2, 9998)) diff --git a/erasure_code/ec65536/tests/test_ec65536.py b/erasure_code/ec65536/tests/test_ec65536.py deleted file mode 100644 index b8a70a6..0000000 --- a/erasure_code/ec65536/tests/test_ec65536.py +++ /dev/null @@ -1,27 +0,0 @@ -import ec65536 -import rlp -import time - -# 12.8 kilobyte test string -testdata = 'the cow jumped over the moon!!! ' * 400 - -t1 = time.time() -prover = ec65536.Prover(testdata) -t2 = time.time() -print("Created prover in %.2f sec" % (t2 - t1)) - -assert ec65536.verify_proof(prover.merkle_root, prover.prove(13), 13) -t3 = time.time() -print("Created and verified a proof in %.2f sec" % (t3 - t2)) - -proofs = [prover.prove(i) for i in range(0, prover.length, 2)] -print("Created merkle proofs") - -t4 = time.time() -print("Starting to attempt fill") -response = ec65536.fill(prover.merkle_root, prover.length // 2, proofs, list(range(0, prover.length, 2))) -t5 = time.time() -print("Completed fill in %.2f sec" % (t5 - t4)) -assert response is not False -assert b''.join(response)[:len(rlp.encode(testdata))] == rlp.encode(testdata) -print("Fill successful") diff --git a/erc4337/compression_schemes.py b/erc4337/compression_schemes.py deleted file mode 100644 index e764381..0000000 --- a/erc4337/compression_schemes.py +++ /dev/null @@ -1,79 +0,0 @@ -import snappy - -data = bytes.fromhex('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'[2:]) - -def zrle_compress(inp): - o = [] - pos = 0 - while pos < len(inp): - zcount = 0 - while pos + zcount < len(inp) and inp[pos + zcount] == 0 and zcount < 255: - zcount += 1 - if zcount > 0: - pos += zcount - o.extend([0, zcount]) - else: - o.append(inp[pos]) - pos += 1 - return bytes(o) - -def zrle_decompress(inp): - o = [] - pos = 0 - while pos < len(inp): - if inp[pos] != 0: - o.append(inp[pos]) - pos += 1 - else: - o.extend([0] * inp[pos + 1]) - pos += 2 - return bytes(o) - -def ctl_compress(inp): - assert len(inp) % 32 == 0 - o = [] - for pos in range(0, len(inp), 32): - chunk = inp[pos: pos+32] - l_stripped_chunk = chunk.lstrip(b'\x00') - r_stripped_chunk = chunk.rstrip(b'\x00') - if len(l_stripped_chunk) < len(r_stripped_chunk): - o.append(len(l_stripped_chunk)) - o.extend(l_stripped_chunk) - else: - o.append(128 + len(r_stripped_chunk)) - o.extend(r_stripped_chunk) - return bytes(o) - -def ctl_decompress(inp): - o = [] - pos = 0 - while pos < len(inp): - chunk_length = inp[pos] - stripped_chunk = inp[pos + 1: pos + 1 + (chunk_length % 128)] - if chunk_length < 128: - o.extend([0] * (32 - chunk_length)) - o.extend(stripped_chunk) - else: - o.extend(stripped_chunk) - o.extend([0] * (160 - chunk_length)) - pos += 1 + (chunk_length % 128) - return bytes(o) - -def gascost(data): - return len(data) * 16 - 12 * data.count(b'\x00') - -print("Raw data: length {} gas cost {}".format(len(data), gascost(data))) - -#for i in range(0, len(data), 32): -# print(data[i:i+32].hex()) - -zdata = zrle_compress(data) -assert data == zrle_decompress(zdata) -print("ZRLE: length {} gas cost {}".format(len(zdata), gascost(zdata))) - -cdata = ctl_compress(data) -assert data == ctl_decompress(cdata) -print("CTL: length {} gas cost {}".format(len(cdata), gascost(cdata))) - -sdata = snappy.compress(data) -print("Snappy: length {} gas cost {}".format(len(sdata), gascost(sdata))) diff --git a/eth1_simple_custody/poly_utils.py b/eth1_simple_custody/poly_utils.py deleted file mode 100644 index 55c6294..0000000 --- a/eth1_simple_custody/poly_utils.py +++ /dev/null @@ -1,224 +0,0 @@ -# Creates an object that includes convenience operations for numbers -# and polynomials in some prime field -class PrimeField(): - def __init__(self, modulus): - assert pow(2, modulus, modulus) == 2 - self.modulus = modulus - - def add(self, x, y): - return (x+y) % self.modulus - - def sub(self, x, y): - return (x-y) % self.modulus - - def mul(self, x, y): - return (x*y) % self.modulus - - def exp(self, x, p): - return pow(x, p, self.modulus) - - # Modular inverse using the extended Euclidean algorithm - def inv(self, a): - if a == 0: - return 0 - lm, hm = 1, 0 - low, high = a % self.modulus, self.modulus - while low > 1: - r = high//low - nm, new = hm-lm*r, high-low*r - lm, low, hm, high = nm, new, lm, low - return lm % self.modulus - - def multi_inv(self, values): - partials = [1] - for i in range(len(values)): - partials.append(self.mul(partials[-1], values[i] or 1)) - inv = self.inv(partials[-1]) - outputs = [0] * len(values) - for i in range(len(values), 0, -1): - outputs[i-1] = self.mul(partials[i-1], inv) if values[i-1] else 0 - inv = self.mul(inv, values[i-1] or 1) - return outputs - - def div(self, x, y): - return self.mul(x, self.inv(y)) - - # Evaluate a polynomial at a point - def eval_poly_at(self, p, x): - y = 0 - power_of_x = 1 - for i, p_coeff in enumerate(p): - y += power_of_x * p_coeff - power_of_x = (power_of_x * x) % self.modulus - return y % self.modulus - - # Arithmetic for polynomials - def add_polys(self, a, b): - return [((a[i] if i < len(a) else 0) + (b[i] if i < len(b) else 0)) - % self.modulus for i in range(max(len(a), len(b)))] - - def sub_polys(self, a, b): - return [((a[i] if i < len(a) else 0) - (b[i] if i < len(b) else 0)) - % self.modulus for i in range(max(len(a), len(b)))] - - def mul_by_const(self, a, c): - return [(x*c) % self.modulus for x in a] - - def mul_polys(self, a, b): - o = [0] * (len(a) + len(b) - 1) - for i, aval in enumerate(a): - for j, bval in enumerate(b): - o[i+j] += a[i] * b[j] - return [x % self.modulus for x in o] - - def div_polys(self, a, b): - assert len(a) >= len(b) - a = [x for x in a] - o = [] - apos = len(a) - 1 - bpos = len(b) - 1 - diff = apos - bpos - while diff >= 0: - quot = self.div(a[apos], b[bpos]) - o.insert(0, quot) - for i in range(bpos, -1, -1): - a[diff+i] -= b[i] * quot - apos -= 1 - diff -= 1 - return [x % self.modulus for x in o] - - def mod_polys(self, a, b): - return self.sub_polys(a, self.mul_polys(b, self.div_polys(a, b)))[:len(b)-1] - - # Build a polynomial from a few coefficients - def sparse(self, coeff_dict): - o = [0] * (max(coeff_dict.keys()) + 1) - for k, v in coeff_dict.items(): - o[k] = v % self.modulus - return o - - # Build a polynomial that returns 0 at all specified xs - def zpoly(self, xs): - root = [1] - for x in xs: - root.insert(0, 0) - for j in range(len(root)-1): - root[j] -= root[j+1] * x - return [x % self.modulus for x in root] - - # Given p+1 y values and x values with no errors, recovers the original - # p+1 degree polynomial. - # Lagrange interpolation works roughly in the following way. - # 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] - # 2. For each x, generate a polynomial which equals its corresponding - # y coordinate at that point and 0 at all other points provided. - # 3. Add these polynomials together. - - def lagrange_interp(self, xs, ys): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - root = self.zpoly(xs) - assert len(root) == len(ys) + 1 - # print(root) - # Generate per-value numerator polynomials, eg. for x=x2, - # (x - x1) * (x - x3) * ... * (x - xn), by dividing the master - # polynomial back by each x coordinate - nums = [self.div_polys(root, [-x, 1]) for x in xs] - # Generate denominators by evaluating numerator polys at each x - denoms = [self.eval_poly_at(nums[i], xs[i]) for i in range(len(xs))] - invdenoms = self.multi_inv(denoms) - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - b = [0 for y in ys] - for i in range(len(xs)): - yslice = self.mul(ys[i], invdenoms[i]) - for j in range(len(ys)): - if nums[i][j] and ys[i]: - b[j] += nums[i][j] * yslice - return [x % self.modulus for x in b] - - def lagrange_polys(self, xs): - ps = [] - for x in xs: - p = [1] - for x2 in xs: - if x != x2: - denominator = self.inv(x - x2) - p = self.mul_polys(p, [- x2 * denominator, denominator]) - ps.append(p) - return ps - - def zero_poly(self, xs): - p = [1] - for x in xs: - p = self.mul_polys(p, [-x, 1]) - return p - - # Optimized poly evaluation for degree 4 - def eval_quartic(self, p, x): - xsq = x * x % self.modulus - xcb = xsq * x - return (p[0] + p[1] * x + p[2] * xsq + p[3] * xcb) % self.modulus - - # Optimized version of the above restricted to deg-4 polynomials - def lagrange_interp_4(self, xs, ys): - x01, x02, x03, x12, x13, x23 = \ - xs[0] * xs[1], xs[0] * xs[2], xs[0] * xs[3], xs[1] * xs[2], xs[1] * xs[3], xs[2] * xs[3] - m = self.modulus - eq0 = [-x12 * xs[3] % m, (x12 + x13 + x23), -xs[1]-xs[2]-xs[3], 1] - eq1 = [-x02 * xs[3] % m, (x02 + x03 + x23), -xs[0]-xs[2]-xs[3], 1] - eq2 = [-x01 * xs[3] % m, (x01 + x03 + x13), -xs[0]-xs[1]-xs[3], 1] - eq3 = [-x01 * xs[2] % m, (x01 + x02 + x12), -xs[0]-xs[1]-xs[2], 1] - e0 = self.eval_poly_at(eq0, xs[0]) - e1 = self.eval_poly_at(eq1, xs[1]) - e2 = self.eval_poly_at(eq2, xs[2]) - e3 = self.eval_poly_at(eq3, xs[3]) - e01 = e0 * e1 - e23 = e2 * e3 - invall = self.inv(e01 * e23) - inv_y0 = ys[0] * invall * e1 * e23 % m - inv_y1 = ys[1] * invall * e0 * e23 % m - inv_y2 = ys[2] * invall * e01 * e3 % m - inv_y3 = ys[3] * invall * e01 * e2 % m - return [(eq0[i] * inv_y0 + eq1[i] * inv_y1 + eq2[i] * inv_y2 + eq3[i] * inv_y3) % m for i in range(4)] - - # Optimized version of the above restricted to deg-2 polynomials - def lagrange_interp_2(self, xs, ys): - m = self.modulus - eq0 = [-xs[1] % m, 1] - eq1 = [-xs[0] % m, 1] - e0 = self.eval_poly_at(eq0, xs[0]) - e1 = self.eval_poly_at(eq1, xs[1]) - invall = self.inv(e0 * e1) - inv_y0 = ys[0] * invall * e1 - inv_y1 = ys[1] * invall * e0 - return [(eq0[i] * inv_y0 + eq1[i] * inv_y1) % m for i in range(2)] - - # Optimized version of the above restricted to deg-4 polynomials - def multi_interp_4(self, xsets, ysets): - data = [] - invtargets = [] - for xs, ys in zip(xsets, ysets): - x01, x02, x03, x12, x13, x23 = \ - xs[0] * xs[1], xs[0] * xs[2], xs[0] * xs[3], xs[1] * xs[2], xs[1] * xs[3], xs[2] * xs[3] - m = self.modulus - eq0 = [-x12 * xs[3] % m, (x12 + x13 + x23), -xs[1]-xs[2]-xs[3], 1] - eq1 = [-x02 * xs[3] % m, (x02 + x03 + x23), -xs[0]-xs[2]-xs[3], 1] - eq2 = [-x01 * xs[3] % m, (x01 + x03 + x13), -xs[0]-xs[1]-xs[3], 1] - eq3 = [-x01 * xs[2] % m, (x01 + x02 + x12), -xs[0]-xs[1]-xs[2], 1] - e0 = self.eval_quartic(eq0, xs[0]) - e1 = self.eval_quartic(eq1, xs[1]) - e2 = self.eval_quartic(eq2, xs[2]) - e3 = self.eval_quartic(eq3, xs[3]) - data.append([ys, eq0, eq1, eq2, eq3]) - invtargets.extend([e0, e1, e2, e3]) - invalls = self.multi_inv(invtargets) - o = [] - for (i, (ys, eq0, eq1, eq2, eq3)) in enumerate(data): - invallz = invalls[i*4:i*4+4] - inv_y0 = ys[0] * invallz[0] % m - inv_y1 = ys[1] * invallz[1] % m - inv_y2 = ys[2] * invallz[2] % m - inv_y3 = ys[3] * invallz[3] % m - o.append([(eq0[i] * inv_y0 + eq1[i] * inv_y1 + eq2[i] * inv_y2 + eq3[i] * inv_y3) % m for i in range(4)]) - # assert o == [self.lagrange_interp_4(xs, ys) for xs, ys in zip(xsets, ysets)] - return o diff --git a/eth1_simple_custody/simple_custody.py b/eth1_simple_custody/simple_custody.py deleted file mode 100644 index 25a6648..0000000 --- a/eth1_simple_custody/simple_custody.py +++ /dev/null @@ -1,218 +0,0 @@ -import blst -import hashlib -from poly_utils import PrimeField -from time import time -import sys -import gmpy2 - - -# -# Proof of concept implementation for Eth1 simple custody -# -# https://notes.ethereum.org/1Rn2MwsoSWuEUHTnaRgLcw -# - -# BLS12_381 curve modulus -MODULUS = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 - -primefield = PrimeField(MODULUS) - -# Proof of custody parameters -N = 15 # bits - -DOMAIN = list(range(N)) - -def hash(x): - if isinstance(x, bytes): - return hashlib.sha256(x).digest() - elif isinstance(x, blst.P1): - return hash(x.compress()) - elif isinstance(x, int): - return hash(x.to_bytes(32, "little")) - b = b"" - for a in x: - if isinstance(a, bytes): - b += a - elif isinstance(a, int): - b += a.to_bytes(32, "little") - elif isinstance(a, blst.P1): - b += hash(a.compress()) - return hash(b) - -C_CONSTANTS = [int.from_bytes(hash(i), "little") for i in range(N)] -D_CONSTANTS = [int.from_bytes(hash(i + N), "little") for i in range(N)] - -def legendre(x): - return gmpy2.jacobi(x, MODULUS) - -def mod_sqrt(a): - assert legendre(a) == 1 - - # Factor p-1 on the form q * 2^s (with Q odd) - q, s = MODULUS - 1, 0 - while q % 2 == 0: - s += 1 - q //= 2 - - # Select a z which is a quadratic non residue - z = 1 - while legendre(z) != -1: - z += 1 - c = pow(z, q, MODULUS) - - # Search for a solution - x = pow(a, (q + 1) // 2, MODULUS) - t = pow(a, q, MODULUS) - m = s - while t != 1: - # Find the lowest i such that t^(2^i) = 1 - i, e = 0, 2 - for i in range(1, m): - if pow(t, e, MODULUS) == 1: - break - e *= 2 - - # Update next value to iterate - b = pow(c, 2**(m - i - 1), MODULUS) - x = (x * b) % MODULUS - t = (t * b * b) % MODULUS - c = (b * b) % MODULUS - m = i - - assert (x ** 2 - a) % MODULUS == 0 - return x - -def is_valid_custody_value(secret_key, custody_value): - for i in range(N): - if legendre(secret_key + C_CONSTANTS[i] * custody_value + D_CONSTANTS[i]) != 1: - return False - return True - -def lincomb_naive(group_elements, factors, start_value = blst.G1().mult(0)): - """ - Direct linear combination - """ - assert len(group_elements) == len(factors) - result = start_value.dup() - for g, f in zip(group_elements, factors): - result.add(g.dup().mult(f)) - return result - -def generate_setup(N, secret): - """ - Generates a setup in the G1 group and G2 group, as well as the Lagrange polynomials in G1 (via FFT) - """ - g1_setup = [blst.G1().mult(pow(secret, i, MODULUS)) for i in range(N + 1)] - g2_setup = [blst.G2().mult(pow(secret, i, MODULUS)) for i in range(N + 1)] - lagrange_polys = primefield.lagrange_polys(list(range(N))) - g1_lagrange = [lincomb_naive(g1_setup[:N], p) for p in lagrange_polys] - g2_lagrange = [lincomb_naive(g2_setup[:N], p, start_value=blst.G2().mult(0)) for p in lagrange_polys] - g2_zero = lincomb_naive(g2_setup, primefield.zero_poly(list(range(N))), start_value=blst.G2().mult(0)) - g2_one = lincomb_naive(g2_lagrange, [1] * N, start_value=blst.G2().mult(0)) - return {"g1": g1_setup, "g2": g2_setup, "g1_lagrange": g1_lagrange, "g2_zero": g2_zero, "g2_one": g2_one} - -def compute_proof(setup, secret_key, custody_value): - values = [secret_key + C_CONSTANTS[i] * custody_value + D_CONSTANTS[i] for i in range(N)] - square_roots = [mod_sqrt(value) for value in values] - d = primefield.lagrange_interp(list(range(N)), square_roots) - D = lincomb_naive(setup["g1"][:N], d) - E = lincomb_naive(setup["g2"][:N], d, start_value=blst.G2().mult(0)) - - q = primefield.div_polys(primefield.mul_polys(d, d), primefield.zero_poly(list(range(N)))) - Pi = lincomb_naive(setup["g1"][:N - 1], q) - return D.compress(), E.compress(), Pi.compress() - -def check_proof_simple(setup, public_key_serialized, custody_value, proof): - D_serialized, E_serialized, Pi_serialized = proof - D = blst.P1(D_serialized) - E = blst.P2(E_serialized) - Pi = blst.P1(Pi_serialized) - public_key = blst.P1(public_key_serialized) - - b_values = [C_CONSTANTS[i] * custody_value + D_CONSTANTS[i] for i in range(N)] - B = lincomb_naive(setup["g1_lagrange"], b_values) - C = public_key.dup().add(B) - - pairing = blst.PT(blst.G2().to_affine(), D.to_affine()) - pairing.mul(blst.PT(E.to_affine(), blst.G1().neg().to_affine())) - if not pairing.final_exp().is_one(): - return False - - pairing = blst.PT(E.to_affine(), D.dup().neg().to_affine()) - pairing.mul(blst.PT(setup["g2_zero"].to_affine(), Pi.to_affine())) - pairing.mul(blst.PT(blst.G2().to_affine(), C.to_affine())) - if not pairing.final_exp().is_one(): - return False - - return True - - -def check_proof_combined(setup, public_key_serialized, custody_value, proof): - D_serialized, E_serialized, Pi_serialized = proof - D = blst.P1(D_serialized) - E = blst.P2(E_serialized) - Pi = blst.P1(Pi_serialized) - - r = int.from_bytes(hash(list(proof) + [public_key_serialized, custody_value]), "little") % MODULUS - r2 = r * r % MODULUS - - public_key = blst.P1(public_key_serialized) - - b_values = [C_CONSTANTS[i] * custody_value + D_CONSTANTS[i] for i in range(N)] - B = lincomb_naive(setup["g1_lagrange"], b_values) - C = public_key.dup().add(B) - - pairing = blst.PT(blst.G2().mult(r).add(E).to_affine(), D.dup().neg().to_affine()) - pairing.mul(blst.PT(E.to_affine(), blst.G1().mult(r).to_affine())) - pairing.mul(blst.PT(blst.G2().to_affine(), C.to_affine())) - pairing.mul(blst.PT(setup["g2_zero"].to_affine(), Pi.to_affine())) - - return pairing.final_exp().is_one() - - -def get_proof_size(proof): - return sum(len(x) for x in proof) - - -if __name__ == "__main__": - time_a = time() - setup = generate_setup(N, 8927347823478352432985) - time_b = time() - - print("Computed setup in {0:.3f} ms".format(1000*(time_b - time_a)), file=sys.stderr) - - secret_key = pow(523487, 253478, MODULUS) + 1 - public_key = blst.G1().mult(secret_key).compress() - - time_a = time() - custody_value = 876354679 - values_tried = 1 - while not is_valid_custody_value(secret_key, custody_value): - custody_value += 1 - values_tried += 1 - time_b = time() - - print("Found custody value in {0:.3f} ms after {1} tries".format(1000*(time_b - time_a), values_tried), file=sys.stderr) - - time_a = time() - proof = compute_proof(setup, secret_key, custody_value) - time_b = time() - - proof_size = get_proof_size(proof) - - print("Computed proof (size = {0} bytes) in {1:.3f} ms".format(proof_size, 1000*(time_b - time_a)), file=sys.stderr) - - time_a = time() - assert check_proof_simple(setup, public_key, custody_value, proof) - time_b = time() - check_time = time_b - time_a - - print("Checked proof in {0:.3f} ms".format(1000*(time_b - time_a)), file=sys.stderr) - - time_a = time() - assert check_proof_combined(setup, public_key, custody_value, proof) - time_b = time() - check_time = time_b - time_a - - print("Checked proof (optimized/combined pairing) in {0:.3f} ms".format(1000*(time_b - time_a)), file=sys.stderr) - diff --git a/exit_queue_tests/exit_queue_tester.py b/exit_queue_tests/exit_queue_tester.py deleted file mode 100644 index 2be58b9..0000000 --- a/exit_queue_tests/exit_queue_tester.py +++ /dev/null @@ -1,108 +0,0 @@ -from numpy.random import poisson -import math - -# Target active staker size -TARGET_AMOUNT_STAKING = 312500 -# Average time staking before withdrawal -AVG_STAKING_TIME = 500 -# How many withdrawals are permitted in -# one day given a certain validator count? -def withdrawals_per_day(validators, total_eth_exiting): - # return (validators + total_eth_exiting) / 1.07 // 100 - return validators // 100 - # return validators * max(1, int(math.log2(total_eth_exiting))) / 13.5 // 100 - # return int(1 + (total_eth_exiting * validators)**0.5) * 4.9 // 100 - -# Get the size of the largest staker. This assumes a -# Zipf's law distribution (ie. power law with power=1) -# where the nth largest staker is n times smaller than the -# largest staker. Calculates a value for the largest staker -# such that the total size of nonzero stakers equals the -# target amount staking. -def get_max_staker_size(): - def get_sum(sz): - tot = 0 - inc = 1 - while sz // inc: - tot += (sz // inc) * inc - inc *= 2 - return tot - size = 0 - offset = TARGET_AMOUNT_STAKING - while offset: - if get_sum(size + offset) < TARGET_AMOUNT_STAKING: - size += offset - else: - offset //= 2 - return size - -# As a simplification, we make all stakers have validator sizes -# be close to the max size divided by a power of two -STAKER_SIZES = [get_max_staker_size()] - -while STAKER_SIZES[-1] > 1: - STAKER_SIZES.append(STAKER_SIZES[-1] // 2) - -# Active and not yet exiting stakers -stakers = {} -# Exiting stakers -exiting = {} - -# The exit queue -exit_queue = [] -# Total eth exiting -total_eth_exiting = 0 -# How much of the first exiter's deposit we have processed -processing_current = 0 - -# Fill the staker set initially -for i, sz in enumerate(STAKER_SIZES): - stakers[sz] = poisson(2**i) - sz //= 2 - -# Count withdrawn stakers of each size, and total delays -# incurred by them, so we can eventually compute the average -withdrawn = {} -tot_delays = {} - -print("Total staking ETH:", sum(k * v for k,v in stakers.items())) - -for day in range(10000): - # Deposit new stakers at the rate needed to maintain the equilibrium size - for i, sz in enumerate(STAKER_SIZES): - stakers[sz] = stakers.get(sz, 0) + poisson(2**i / AVG_STAKING_TIME) - sz //= 2 - - # Each staker has a 1/AVG_STAKING_TIME probability of deciding to leave each day - for k in stakers.keys(): - exit_count = min(poisson(stakers[k] / AVG_STAKING_TIME), stakers[k]) - if exit_count > 0: - exit_queue.append((k, exit_count, day)) - stakers[k] -= exit_count - exiting[k] = exiting.get(k, 0) + exit_count - total_eth_exiting += exit_count * k - total_validators = sum(k * v for k,v in stakers.items()) + sum(k * v for k,v in exiting.items()) - - # Process the queue - queue_to_empty_today = withdrawals_per_day(total_validators, total_eth_exiting) - while queue_to_empty_today > 0 and len(exit_queue) > 0: - key, exit_count, exit_day = exit_queue[0] - # Partially process the first exiter (exit next loop) - if key * exit_count > queue_to_empty_today + processing_current: - processing_current += queue_to_empty_today - queue_to_empty_today = 0 - # Finish processing the first exiter (continue next loop) - else: - processing_current = 0 - queue_to_empty_today -= key * exit_count - processing_current - exit_queue.pop(0) - exiting[key] -= exit_count - total_eth_exiting -= exit_count * key - withdrawn[key] = withdrawn.get(key, 0) + exit_count - tot_delays[key] = tot_delays.get(key, 0) + (day - exit_day) * exit_count - if day % 1000 == 999: - print("Report for day %d: %d total validators %d ETH in exit queue" % ((day+1), total_validators, total_eth_exiting)) - -print("Total delays in days") -for key in STAKER_SIZES: - print("%d: % .3f (min %.3f)" % (key, (tot_delays.get(key, 0) / withdrawn.get(key, 0.0001)), key / withdrawals_per_day(TARGET_AMOUNT_STAKING, key))) diff --git a/fast_cross_shard_execution/optimistic_dependency_test.py b/fast_cross_shard_execution/optimistic_dependency_test.py deleted file mode 100644 index e943f83..0000000 --- a/fast_cross_shard_execution/optimistic_dependency_test.py +++ /dev/null @@ -1,131 +0,0 @@ -import copy, os, random, binascii - -zero_hash = '00000000' - -def new_hash(): - return binascii.hexlify(os.urandom(4)).decode('utf-8') - -# Account state record -class Account(): - def __init__(self, yes_dep, no_deps, balance): - # This state is conditional on this dependency being CORRECT - self.yes_dep = yes_dep - # This state is conditional on these dependencies being INCORRECT - self.no_deps = no_deps - # Account balance - self.balance = balance - - def __repr__(self): - return "[yes_dep: %r, no_deps: %r, balance: %d]" % (self.yes_dep, self.no_deps, self.balance) - -# Dependency object: (hash, height) -class Dependency(): - def __init__(self, height, hash): - self.height = height - self.hash = hash - - def __repr__(self): - return "[height: %d, hash: %s]" % (self.height, self.hash) - -# Test with 5 accounts -actors = ["Alice", "Bob", "Charlie", "David", "Epsie"] - -# Initial empty state -state = {a: Account(Dependency(0, zero_hash), [], 100) for a in actors} - -# The set of dependencies that the protocol thinks is most likely to be correct -# Think of these as being receipt roots of all shards, with the i'th hash -# corresponding to the receipt root from the i'th slot. This list gets extended -# as the protocol finds out about new dependencies, and dependencies can get popped -# off the end if the protocol realizes that they are incorrect -deps = [zero_hash] - -# Alternate states corresponding to dependencies other than those the protocol thinks -# is most likely to be correct. In a real implementation these can be stored as -# receipts rather than state objects if desired -alt_states = {a: [] for a in actors} - -# Does the current account state match the dependencies? -def is_account_state_active(account): - for dep in account.no_deps: - if (dep.height < len(deps) and dep.hash == deps[dep.height]): - return False - yes_dep_ht = account.yes_dep.height - if yes_dep_ht >= len(deps) or account.yes_dep.hash != deps[yes_dep_ht]: - return False - return True - -# Set the main account state to be the correct one -def reorg(address): - if is_account_state_active(state[address]): - return - for i,r in enumerate(alt_states[address]): - if is_account_state_active(r): - state[address], alt_states[address][i] = alt_states[address][i], state[address] - return - raise Exception("wtf m8") - -# Adjusts balance of an account. UNSAFE unless checks are done! -def balance_delta(to, value, height, hash): - if height > state[to].yes_dep.height: - alt_states[to].append(Account( - state[to].yes_dep, - state[to].no_deps + [Dependency(height, hash)], - state[to].balance - )) - state[to].yes_dep = Dependency(height, hash) - state[to].balance += value - assert state[to].balance >= 0 - -# Transfer from an account (or from the outside) to another account -def transfer(frm, to, value, height, hash): - # print("<------- Xferring", frm, to, value, height, hash) - if len(deps) <= height or deps[height] != hash: - return False - if not (is_account_state_active(state[to]) and height >= state[to].yes_dep.height): - return False - if frm is not None and not (is_account_state_active(state[frm]) and height >= state[frm].yes_dep.height): - return False - balance_delta(to, value, height, hash) - if frm is not None: - balance_delta(frm, -value, height, hash) - return True - -print("Starting balance: %d" % state["Charlie"].balance) - -# Run the main test.... -for i in range(200): - r = random.random() - # 16% chance: new dependency - if r < 0.16: - deps.append(new_hash()) - # 20% chance: xfer from another shard - elif r < 0.36: - to = random.choice(actors) - reorg(to) - value = random.randrange(100) - assert transfer(None, to, value, len(deps)-1, deps[-1]) - if to == "Charlie": - print("Received %d coins, new balance %d, conditional on (%d, %s)" % (value, state[to].balance, len(deps)-1, deps[-1])) - # 60% chance: xfer between two accounts inside the shard - elif r < 0.96: - to = random.choice(actors) - frm = random.choice([x for x in actors if x != to]) - reorg(to) - reorg(frm) - common_ht = max(state[to].yes_dep.height, state[frm].yes_dep.height) - value = random.randrange(state[frm].balance + 1) - assert transfer(frm, to, value, common_ht, deps[common_ht]) - if frm == "Charlie": - print("Sent %d coins, new balance %d, conditional on (%d, %s)" % (value, state[frm].balance, common_ht, deps[common_ht])) - if to == "Charlie": - print("Received %d coins from %s, new balance %d, conditional on (%d, %s)" % (value, frm, state[to].balance, common_ht, deps[common_ht])) - # 4% chance: revert some dependencies - else: - num_to_revert = min(random.randrange(8), len(deps) - 1) - for i in range(num_to_revert): - print("Reverted (%d, %s)" % (len(deps)-1, deps.pop())) - for i in range(num_to_revert): - deps.append(new_hash()) - reorg("Charlie") - print("New balance: %d" % state["Charlie"].balance) diff --git a/fast_linear_combinations/multicombs.py b/fast_linear_combinations/multicombs.py deleted file mode 100644 index 4553bca..0000000 --- a/fast_linear_combinations/multicombs.py +++ /dev/null @@ -1,131 +0,0 @@ -import random, time, sys, math - -# For each subset in `subsets` (provided as a list of indices into `numbers`), -# compute the sum of that subset of `numbers`. More efficient than the naive method. -def multisubset(numbers, subsets, adder=lambda x,y: x+y, zero=0): - numbers = numbers[::] - subsets = {i: {x for x in subset} for i, subset in enumerate(subsets)} - output = [zero for _ in range(len(subsets))] - - for roundcount in range(9999999): - # Compute counts of every pair of indices in the subset list - pair_count = {} - for index, subset in subsets.items(): - for x in subset: - for y in subset: - if y > x: - pair_count[(x, y)] = pair_count.get((x, y), 0) + 1 - - # Determine pairs with highest count. The cutoff parameter [:len(numbers)] - # determines a tradeoff between group operation count and other forms of overhead - pairs_by_count = sorted([el for el in pair_count.keys()], key=lambda el: pair_count[el], reverse=True)[:len(numbers)*int(math.log(len(numbers)))] - - # Exit condition: all subsets have size 1, no pairs - if len(pairs_by_count) == 0: - for key, subset in subsets.items(): - for index in subset: - output[key] = adder(output[key], numbers[index]) - return output - - # In each of the highest-count pairs, take the sum of the numbers at those indices, - # and add the result as a new value, and modify `subsets` to include the new value - # wherever possible - used = set() - for maxx, maxy in pairs_by_count: - if maxx in used or maxy in used: - continue - used.add(maxx) - used.add(maxy) - numbers.append(adder(numbers[maxx], numbers[maxy])) - for key, subset in list(subsets.items()): - if maxx in subset and maxy in subset: - subset.remove(maxx) - subset.remove(maxy) - if not subset: - output[key] = numbers[-1] - del subsets[key] - else: - subset.add(len(numbers)-1) - -# Alternative algorithm. Less optimal than the above, but much lower bit twiddling -# overhead and much simpler. -def multisubset2(numbers, subsets, adder=lambda x,y: x+y, zero=0): - # Split up the numbers into partitions - partition_size = 1 + int(math.log(len(subsets) + 1)) - # Align number count to partition size (for simplicity) - numbers = numbers[::] - while len(numbers) % partition_size != 0: - numbers.append(zero) - # Compute power set for each partition (eg. a, b, c -> {0, a, b, a+b, c, a+c, b+c, a+b+c}) - power_sets = [] - for i in range(0, len(numbers), partition_size): - new_power_set = [zero] - for dimension, value in enumerate(numbers[i:i+partition_size]): - new_power_set += [adder(n, value) for n in new_power_set] - power_sets.append(new_power_set) - # Compute subset sums, using elements from power set for each range of values - # ie. with a single power set lookup you can get the sum of _all_ elements in - # the range partition_size*k...partition_size*(k+1) that are in that subset - subset_sums = [] - for subset in subsets: - o = zero - for i in range(len(power_sets)): - index_in_power_set = 0 - for j in range(partition_size): - if i * partition_size + j in subset: - index_in_power_set += 2 ** j - o = adder(o, power_sets[i][index_in_power_set]) - subset_sums.append(o) - return subset_sums - -# Reduces a linear combination `numbers[0] * factors[0] + numbers[1] * factors[1] + ...` -# into a multi-subset problem, and computes the result efficiently -def lincomb(numbers, factors, adder=lambda x,y: x+y, zero=0): - # Maximum bit length of a number; how many subsets we need to make - maxbitlen = max(len(bin(f))-2 for f in factors) - # Compute the subsets: the ith subset contains the numbers whose corresponding factor - # has a 1 at the ith bit - subsets = [{i for i in range(len(numbers)) if factors[i] & (1 << j)} for j in range(maxbitlen+1)] - subset_sums = multisubset(numbers, subsets, adder=adder, zero=zero) - # For example, suppose a value V has factor 6 (011 in increasing-order binary). Subset 0 - # will not have V, subset 1 will, and subset 2 will. So if we multiply the output of adding - # subset 0 with twice the output of adding subset 1, with four times the output of adding - # subset 2, then V will be represented 0 + 2 + 4 = 6 times. This reasoning applies for every - # value. So `subset_0_sum + 2 * subset_1_sum + 4 * subset_2_sum` gives us the result we want. - # Here, we compute this as `((subset_2_sum * 2) + subset_1_sum) * 2 + subset_0_sum` for - # efficiency: an extra `maxbitlen * 2` group operations. - o = zero - for i in range(len(subsets)-1, -1, -1): - o = adder(adder(o, o), subset_sums[i]) - return o - -# Tests go here -def make_mock_adder(): - counter = [0] - def adder(x, y): - if x and y: - counter[0] += 1 - return x+y - return adder, counter - -def test_multisubset(numcount, setcount): - numbers = [random.randrange(10**20) for _ in range(numcount)] - subsets = [{i for i in range(numcount) if random.randrange(2)} for i in range(setcount)] - adder, counter = make_mock_adder() - o = multisubset(numbers, subsets, adder=adder) - for output, subset in zip(o, subsets): - assert output == sum([numbers[x] for x in subset]) - -def test_lincomb(numcount, bitlength=256): - numbers = [random.randrange(10**20) for _ in range(numcount)] - factors = [random.randrange(2**bitlength) for _ in range(numcount)] - adder, counter = make_mock_adder() - o = lincomb(numbers, factors, adder=adder) - assert o == sum([n*f for n,f in zip(numbers, factors)]) - total_ones = sum(bin(f).count('1') for f in factors) - print("Naive operation count: %d" % (bitlength * numcount + total_ones)) - print("Optimized operation count: %d" % (bitlength * 2 + counter[0])) - print("Optimization factor: %.2f" % ((bitlength * numcount + total_ones) / (bitlength * 2 + counter[0]))) - -if __name__ == '__main__': - test_lincomb(int(sys.argv[1]) if len(sys.argv) >= 2 else 80) diff --git a/generic_in_place_tree/tree.py b/generic_in_place_tree/tree.py deleted file mode 100644 index f4bf55e..0000000 --- a/generic_in_place_tree/tree.py +++ /dev/null @@ -1,258 +0,0 @@ -import leveldb -import hashlib -import sys - -ZERO = b'\x00'*32 - - -def hash(x): - return hashlib.sha256(x).digest() - - -def hash_to_display_form(h): - return '0x'+h.hex()[:12] if h else None - - -def get_common_prefix(a, b): - L = 0 - while L < len(a) and L < len(b) and a[L] == b[L]: - L += 1 - return a[:L] - - -class LeafNode(): - - def __init__(self, key, value): - assert len(key) == 32 - self.key, self.value = key, value - - def serialize(self): - return b'L' + self.key + self.value - - def __repr__(self): - return "Leaf[Key={}, value={}, hash={}]".format(self.key.rstrip(b'\x00'), self.value.rstrip(b'\x00'), hash_to_display_form(hash_node(self))) - - -class BranchNode(): - - def __init__(self, values={}): - if isinstance(values, list): - assert len(values) == 256 - self.values = values - elif isinstance(values, dict): - self.values = [ZERO] * 256 - for k, v in values.items(): - self.values[k] = v - else: - raise Exception("Invalid values for branch node") - - def serialize(self): - if self.values.count(ZERO) == 256: - return None - else: - return b'B' + b''.join(self.values) - - def __repr__(self): - if self.values.count(ZERO) == 256: - return "BranchNode[]" - o = "BranchNode[" - for i in range(256): - if self.values[i] != ZERO: - o += '{}: {}, '.format(chr(i), hash_to_display_form(self.values[i])) - o += 'hash=' + hash_to_display_form(hash_node(self)) + ']' - return o - - -def deserialize(node): - if node is None: - return None - elif node[0] == ord(b'L'): - return LeafNode(node[1:33], node[33:]) - elif node[0] == ord(b'B'): - assert len(node) == 1 + 32 * 256 - return BranchNode([node[32*i+1:32*i+33] for i in range(256)]) - else: - raise Exception("Broken node in DB: {}".format(node)) - - -def hash_node(node): - if isinstance(node, LeafNode): - return hash(node.serialize()) - elif isinstance(node, BranchNode): - # replace with Kate commitment - serialized = node.serialize() - return None if serialized is None else hash(serialized) - elif node is None: - return None - else: - raise Exception("Bad node type") - - -def db_get(db, key): - try: - return db.Get(key) - except: - return None - - -def db_put(db, key, value): - print('putting', key, deserialize(value)) - if value is not None: - db.Put(key, value) - else: - db.Delete(key) - - -def propagate_deletions(db, batch, path): - - for i in reversed(range(len(path))): - current_node = deserialize(db_get(db, path[:i])) - print(path[:i], current_node) - assert isinstance(current_node, BranchNode) - if current_node.values.count(ZERO) == 255: - print('one nonzero; continuing') - db_put(batch, path[:i], None) - elif current_node.values.count(ZERO) == 254: - print('two nonzeroes; replacing with leaf') - db_put(batch, path[:i], sister_leaf.serialize()) - propagate_along_path(db, batch, path[:i], hash_node(sister_leaf)) - return - else: - print('3+ nonzeroes; removing') - current_node.values[path[i]] = ZERO - db_put(batch, path[:i], current_node.serialize()) - propagate_along_path(db, batch, path[:i], hash_node(current_node)) - return - - -def propagate_along_path(db, batch, path, new_node_hash): - for i in reversed(range(len(path))): - current_node = deserialize(db_get(db, path[:i])) - if current_node is None or isinstance(current_node, LeafNode): - current_node = BranchNode() - current_node.values[path[i]] = new_node_hash or ZERO - db_put(batch, path[:i], current_node.serialize()) - new_node_hash = hash_node(current_node) - db.Write(batch) - - - -def add(db, key, value): - print('## ADDING {} {} ##'.format(key.rstrip(b'\x00'), value.rstrip(b'\x00'))) - assert len(key) == 32 - batch = leveldb.WriteBatch() - for i, byte in enumerate(key): - path = key[:i] - node_at_path = deserialize(db_get(db, path)) - if node_at_path is None: - new_leaf = LeafNode(key, value) - db_put(batch, path, new_leaf.serialize()) - propagate_along_path(db, batch, path, hash_node(new_leaf)) - return - if isinstance(node_at_path, LeafNode): - new_leaf = LeafNode(key, value) - if node_at_path.key == key: - db_put(batch, path, new_leaf.serialize()) - propagate_along_path(db, batch, path, hash_node(new_leaf)) - else: - propagation_path = get_common_prefix(key, node_at_path.key) - common_prefix_length = len(propagation_path) - db_put(batch, key[:common_prefix_length+1], new_leaf.serialize()) - db_put(batch, node_at_path.key[:common_prefix_length+1], node_at_path.serialize()) - new_branch_node = BranchNode({ - key[common_prefix_length]: hash_node(new_leaf), - node_at_path.key[common_prefix_length]: hash_node(node_at_path) - }) - db_put(batch, key[:common_prefix_length], new_branch_node.serialize()) - propagate_along_path(db, batch, propagation_path, hash_node(new_branch_node)) - return - raise Exception("How did we get here?") - -def delete(db, key): - print('## DELETING {} ##'.format(key.rstrip(b'\x00'))) - assert len(key) == 32 - batch = leveldb.WriteBatch() - node_at_path = None - for i, byte in enumerate(key): - path = key[:i] - penultimate_node = node_at_path - node_at_path = deserialize(db_get(db, path)) - if node_at_path is None: - return - if isinstance(node_at_path, LeafNode): - if node_at_path.key == key: - db_put(batch, path, None) - penultimate_path = key[:i-1] - # Trivial case: last key is being removed - if penultimate_node is None: - db.Write(batch) - return - # Invariant: the immediately prior branch node cannot have only one child - assert isinstance(penultimate_node, BranchNode) - assert penultimate_node.values.count(ZERO) <= 254 - # Easy case: > 2 children - if penultimate_node.values.count(ZERO) < 254: - penultimate_node.values[key[i-1]] = ZERO - db_put(batch, penultimate_path, penultimate_node.serialize()) - propagate_along_path(db, batch, penultimate_path, hash_node(penultimate_node)) - return - # Hard case: 2 children - sister_leaf_index = min( - j for j in range(256) if penultimate_node.values[j] != ZERO and j != key[i-1] - ) - sister_leaf = deserialize(db_get(db, penultimate_path + bytes([sister_leaf_index]))) - db_put(batch, penultimate_path, None) - for j in reversed(range(i-1)): - path = key[:j] - node_at_path = deserialize(db_get(db, path)) - assert isinstance(node_at_path, BranchNode) - if node_at_path.values.count(ZERO) == 255: - db_put(batch, path, None) - else: - node_at_path.values[key[j]] = hash_node(sister_leaf) - db_put(batch, path + bytes([key[j]]), sister_leaf.serialize()) - db_put(batch, path, node_at_path.serialize()) - propagate_along_path(db, batch, path, hash_node(node_at_path)) - return - db_put(batch, b'', sister_leaf.serialize()) - db.Write(batch) - return - else: - return - raise Exception("How did we get here?") - - -def get(db, key): - for i in range(len(key)): - node = deserialize(db_get(db, key[:i])) - if node is None: - return None - elif isinstance(node, LeafNode): - return node.value - elif isinstance(node, BranchNode): - continue - - -def zpad32(x): - return x + b'\x00' * (32 - len(x)) - - -if __name__ == '__main__': - db = leveldb.LevelDB(sys.argv[1]) - values = { - b'cow': b'bovine', - b'dog': b'canine', - b'hippopotamus': b'riverhorse', - b'hippogriff': b'harry', - } - hashes = [None] - for k, v in values.items(): - add(db, zpad32(k), zpad32(v)) - hashes.append(hash_node(deserialize(db_get(db, b'')))) - print([hash_to_display_form(x) for x in hashes]) - print("Created full tree, hash: {}".format("0x"+hashes.pop().hex())) - for k, v in values.items(): - assert get(db, zpad32(k)) == zpad32(v) - for k, v in reversed(values.items()): - delete(db, zpad32(k)) - assert hashes.pop() == hash_node(deserialize(db_get(db, b''))) diff --git a/ghost/ghost.py b/ghost/ghost.py deleted file mode 100644 index 2155cd8..0000000 --- a/ghost/ghost.py +++ /dev/null @@ -1,167 +0,0 @@ -import os, random, time, struct -from binascii import hexlify - -LATENCY_FACTOR = 0.5 -NODE_COUNT = 131072 -BLOCK_ONCE_EVERY = 1024 -SIM_LENGTH = 131072 - -balances = [1] * NODE_COUNT -latest_message = [b'\x00' * 32] * NODE_COUNT -blocks = {b'\x00' * 32: (0, None)} -children = {} -ancestors = [{b'\x00' * 32: b'\x00' * 32} for i in range(16)] -max_known_height = [0] - -logz = [0, 0] -for i in range(2, 10000): - logz.append(logz[i // 2] + 1) -height_to_bytes = [i.to_bytes(4, 'big') for i in range(10000)] - -def get_height(block): - return blocks[block][0] - -cache = {} -def get_ancestor(block, at_height): - h = blocks[block][0] - if at_height >= h: - if at_height > h: - return None - else: - return block - cachekey = block + height_to_bytes[at_height] - if cachekey in cache: - return cache[cachekey] - # assert get_height(ancestors[logz[h - at_height - 1]][block]) >= at_height - o = get_ancestor(ancestors[logz[h - at_height - 1]][block], at_height) - # assert get_height(o) == at_height - cache[cachekey] = o - return o - -def add_block(parent): - new_block_hash = os.urandom(32) - h = get_height(parent) - blocks[new_block_hash] = (h+1, parent) - if parent not in children: - children[parent] = [] - children[parent].append(new_block_hash) - for i in range(16): - if h % 2**i == 0: - ancestors[i][new_block_hash] = parent - else: - ancestors[i][new_block_hash] = ancestors[i][parent] - max_known_height[0] = max(max_known_height[0], h+1) - -def add_attestation(block, validator_index): - latest_message[validator_index] = block - -def get_clear_winner(latest_votes, h): - at_height = {} - total_vote_count = 0 - for k, v in latest_votes.items(): - anc = get_ancestor(k, h) - at_height[anc] = at_height.get(anc, 0) + v - if anc is not None: - total_vote_count += v - for k, v in at_height.items(): - if v >= total_vote_count // 2: - return k - return None - -def choose_best_child(votes): - bitmask = 0 - for bit in range(255, -1, -1): - zero_votes = 0 - one_votes = 0 - single_candidate = None - for candidate in votes.keys(): - votes_for_candidate = votes[candidate] - candidate_as_int = int.from_bytes(candidate, 'big') - if candidate_as_int >> (bit+1) != bitmask: - continue - if (candidate_as_int >> bit) % 2 == 0: - zero_votes += votes_for_candidate - else: - one_votes += votes_for_candidate - if single_candidate is None: - single_candidate = candidate - else: - single_candidate = False - # print(bit, bitmask, zero_votes, one_votes) - bitmask = (bitmask * 2) + (1 if one_votes > zero_votes else 0) - if single_candidate: - return single_candidate - assert bit >= 1 - -def get_power_of_2_below(x): - return 2**logz[x] - -def ghost(): - # Get latest votes as key-value map - latest_votes = {} - for i in range(len(balances)): - latest_votes[latest_message[i]] = latest_votes.get(latest_message[i], 0) + balances[i] - - head = b'\x00' * 32 - height = 0 - while 1: - # print('at', height, 'votes', sum(latest_votes.values())) - c = children.get(head, []) - if len(c) == 0: - return head - step = get_power_of_2_below(max_known_height[0] - height) // 2 - while step > 0: - possible_clear_winner = get_clear_winner(latest_votes, height - (height % step) + step) - if possible_clear_winner is not None: - # print("Skipping from height %d to %d" % (get_height(head), get_height(possible_clear_winner))) - head = possible_clear_winner - break - step //= 2 - if step > 0: - pass - elif len(c) == 1: - # print("Only child fast path", latest_votes.get(head, 0)) - head = c[0] - else: - # print("Block %s at height %d with %d children!" % - # (hexlify(head[:4]), height, len(c)), [hexlify(x[:4]) for x in c]) - child_votes = {x: 0.01 for x in c} - for k, v in latest_votes.items(): - child = get_ancestor(k, height + 1) - if child is not None: - child_votes[child] = child_votes.get(child, 0) + v - head = choose_best_child(child_votes) - height = get_height(head) - deletes = [] - for k, v in latest_votes.items(): - if get_ancestor(k, height) != head: - deletes.append(k) - for k in deletes: - del latest_votes[k] - -def get_perturbed_head(head): - up_count = 0 - while get_height(head) > 0 and random.random() < LATENCY_FACTOR: - head = blocks[head][1] - up_count += 1 - for _ in range(random.randrange(up_count + 1)): - if head in children: - head = random.choice(children[head]) - return head - -def simulate_chain(): - start_time = time.time() - for i in range(0, SIM_LENGTH, BLOCK_ONCE_EVERY): - head = ghost() - for j in range(i, i + BLOCK_ONCE_EVERY): - phead = get_perturbed_head(head) - add_attestation(phead, i % NODE_COUNT) - print("Adding new block on top of block %d %s. Time so far: %.3f" % - (blocks[phead][0], hexlify(phead[:4]), time.time() - start_time)) - add_block(phead) - # print([get_height(latest_message[i]) for i in range(NODE_COUNT)]) - -simulate_chain() -print(len(str(cache))) -print(len(str(ancestors))) -print(len(str(blocks))) diff --git a/graph_cbc/graph_cbc.py b/graph_cbc/graph_cbc.py deleted file mode 100644 index ba9f409..0000000 --- a/graph_cbc/graph_cbc.py +++ /dev/null @@ -1,80 +0,0 @@ -import random - -VALIDATORS = 5000 -EDGES = 255 -FINALITY = 4000 - -assert EDGES % 2 == 1 - -neighbors = list(range(VALIDATORS)) -edgelist = neighbors * EDGES -random.shuffle(edgelist) -edges = [edgelist[i*EDGES:i*EDGES+EDGES] for i in range(VALIDATORS)] - -last_votes = '1' * FINALITY + '0' * (VALIDATORS - FINALITY) - -while 1: - new_zeroes = [] - for i in range(VALIDATORS): - votes_for_0 = len([e for e in edges[i] if last_votes[e] == '0']) - if votes_for_0 * 2 > EDGES: - new_zeroes.append(i) - new_last_votes = ''.join(['01'[last_votes[j]=='1' and j not in new_zeroes] - for j in range(VALIDATORS)]) - print(new_last_votes.count('0')) - if new_last_votes == last_votes: - break - last_votes = new_last_votes - -print(last_votes.count('0')) - -print("Initiating repeat-pivotal strategy") - -threshold = EDGES // 2 -corrupted = 0 - -while last_votes != '0' * VALIDATORS: - # Attempt strategy of finding the single pivotal validator that can - # corrupt the most other validators - pivotals = {} - for i in range(VALIDATORS): - votes_for_0 = len([e for e in edges[i] if last_votes[e] == '0']) - assert last_votes[i] == '0' or votes_for_0 * 2 < EDGES - if votes_for_0 == threshold: - for e in edges[i]: - if last_votes[e] == '1': - pivotals[e] = pivotals.get(e, 0) + 1 - if len(pivotals) > 0: - corrupt = [max(zip(pivotals.values(), pivotals.keys()))[1]] - # Attempt strategy of finding the smallest group of validators that - # can be corrupted to turn 1 more - else: - corrupt = [] - max_votes = 0 - for i in range(VALIDATORS): - if last_votes[i] == '0': - continue - votes_for_0 = len([e for e in edges[i] if last_votes[e] == '0']) - if votes_for_0 > max_votes: - amount_to_corrupt = EDGES // 2 - votes_for_0 + 1 - corrupt = [e for e in edges[i] if last_votes[e] == '1'][:amount_to_corrupt] - max_votes = votes_for_0 - - last_votes = ''.join(['01'[last_votes[j]=='1' and j not in corrupt] - for j in range(VALIDATORS)]) - corrupted += len(corrupt) - while 1: - new_zeroes = [] - for i in range(VALIDATORS): - votes_for_0 = len([e for e in edges[i] if last_votes[e] == '0']) - if votes_for_0 * 2 > EDGES: - new_zeroes.append(i) - new_last_votes = ''.join(['01'[last_votes[j]=='1' and j not in new_zeroes] - for j in range(VALIDATORS)]) - if new_last_votes == last_votes: - break - last_votes = new_last_votes - print("Corrupted %r (total %d), now on fork chain: %d" % - (corrupt, corrupted, new_last_votes.count('0'))) - -print("Total corrupted: %d" % corrupted) diff --git a/iceage.py b/iceage.py deleted file mode 100644 index 170e0ee..0000000 --- a/iceage.py +++ /dev/null @@ -1,21 +0,0 @@ -import random -import datetime - -diffs = [3005 * 10**12] -hashpower = diffs[0] / 14 -times = [1541247118] - - -for i in range(6635692, 13000000): - blocktime = random.expovariate(hashpower / diffs[-1]) - adjfac = max(1 - int(blocktime / 10), -99) / 2048. - newdiff = diffs[-1] * (1 + adjfac) - period = (i - 200000) // 100000 - 32 - if i > 200000: - newdiff += 2 ** period - diffs.append(newdiff) - times.append(times[-1] + blocktime) - if i % 10000 == 0: - print('Block %d, approx ETH supply %d, time %r blocktime %.2f' % \ - (i, 60102216 * 1.199 + 5.3 * i, datetime.datetime.utcfromtimestamp(times[-1]).isoformat().replace('T',' '), diffs[-1] / hashpower)) - # print int(adjfac * 2048) diff --git a/impurity/check_for_impurity.se b/impurity/check_for_impurity.se deleted file mode 100644 index 3de9bf0..0000000 --- a/impurity/check_for_impurity.se +++ /dev/null @@ -1,70 +0,0 @@ -macro calldatachar($x): - div(calldataload($x), 2**248) - -# sum([2**x for x in [0x31, 0x32, 0x33, 0x3a, 0x3b, 0x3c, 0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f, 0x54, 0x55, 0xf0, 0xff]]) -mask = 57897811465722876096115075801844696845150819816717216876035649536196444422144 - -data approved_addrs[] - -def submit(addr: address): - # Copy external contract code - extcode = string(~extcodesize(addr)) - ~extcodecopy(addr, extcode, 0, ~extcodesize(addr)) - ops = array(~extcodesize(addr)) - pushargs = array(~extcodesize(addr)) - # Loop through the code - with i = 0: - with op = 0: - while i < len(extcode): - with c = ~mod(~mload(extcode + i - 31), 256): - # Banned opcode - if ~and(2**c, mask): - ~invalid() - # PUSH - if 0x60 <= c and c <= 0x7f: - pushargs[op] = ~div(~mload(extcode + i + 1), 256 ** (0x7f - c)) - i += c - 0x5e - # Call, callcode, delegatecall - elif c == 0xf1 or c == 0xf2 or c == 0xf4: - # Pattern-match four ways of setting the gas parameter: - # - # 1. PUSH - # 2. sub(GAS, PUSH) - # 3. GAS - # 4. SWAP1
( ... ) - # 5. DUP - if op >= 2 and ops[op - 1] >= 0x60 and ops[op - 1] <= 0x7f: - address_entry = op - 2 - elif op >= 4 and ops[op - 1] == 0x03 and ops[op - 2] == 0x5a and ops[op - 3] >= 0x60 and ops[op - 3] <= 0x7f: - address_entry = op - 4 - elif op >= 2 and ops[op - 1] == 0x5a: - address_entry = op - 2 - elif op >= 2 and ops[op - 1] == 0x90: - address_entry = op - 2 - elif op >= 2 and ops[op - 1] >= 0x80 and ops[op - 1] < 0x90: - address_entry = op - 2 - else: - ~invalid() - # Operation before the gas parameter must satisfy one of three conditions: - # - # 1. It is a PUSH of an already approved address - # 2. It is the address itself, through the ADDRESS opcode (ie. self-calling is permitted) - # 3. It is a PUSH1, ie. less than 256 (ie. a present or future precompile) - if self.approved_addrs[pushargs[address_entry]]: - success = 1 - elif ops[address_entry] == 0x30: - success = 1 - elif ops[address_entry] == 0x60: - success = 1 - if not success: - ~invalid() - i += 1 - else: - i += 1 - ops[op] = c - op += 1 - self.approved_addrs[addr] = 1 - return(1: bool) - -def const check(addr: address): - return(self.approved_addrs[addr]:bool) diff --git a/impurity/impurity_tester.py b/impurity/impurity_tester.py deleted file mode 100644 index f73b90e..0000000 --- a/impurity/impurity_tester.py +++ /dev/null @@ -1,123 +0,0 @@ -from ethereum import tester as t -from ethereum import utils -from ethereum import transactions -import rlp -import serpent -s = t.state() -c = s.abi_contract('check_for_impurity.se') - -#from ethereum.slogging import LogRecorder, configure_logging, set_level -#config_string = ':info,eth.vm.log:trace,eth.vm.op:trace,eth.vm.stack:trace,eth.vm.exit:trace,eth.pb.msg:trace,eth.pb.tx:debug' -#configure_logging(config_string=config_string) - -test1 = s.abi_contract(""" - -data horse - -def foo(): - return self.horse - -""") - -try: - c.submit(test1.address) - success = True -except: - success = False -assert not success - -failedtest_addr = "0x"+utils.encode_hex(test1.address) - -test2 = s.abi_contract(""" - -def foo(): - return block.number - -""") - -try: - c.submit(test2.address) - success = True -except: - success = False -assert not success - -test3 = s.abi_contract(""" - -def foo(x): - return x * 2 -""") - -c.submit(test3.address) - - - -test4 = s.abi_contract(""" - -def modexp(b: uint256, e: uint256, m: uint256): - if e == 0: - return 1 - elif e == 1: - return b - elif e % 2 == 0: - return self.modexp(~mulmod(b, b, m), ~div(e, 2), m) - elif e % 2 == 1: - return ~mulmod(self.modexp(~mulmod(b, b, m), ~div(e, 2), m), b, m) - -""") - -c.submit(test4.address) -modexp_addr = "0x"+utils.encode_hex(test4.address) - -test5 = s.abi_contract(""" - -def modinv(b, m): - inpdata = [0xa7d4bbe6, b, m-2, m] - outdata = [0] - ~call(100000, %s, 0, inpdata + 28, 100, outdata, 32) - return outdata[0] - -""" % modexp_addr) - -c.submit(test5.address) - -test6 = s.abi_contract(""" -def phooey(h, v, r, s): - return ecrecover(h, v, r, s) -""") - -c.submit(test6.address) - -test7 = s.abi_contract(""" - -def modinv(b, m): - inpdata = [0xa7d4bbe6, b, m-2, m] - outdata = [0] - ~call(msg.gas - 10000, %s, 0, inpdata + 28, 100, outdata, 32) - return outdata[0] - -""" % failedtest_addr) - -try: - c.submit(test7.address) - success = True -except: - success = False -assert not success - -print('All tests passed') - -kode = serpent.compile('check_for_impurity.se') - -# Create transaction -t = transactions.Transaction(0, 30 * 10**9, 2999999, '', 0, kode) -t.startgas = t.intrinsic_gas_used + 50000 + 200 * len(kode) -t.v = 27 -t.r = 45 -t.s = 79 -print('Send %d wei to %s' % (t.startgas * t.gasprice, - '0x'+utils.encode_hex(t.sender))) - -print('Contract address: 0x'+utils.encode_hex(utils.mk_contract_address(t.sender, 0))) -print('Code: 0x'+utils.encode_hex(rlp.encode(t))) -print('ABI declaration: '+repr(serpent.mk_full_signature('check_for_impurity.se'))) diff --git a/interface_generator/README.md b/interface_generator/README.md deleted file mode 100644 index 4392783..0000000 --- a/interface_generator/README.md +++ /dev/null @@ -1,19 +0,0 @@ -### Interface generator - -This is a quick-and-dirty draft of a medium-level interface-generating language targeting Ethereum ABI contracts. The goal is to allow a user to write an "interface file" that specifies some details about what the layout of an interface for a contract should look like, but in a highly restricted form that ensures that the interface cannot be misleading as long as the given contract code/ABI is "honest". - -This is intended to reduce barriers to entry to using smart contracts by generating a "default interface" for any contract, and this code should ideally be ported to Javascript and put into an extension (plus a traditional centralized website), so users can enter something like eg. `http://coolwebsiteurl.fancytld/0xde0b295669a9fd93d5f28d9ec85e40f4cb697bae/my_interface_ptr` and have it pop up an automatically generated trustable interface for the contract. - -There have already been experiments in automated interface generators that look at contract code alone, eg. for the contract above see https://etherscan.io/address/0xde0b295669a9fd93d5f28d9ec85e40f4cb697bae#readContract, but so far use of these has not taken off because contract code simply does not contain enough UI-critical information about what functions are more "important", what suggestions to make to users, etc. However, simply using Javascript to generate interfaces faces the problem that it is _too_ liberal, allowing a malicious interface designer to easily make a misleading interface. The goal here is to make a language that is in the middle, expressive enough to be somewhat usable in some circumstances, but not expressive enough to allow misleading users. - -The author is allowed to create a list of "tabs", each tab corresponding to one function execution (the language could and should be extended to offer a "dashboard" tab that simply shows info without offering any functions to execute), with a textbox for each argument. The interface designer can suggest prefilled values for arguments, which can be either constant values or calls of a constant function of the same contract, and can also give information to the user in the form of calls of constant functions with preset arguments that are repeated once per second. - -See examples/foundation_out.html in this repo for a simple example using the Ethereum Foundation multisig wallet (only seven people in the world can use this to do anything useful; it is intended for illustrative purposes only). See examples/foundation_interface.json for the interface file that produces this. - -### TODOs - -* Translate the interface generator from python to javascript so it can be run inside a web browser -* Allow interface files ("interface.json" here) to be written in YAML rather than JS -* If the contract source code has variable-specific docstrings, display those beside the variable name and the textbox -* Allow input types other than textboxes, eg. dropdowns, sliders, and specialized text boxes for ETH or token values so users do not have to multiply by 10\*\*18 manually; this could be done via a "specialInputFormats" list in the interface similar to the "prefills" list. -* Allow outputs of shows to be represented in multiple ways. diff --git a/interface_generator/example.py b/interface_generator/example.py deleted file mode 100644 index eedd980..0000000 --- a/interface_generator/example.py +++ /dev/null @@ -1,19 +0,0 @@ -import interface_generator as ig -import json -import sys - -file2json = lambda x: json.load(open(x)) - -examples = file2json('examples/addresses.json') - -if len(sys.argv) == 1: - print("Available examples: " + ", ".join(examples.keys())) -elif sys.argv[1] in examples: - address = examples[sys.argv[1]] - abi = file2json('examples/%s_abi.json' % sys.argv[1]) - instructions = file2json('examples/%s_instructions.json' % sys.argv[1]) - interface = ig.generate_interface(address, abi, instructions) - open('examples/%s_out.html' % sys.argv[1], 'w+').write(interface) - print("Outputted file to examples/%s_out.html" % sys.argv[1]) -else: - print("Example %s not found" % sys.argv[1]) diff --git a/interface_generator/examples/addresses.json b/interface_generator/examples/addresses.json deleted file mode 100644 index d9dc317..0000000 --- a/interface_generator/examples/addresses.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "foundation": "0xde0b295669a9fd93d5f28d9ec85e40f4cb697bae", - "uniswap": "0x09cabec1ead1c0ba254b09efb3ee13841712be14" -} diff --git a/interface_generator/examples/foundation_abi.json b/interface_generator/examples/foundation_abi.json deleted file mode 100644 index 41d4373..0000000 --- a/interface_generator/examples/foundation_abi.json +++ /dev/null @@ -1,425 +0,0 @@ -[ - { - "constant": false, - "inputs": [ - { - "name": "_owner", - "type": "address" - } - ], - "name": "removeOwner", - "outputs": [], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_addr", - "type": "address" - } - ], - "name": "isOwner", - "outputs": [ - { - "name": "", - "type": "bool" - } - ], - "type": "function" - }, - { - "constant": true, - "inputs": [], - "name": "m_numOwners", - "outputs": [ - { - "name": "", - "type": "uint256" - } - ], - "type": "function" - }, - { - "constant": false, - "inputs": [], - "name": "resetSpentToday", - "outputs": [], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_owner", - "type": "address" - } - ], - "name": "addOwner", - "outputs": [], - "type": "function" - }, - { - "constant": true, - "inputs": [], - "name": "m_required", - "outputs": [ - { - "name": "", - "type": "uint256" - } - ], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_h", - "type": "bytes32" - } - ], - "name": "confirm", - "outputs": [ - { - "name": "", - "type": "bool" - } - ], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_newLimit", - "type": "uint256" - } - ], - "name": "setDailyLimit", - "outputs": [], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_to", - "type": "address" - }, - { - "name": "_value", - "type": "uint256" - }, - { - "name": "_data", - "type": "bytes" - } - ], - "name": "execute", - "outputs": [ - { - "name": "_r", - "type": "bytes32" - } - ], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_operation", - "type": "bytes32" - } - ], - "name": "revoke", - "outputs": [], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_newRequired", - "type": "uint256" - } - ], - "name": "changeRequirement", - "outputs": [], - "type": "function" - }, - { - "constant": true, - "inputs": [ - { - "name": "_operation", - "type": "bytes32" - }, - { - "name": "_owner", - "type": "address" - } - ], - "name": "hasConfirmed", - "outputs": [ - { - "name": "", - "type": "bool" - } - ], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_to", - "type": "address" - } - ], - "name": "kill", - "outputs": [], - "type": "function" - }, - { - "constant": false, - "inputs": [ - { - "name": "_from", - "type": "address" - }, - { - "name": "_to", - "type": "address" - } - ], - "name": "changeOwner", - "outputs": [], - "type": "function" - }, - { - "constant": true, - "inputs": [], - "name": "m_dailyLimit", - "outputs": [ - { - "name": "", - "type": "uint256" - } - ], - "type": "function" - }, - { - "inputs": [ - { - "name": "_owners", - "type": "address[]" - }, - { - "name": "_required", - "type": "uint256" - }, - { - "name": "_daylimit", - "type": "uint256" - } - ], - "type": "constructor" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "owner", - "type": "address" - }, - { - "indexed": false, - "name": "operation", - "type": "bytes32" - } - ], - "name": "Confirmation", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "owner", - "type": "address" - }, - { - "indexed": false, - "name": "operation", - "type": "bytes32" - } - ], - "name": "Revoke", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "oldOwner", - "type": "address" - }, - { - "indexed": false, - "name": "newOwner", - "type": "address" - } - ], - "name": "OwnerChanged", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "newOwner", - "type": "address" - } - ], - "name": "OwnerAdded", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "oldOwner", - "type": "address" - } - ], - "name": "OwnerRemoved", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "newRequirement", - "type": "uint256" - } - ], - "name": "RequirementChanged", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "_from", - "type": "address" - }, - { - "indexed": false, - "name": "value", - "type": "uint256" - } - ], - "name": "Deposit", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "owner", - "type": "address" - }, - { - "indexed": false, - "name": "value", - "type": "uint256" - }, - { - "indexed": false, - "name": "to", - "type": "address" - }, - { - "indexed": false, - "name": "data", - "type": "bytes" - } - ], - "name": "SingleTransact", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "owner", - "type": "address" - }, - { - "indexed": false, - "name": "operation", - "type": "bytes32" - }, - { - "indexed": false, - "name": "value", - "type": "uint256" - }, - { - "indexed": false, - "name": "to", - "type": "address" - }, - { - "indexed": false, - "name": "data", - "type": "bytes" - } - ], - "name": "MultiTransact", - "type": "event" - }, - { - "anonymous": false, - "inputs": [ - { - "indexed": false, - "name": "operation", - "type": "bytes32" - }, - { - "indexed": false, - "name": "initiator", - "type": "address" - }, - { - "indexed": false, - "name": "value", - "type": "uint256" - }, - { - "indexed": false, - "name": "to", - "type": "address" - }, - { - "indexed": false, - "name": "data", - "type": "bytes" - } - ], - "name": "ConfirmationNeeded", - "type": "event" - } -] diff --git a/interface_generator/examples/foundation_instructions.json b/interface_generator/examples/foundation_instructions.json deleted file mode 100644 index 9e1f112..0000000 --- a/interface_generator/examples/foundation_instructions.json +++ /dev/null @@ -1,8 +0,0 @@ -[ - { - "fun": "execute", - "prefills": [{"arg": "_data", "value": "0x"}, - {"arg": "_value", "fun": "m_dailyLimit", "inputs": []}], - "shows": [{"fun": "m_dailyLimit", "inputs": []}] - } -] diff --git a/interface_generator/examples/foundation_out.html b/interface_generator/examples/foundation_out.html deleted file mode 100644 index 7123c93..0000000 --- a/interface_generator/examples/foundation_out.html +++ /dev/null @@ -1,63 +0,0 @@ - - - -execute - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
_to
_value
_data
m_dailyLimit
diff --git a/interface_generator/examples/uniswap_abi.json b/interface_generator/examples/uniswap_abi.json deleted file mode 100644 index 8725f78..0000000 --- a/interface_generator/examples/uniswap_abi.json +++ /dev/null @@ -1,2 +0,0 @@ -[{"name": "TokenPurchase", "inputs": [{"type": "address", "name": "buyer", "indexed": true}, {"type": "uint256", "name": "eth_sold", "indexed": true}, {"type": "uint256", "name": "tokens_bought", "indexed": true}], "anonymous": false, "type": "event"}, {"name": "EthPurchase", "inputs": [{"type": "address", "name": "buyer", "indexed": true}, {"type": "uint256", "name": "tokens_sold", "indexed": true}, {"type": "uint256", "name": "eth_bought", "indexed": true}], "anonymous": false, "type": "event"}, {"name": "AddLiquidity", "inputs": [{"type": "address", "name": "provider", "indexed": true}, {"type": "uint256", "name": "eth_amount", "indexed": true}, {"type": "uint256", "name": "token_amount", "indexed": true}], "anonymous": false, "type": "event"}, {"name": "RemoveLiquidity", "inputs": [{"type": "address", "name": "provider", "indexed": true}, {"type": "uint256", "name": "eth_amount", "indexed": true}, {"type": "uint256", "name": "token_amount", "indexed": true}], "anonymous": false, "type": "event"}, {"name": "Transfer", "inputs": [{"type": "address", "name": "_from", "indexed": true}, {"type": "address", "name": "_to", "indexed": true}, {"type": "uint256", "name": "_value", "indexed": false}], "anonymous": false, "type": "event"}, {"name": "Approval", "inputs": [{"type": "address", "name": "_owner", "indexed": true}, {"type": "address", "name": "_spender", "indexed": true}, {"type": "uint256", "name": "_value", "indexed": false}], "anonymous": false, "type": "event"}, {"name": "setup", "outputs": [], "inputs": [{"type": "address", "name": "token_addr"}], "constant": false, "payable": false, "type": "function", "gas": 175875}, {"name": "addLiquidity", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "min_liquidity"}, {"type": "uint256", "name": "max_tokens"}, {"type": "uint256", "name": "deadline"}], "constant": false, "payable": true, "type": "function", "gas": 82616}, {"name": "removeLiquidity", "outputs": [{"type": "uint256", "name": "out"}, {"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "amount"}, {"type": "uint256", "name": "min_eth"}, {"type": "uint256", "name": "min_tokens"}, {"type": "uint256", "name": "deadline"}], "constant": false, "payable": false, "type": "function", "gas": 116814}, {"name": "__default__", "outputs": [], "inputs": [], "constant": false, "payable": true, "type": "function"}, {"name": "ethToTokenSwapInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "min_tokens"}, {"type": "uint256", "name": "deadline"}], "constant": false, "payable": true, "type": "function", "gas": 12757}, {"name": "ethToTokenTransferInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "min_tokens"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}], "constant": false, "payable": true, "type": "function", "gas": 12965}, {"name": "ethToTokenSwapOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_bought"}, {"type": "uint256", "name": "deadline"}], "constant": false, "payable": true, "type": "function", "gas": 50463}, {"name": "ethToTokenTransferOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_bought"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}], "constant": false, "payable": true, "type": "function", "gas": 50671}, {"name": "tokenToEthSwapInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_sold"}, {"type": "uint256", "name": "min_eth"}, {"type": "uint256", "name": "deadline"}], "constant": false, "payable": false, "type": "function", "gas": 47503}, {"name": "tokenToEthTransferInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_sold"}, {"type": "uint256", "name": "min_eth"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}], "constant": false, "payable": false, "type": "function", "gas": 47712}, {"name": "tokenToEthSwapOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "eth_bought"}, {"type": "uint256", "name": "max_tokens"}, {"type": "uint256", "name": "deadline"}], "constant": false, "payable": false, "type": "function", "gas": 50175}, {"name": "tokenToEthTransferOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "eth_bought"}, {"type": "uint256", "name": "max_tokens"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}], "constant": false, "payable": false, "type": "function", "gas": 50384}, {"name": "tokenToTokenSwapInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_sold"}, {"type": "uint256", "name": "min_tokens_bought"}, {"type": "uint256", "name": "min_eth_bought"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "token_addr"}], "constant": false, "payable": false, "type": "function", "gas": 51007}, {"name": "tokenToTokenTransferInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_sold"}, {"type": "uint256", "name": "min_tokens_bought"}, {"type": "uint256", "name": "min_eth_bought"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}, {"type": "address", "name": "token_addr"}], "constant": false, "payable": false, "type": "function", "gas": 51098}, {"name": "tokenToTokenSwapOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_bought"}, {"type": "uint256", "name": "max_tokens_sold"}, {"type": "uint256", "name": "max_eth_sold"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "token_addr"}], "constant": false, "payable": false, "type": "function", "gas": 54928}, {"name": "tokenToTokenTransferOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_bought"}, {"type": "uint256", "name": "max_tokens_sold"}, {"type": "uint256", "name": "max_eth_sold"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}, {"type": "address", "name": "token_addr"}], "constant": false, "payable": false, "type": "function", "gas": 55019}, {"name": "tokenToExchangeSwapInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_sold"}, {"type": "uint256", "name": "min_tokens_bought"}, {"type": "uint256", "name": "min_eth_bought"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "exchange_addr"}], "constant": false, "payable": false, "type": "function", "gas": 49342}, {"name": "tokenToExchangeTransferInput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_sold"}, {"type": "uint256", "name": "min_tokens_bought"}, {"type": "uint256", "name": "min_eth_bought"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}, {"type": "address", "name": "exchange_addr"}], "constant": false, "payable": false, "type": "function", "gas": 49532}, {"name": "tokenToExchangeSwapOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_bought"}, {"type": "uint256", "name": "max_tokens_sold"}, {"type": "uint256", "name": "max_eth_sold"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "exchange_addr"}], "constant": false, "payable": false, "type": "function", "gas": 53233}, {"name": "tokenToExchangeTransferOutput", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_bought"}, {"type": "uint256", "name": "max_tokens_sold"}, {"type": "uint256", "name": "max_eth_sold"}, {"type": "uint256", "name": "deadline"}, {"type": "address", "name": "recipient"}, {"type": "address", "name": "exchange_addr"}], "constant": false, "payable": false, "type": "function", "gas": 53423}, {"name": "getEthToTokenInputPrice", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "eth_sold"}], "constant": true, "payable": false, "type": "function", "gas": 5542}, {"name": "getEthToTokenOutputPrice", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_bought"}], "constant": true, "payable": false, "type": "function", "gas": 6872}, {"name": "getTokenToEthInputPrice", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "tokens_sold"}], "constant": true, "payable": false, "type": "function", "gas": 5637}, {"name": "getTokenToEthOutputPrice", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "uint256", "name": "eth_bought"}], "constant": true, "payable": false, "type": "function", "gas": 6897}, {"name": "tokenAddress", "outputs": [{"type": "address", "name": "out"}], "inputs": [], "constant": true, "payable": false, "type": "function", "gas": 1413}, {"name": "factoryAddress", "outputs": [{"type": "address", "name": "out"}], "inputs": [], "constant": true, "payable": false, "type": "function", "gas": 1443}, {"name": "balanceOf", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "address", "name": "_owner"}], "constant": true, "payable": false, "type": "function", "gas": 1645}, {"name": "transfer", "outputs": [{"type": "bool", "name": "out"}], "inputs": [{"type": "address", "name": "_to"}, {"type": "uint256", "name": "_value"}], "constant": false, "payable": false, "type": "function", "gas": 75034}, {"name": "transferFrom", "outputs": [{"type": "bool", "name": "out"}], "inputs": [{"type": "address", "name": "_from"}, {"type": "address", "name": "_to"}, {"type": "uint256", "name": "_value"}], "constant": false, "payable": false, "type": "function", "gas": 110907}, {"name": "approve", "outputs": [{"type": "bool", "name": "out"}], "inputs": [{"type": "address", "name": "_spender"}, {"type": "uint256", "name": "_value"}], "constant": false, "payable": false, "type": "function", "gas": 38769}, {"name": "allowance", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [{"type": "address", "name": "_owner"}, {"type": "address", "name": "_spender"}], "constant": true, "payable": false, "type": "function", "gas": 1925}, {"name": "name", "outputs": [{"type": "bytes32", "name": "out"}], "inputs": [], "constant": true, "payable": false, "type": "function", "gas": 1623}, {"name": "symbol", "outputs": [{"type": "bytes32", "name": "out"}], "inputs": [], "constant": true, "payable": false, "type": "function", "gas": 1653}, {"name": "decimals", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [], "constant": true, "payable": false, "type": "function", "gas": 1683}, {"name": "totalSupply", "outputs": [{"type": "uint256", "name": "out"}], "inputs": [], "constant": true, "payable": false, "type": "function", "gas": 1713}] - diff --git a/interface_generator/examples/uniswap_instructions.json b/interface_generator/examples/uniswap_instructions.json deleted file mode 100644 index 6d8377b..0000000 --- a/interface_generator/examples/uniswap_instructions.json +++ /dev/null @@ -1,7 +0,0 @@ -[ - { - "fun": "ethToTokenSwapInput", - "prefills": [], - "shows": [{"fun": "getEthToTokenInputPrice", "inputs": ["1"]}] - } -] diff --git a/interface_generator/examples/uniswap_out.html b/interface_generator/examples/uniswap_out.html deleted file mode 100644 index 0b55ebb..0000000 --- a/interface_generator/examples/uniswap_out.html +++ /dev/null @@ -1,51 +0,0 @@ - - - -ethToTokenSwapInput - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
min_tokens
deadline
ETH amount to send
getEthToTokenInputPrice(1)
diff --git a/interface_generator/interface_generator.py b/interface_generator/interface_generator.py deleted file mode 100644 index 0ed5d77..0000000 --- a/interface_generator/interface_generator.py +++ /dev/null @@ -1,117 +0,0 @@ -import binascii -import json - -header_template = """ - -""" - -function_top_template = """ -%s - -""" - -argument_template = """ - - - - -""" - -simple_prefill_template = """ - -""" - -prefill_by_call_script_template = """ - -""" - -click_template = """ - - - - - -""" - -show_template = """ - - - - - -""" - -function_bottom_template = """ - - - - -
%s
%s(%s)
-""" - -def generate_interface(address, abi, instructions): - code = header_template % (json.dumps(abi), address) - for page in instructions: - function_name = page['fun'] - code += function_top_template % (function_name, function_name) - abi_args = [x for x in abi if x.get("name", None) == function_name][0] - for inp in abi_args["inputs"]: - code += argument_template % (inp["name"], function_name + "___" + inp["name"]) - if abi_args.get("payable", None): - code += argument_template % ("ETH amount to send", function_name + "___" + "ETH_AMOUNT_") - for prefill in page.get('prefills', []): - assert prefill['arg'] in [x['name'] for x in abi_args['inputs']] - element_id = function_name + "___" + prefill['arg'] - if "value" in prefill: - code += simple_prefill_template % (element_id, prefill["value"]) - else: - code += prefill_by_call_script_template % ( - prefill['fun'], - ','.join(map(str, prefill['inputs'] + [' '])), - element_id, - ) - input_args = '' - for inp in abi_args['inputs']: - input_args += 'document.getElementById("' + function_name + "___" + inp["name"] + '").value, ' - if abi_args.get('payable', None): - input_args += '{value: web3.toWei(document.getElementById("' + function_name + '___ETH_AMOUNT_").value)}, ' - code += click_template % ( - function_name, - function_name, - input_args, - function_name, - function_name - ) - for i, show in enumerate(page.get('shows', [])): - element_id = function_name + "__show__" + str(i) - code += show_template % ( - show['fun'], - ','.join(map(str, show['inputs'])), - element_id, - show['fun'], - ','.join(map(str, show['inputs'] + [' '])), - element_id, - ) - code += function_bottom_template % (function_name) - return code diff --git a/kzg_data_availability/README.md b/kzg_data_availability/README.md deleted file mode 100644 index 2408e8e..0000000 --- a/kzg_data_availability/README.md +++ /dev/null @@ -1,5 +0,0 @@ -This implmentation uses the BLST signature library -github.com/supranational/blst - -For python, the library use SWIG definitions to create the binding. -To test the library and generate the pythong bindings, run `/bindings/python/run.me` on your BLST implementation, then copy the resultant files to [./blst/]() directory. You need to have SWIG installed from your prefered package manager. \ No newline at end of file diff --git a/kzg_data_availability/blst/__init__.py b/kzg_data_availability/blst/__init__.py deleted file mode 100644 index 09d908b..0000000 --- a/kzg_data_availability/blst/__init__.py +++ /dev/null @@ -1 +0,0 @@ -from blst.blst import * \ No newline at end of file diff --git a/kzg_data_availability/fft.py b/kzg_data_availability/fft.py deleted file mode 100644 index 927e668..0000000 --- a/kzg_data_availability/fft.py +++ /dev/null @@ -1,129 +0,0 @@ - -import blst - -P1_INF = blst.P1(bytes.fromhex("400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")) - - -def _simple_ft(vals, modulus, roots_of_unity): - L = len(roots_of_unity) - o = [] - for i in range(L): - last = P1_INF if type(vals[0]) == blst.P1 else 0 - for j in range(L): - if type(vals[0]) == blst.P1: - #last = b.add(last, b.multiply(vals[j], roots_of_unity[(i*j)%L])) - last.add(vals[j].dup().mul(roots_of_unity[(i*j)%L])) - else: - last += vals[j] * roots_of_unity[(i*j)%L] - o.append(last if type(last) == blst.P1 else last % modulus) - return o - -def _fft(vals, modulus, roots_of_unity): - if len(vals) <= 4 and type(vals[0]) != blst.P1: - #return vals - return _simple_ft(vals, modulus, roots_of_unity) - elif len(vals) == 1 and type(vals[0]) == blst.P1: - return vals - L = _fft(vals[::2], modulus, roots_of_unity[::2]) - R = _fft(vals[1::2], modulus, roots_of_unity[::2]) - o = [0 for i in vals] - for i, (x, y) in enumerate(zip(L, R)): - #y_times_root = b.multiply(y, roots_of_unity[i]) if type(y) == tuple else y*roots_of_unity[i] - y_times_root = y.dup().mult(roots_of_unity[i]) if type(y) == blst.P1 else y*roots_of_unity[i] - #o[i] = b.add(x, y_times_root) if type(x) == tuple else (x+y_times_root) % modulus - o[i] = x.dup().add(y_times_root) if type(y) == blst.P1 else (x+y_times_root) % modulus - #o[i+len(L)] = b.add(x, b.neg(y_times_root)) if type(x) == tuple else (x-y_times_root) % modulus - o[i+len(L)] = x.dup().add(y_times_root.dup().neg()) if type(x) == blst.P1 else (x-y_times_root) % modulus - return o - -def expand_root_of_unity(root_of_unity, modulus): - # Build up roots of unity - rootz = [1, root_of_unity] - while rootz[-1] != 1: - rootz.append((rootz[-1] * root_of_unity) % modulus) - return rootz - -def fft(vals, modulus, root_of_unity, inv=False): - rootz = expand_root_of_unity(root_of_unity, modulus) - # Fill in vals with zeroes if needed - if len(rootz) > len(vals) + 1: - vals = vals + [0] * (len(rootz) - len(vals) - 1) - if inv: - # Inverse FFT - invlen = pow(len(vals), modulus-2, modulus) - if type(vals[0]) == blst.P1: - return [x.dup().mult(invlen) for x in - _fft(vals, modulus, rootz[:0:-1])] - else: - return [(x*invlen) % modulus for x in - _fft(vals, modulus, rootz[:0:-1])] - else: - # Regular FFT - return _fft(vals, modulus, rootz[:-1]) - -#Note on call hierarchy: the project is not using the functions below. - -# Evaluates f(x) for f in evaluation form -def inv_fft_at_point(vals, modulus, root_of_unity, x): - if len(vals) == 1: - return vals[0] - # 1/2 in the field - half = (modulus + 1)//2 - # 1/w - inv_root = pow(root_of_unity, len(vals)-1, modulus) - # f(-x) in evaluation form - f_of_minus_x_vals = vals[len(vals)//2:] + vals[:len(vals)//2] - # e(x) = (f(x) + f(-x)) / 2 in evaluation form - evens = [(f+g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - # o(x) = (f(x) - f(-x)) / 2 in evaluation form - odds = [(f-g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - # e(x^2) + coordinate * x * o(x^2) in evaluation form - comb = [(o * x * inv_root**i + e) % modulus for i, (o, e) in enumerate(zip(odds, evens))] - return inv_fft_at_point(comb[:len(comb)//2], modulus, root_of_unity ** 2 % modulus, x**2 % modulus) - -def shift_domain(vals, modulus, root_of_unity, factor): - if len(vals) == 1: - return vals - # 1/2 in the field - half = (modulus + 1)//2 - # 1/w - inv_factor = pow(factor, modulus - 2, modulus) - half_length = len(vals)//2 - # f(-x) in evaluation form - f_of_minus_x_vals = vals[half_length:] + vals[:half_length] - # e(x) = (f(x) + f(-x)) / 2 in evaluation form - evens = [(f+g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - print('e', evens) - # o(x) = (f(x) - f(-x)) / 2 in evaluation form - odds = [(f-g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - print('o', odds) - shifted_evens = shift_domain(evens[:half_length], modulus, root_of_unity ** 2 % modulus, factor ** 2 % modulus) - print('se', shifted_evens) - shifted_odds = shift_domain(odds[:half_length], modulus, root_of_unity ** 2 % modulus, factor ** 2 % modulus) - print('so', shifted_odds) - return ( - [(e + inv_factor * o) % modulus for e, o in zip(shifted_evens, shifted_odds)] + - [(e - inv_factor * o) % modulus for e, o in zip(shifted_evens, shifted_odds)] - ) - -def shift_poly(poly, modulus, factor): - factor_power = 1 - inv_factor = pow(factor, modulus - 2, modulus) - o = [] - for p in poly: - o.append(p * factor_power % modulus) - factor_power = factor_power * inv_factor % modulus - return o - -def mul_polys(a, b, modulus, root_of_unity): - rootz = [1, root_of_unity] - while rootz[-1] != 1: - rootz.append((rootz[-1] * root_of_unity) % modulus) - if len(rootz) > len(a) + 1: - a = a + [0] * (len(rootz) - len(a) - 1) - if len(rootz) > len(b) + 1: - b = b + [0] * (len(rootz) - len(b) - 1) - x1 = _fft(a, modulus, rootz[:-1]) - x2 = _fft(b, modulus, rootz[:-1]) - return _fft([(v1*v2)%modulus for v1,v2 in zip(x1,x2)], - modulus, rootz[:0:-1]) diff --git a/kzg_data_availability/fk20_multi.py b/kzg_data_availability/fk20_multi.py deleted file mode 100644 index c0e2799..0000000 --- a/kzg_data_availability/fk20_multi.py +++ /dev/null @@ -1,181 +0,0 @@ -import blst -from fft import fft -import kzg_proofs -from kzg_proofs import ( - MODULUS, - check_proof_multi, - generate_setup, - commit_to_poly, - list_to_reverse_bit_order, - get_root_of_unity, - reverse_bit_order, - is_power_of_two, - eval_poly_at, - get_extended_data, - P1_INF -) -from fk20_single import ( - toeplitz_part1, - toeplitz_part2, - toeplitz_part3 -) - -# FK20 Method to compute all proofs -# Toeplitz multiplication via http://www.netlib.org/utk/people/JackDongarra/etemplates/node384.html -# Multi proof method - -def fk20_multi(polynomial, l, setup): - """ - For a polynomial of size n, let w be a n-th root of unity. Then this method will return - k=n/l KZG proofs for the points - proof[0]: w^(0*l + 0), w^(0*l + 1), ... w^(0*l + l - 1) - proof[0]: w^(0*l + 0), w^(0*l + 1), ... w^(0*l + l - 1) - ... - proof[i]: w^(i*l + 0), w^(i*l + 1), ... w^(i*l + l - 1) - ... - """ - - n = len(polynomial) - k = n // l - assert is_power_of_two(n) - assert is_power_of_two(l) - assert k >= 1 - - # Preprocessing part -- this is independent from the polynomial coefficients and can be - # done before the polynomial is known, it only needs to be computed once - xext_fft = [] - for i in range(l): - x = setup[0][n - l - 1 - i::-l] + [P1_INF.dup()] - xext_fft.append(toeplitz_part1(x)) - - hext_fft = [P1_INF.dup()] * 2 * k - for i in range(l): - - toeplitz_coefficients = polynomial[- i - 1::l] + [0] * (k + 1) + polynomial[2 * l - i - 1: - l - i:l] - - # Compute the vector h from the paper using a Toeplitz matric multiplication - hext_fft = [v.dup().add(w) for v, w in zip(hext_fft, toeplitz_part2(toeplitz_coefficients, xext_fft[i]))] - - h = toeplitz_part3(hext_fft) - - # The proofs are the DFT of the h vector - return fft(h, MODULUS, get_root_of_unity(k)) - - -def fk20_multi_data_availability_optimized(polynomial, l, setup): - """ - FK20 multi-proof method, optimized for dava availability where the top half of polynomial - coefficients == 0 - """ - - assert is_power_of_two(len(polynomial)) - n = len(polynomial) // 2 - k = n // l - assert is_power_of_two(n) - assert is_power_of_two(l) - assert k >= 1 - - assert all(x == 0 for x in polynomial[n:]) - reduced_polynomial = polynomial[:n] - - # Preprocessing part -- this is independent from the polynomial coefficients and can be - # done before the polynomial is known, it only needs to be computed once - xext_fft = [] - for i in range(l): - x = setup[0][n - l - 1 - i::-l] + [P1_INF.dup()] - xext_fft.append(toeplitz_part1(x)) - - add_instrumentation() - - hext_fft = [P1_INF.dup()] * 2 * k - for i in range(l): - - toeplitz_coefficients = reduced_polynomial[- i - 1::l] + [0] * (k + 1) \ - + reduced_polynomial[2 * l - i - 1: - l - i:l] - - # Compute the vector h from the paper using a Toeplitz matric multiplication - hext_fft = [v.dup().add(w) for v, w in zip(hext_fft, toeplitz_part2(toeplitz_coefficients, xext_fft[i]))] - - # Final FFT done after summing all h vectors - h = toeplitz_part3(hext_fft) - - h = h + [P1_INF.dup()] * k - - # The proofs are the DFT of the h vector - return fft(h, MODULUS, get_root_of_unity(2 * k)) - - -def data_availabilty_using_fk20_multi(polynomial, l, setup): - """ - Computes all the KZG proofs for data availability checks. This involves sampling on the double domain - and reordering according to reverse bit order - """ - assert is_power_of_two(len(polynomial)) - n = len(polynomial) - extended_polynomial = polynomial + [0] * n - - all_proofs = fk20_multi_data_availability_optimized(extended_polynomial, l, setup) - - return list_to_reverse_bit_order(all_proofs) - - -def add_instrumentation(): - global multiplication_count - - multiplication_count = 0 - - # Add counter to multiply function for statistics - b_multiply_ = blst.P1.mult - def multiply_and_count(*args): - global multiplication_count - multiplication_count += 1 - - return b_multiply_(*args) - - blst.P1.mult = multiply_and_count - - -if __name__ == "__main__": - #uncomment to report time for the functions - #from timer import chrono - #generate_setup = chrono(generate_setup) - #data_availabilty_using_fk20_multi = chrono(data_availabilty_using_fk20_multi) - #check_proof_multi = chrono(check_proof_multi) - - import random - from tqdm import tqdm - - MAX_DEGREE_POLY = MODULUS-1 - N_POINTS = 512 - - - polynomial = [random.randint(1, MAX_DEGREE_POLY) for _ in range(512)] - n = N_POINTS - - setup = generate_setup(random.getrandbits(256), n) - - commitment = commit_to_poly(polynomial, setup) - - l = 16 - - all_proofs = data_availabilty_using_fk20_multi(polynomial, l, setup) - print("All KZG proofs computed for data availability (supersampled by factor 2)") - print("Required {0} G1 multiplications".format(multiplication_count)) - print(n, l, multiplication_count) - - # Now check all positions - extended_data = get_extended_data(polynomial) - - for pos in range(2 * n // l): - root_of_unity = get_root_of_unity(n * 2) - x = pow(root_of_unity, reverse_bit_order(pos, 2 * n // l), MODULUS) - ys = extended_data[l * pos:l * (pos + 1)] - - subgroup_root_of_unity = get_root_of_unity(l) - coset = [x * pow(subgroup_root_of_unity, i, MODULUS) for i in range(l)] - ys2 = [eval_poly_at(polynomial, z) for z in coset] - assert list_to_reverse_bit_order(ys) == ys2 - - assert check_proof_multi(commitment, all_proofs[pos], x, list_to_reverse_bit_order(ys), setup) - print("Data availability sample check {0} passed".format(pos)) - diff --git a/kzg_data_availability/fk20_single.py b/kzg_data_availability/fk20_single.py deleted file mode 100644 index 7bcd657..0000000 --- a/kzg_data_availability/fk20_single.py +++ /dev/null @@ -1,182 +0,0 @@ -import blst -from fft import fft -import kzg_proofs -from kzg_proofs import ( - MODULUS, - check_proof_single, - generate_setup, - commit_to_poly, - list_to_reverse_bit_order, - get_root_of_unity, - reverse_bit_order, - is_power_of_two, - eval_poly_at, - P1_INF -) - -# FK20 Method to compute all proofs -# Toeplitz multiplication via http://www.netlib.org/utk/people/JackDongarra/etemplates/node384.html -# Single proof method - -# A Toeplitz matrix is of the form -# -# t_0 t_(-1) t_(-2) ... t_(1-n) -# t_1 t_0 t_(-1) ... t_(2-n) -# t_2 t_1 . -# . . . -# . . . -# . . t(-1) -# t_(n-1) ... t_1 t_0 -# -# The vector [t_0, t_1, ..., t_(n-2), t_(n-1), 0, t_(1-n), t_(2-n), ..., t_(-2), t_(-1)] -# completely determines the Toeplitz matrix and is called the "toeplitz_coefficients" below - - -# The composition toeplitz_part3(toeplitz_part2(toeplitz_coefficients, toeplitz_part1(x))) -# compute the matrix-vector multiplication T * x -# -# The algorithm here is written under the assumption x = G1 elements, T scalars -# -# For clarity, vectors in "Fourier space" are written with _fft. So for example, the vector -# xext is the extended x vector (padded with zero), and xext_fft is its Fourier transform. - - -# Toeplitz matrix multiplication part 1 -- precompute (independent of polynomial) -def toeplitz_part1(x): - """ - Performs the first part of the Toeplitz matrix multiplication algorithm, which is a Fourier - transform of the vector x extended - """ - assert is_power_of_two(len(x)) - - root_of_unity = get_root_of_unity(len(x) * 2) - - # Extend x with zeros (neutral element of G1) - xext = x + [P1_INF.dup() for _ in range(len(x))] - - xext_fft = fft(xext, MODULUS, root_of_unity, inv=False) - - return xext_fft - -def toeplitz_part2(toeplitz_coefficients, xext_fft): - """ - Performs the second part of the Toeplitz matrix multiplication algorithm - """ - # Extend the toeplitz coefficients to get a circulant matrix into which the Toeplitz - # matrix is embedded - assert is_power_of_two(len(toeplitz_coefficients)) - - root_of_unity = get_root_of_unity(len(xext_fft)) - - toeplitz_coefficients_fft = fft(toeplitz_coefficients, MODULUS, root_of_unity, inv=False) - hext_fft = [v.dup().mult(w) for v, w in zip(xext_fft, toeplitz_coefficients_fft)] - - return hext_fft - -def toeplitz_part3(hext_fft): - root_of_unity = get_root_of_unity(len(hext_fft)) - - # Transform back and return the first half of the vector - # Only the top half is the Toeplitz product, the rest is padding - return fft(hext_fft, MODULUS, root_of_unity, inv=True)[:len(hext_fft) // 2] - - -def fk20_single(polynomial, setup): - """ - Compute all n (single) proofs according to FK20 method - """ - - assert is_power_of_two(len(polynomial)) - n = len(polynomial) - - x = setup[0][n - 2::-1] + [P1_INF.dup()] - xext_fft = toeplitz_part1(x) - - toeplitz_coefficients = polynomial[-1::] + [0] * (n + 1) + polynomial[1:-1] - - # Compute the vector h from the paper using a Toeplitz matric multiplication - h = toeplitz_part3(toeplitz_part2(toeplitz_coefficients, xext_fft)) - - # The proofs are the DFT of the h vector - return fft(h, MODULUS, get_root_of_unity(n)) - - -# Compute all n (single) proofs according to FK20 method -def fk20_single_data_availability_optimized(polynomial: list[int], setup: tuple[list[blst.P1], list[blst.P2]]) -> list[blst.P1]: - """ - Special version of the FK20 for the situation of data availability checks: - The upper half of the polynomial coefficients is always 0, so we do not need to extend to twice the size - for Toeplitz matrix multiplication - """ - assert is_power_of_two(len(polynomial)) - - n = len(polynomial) // 2 - - assert all(x == 0 for x in polynomial[n:]) - reduced_polynomial = polynomial[:n] - - # Preprocessing part -- this is independent from the polynomial coefficients and can be - # done before the polynomial is known, it only needs to be computed once - x = setup[0][n - 2::-1] + [P1_INF] - xext_fft = toeplitz_part1(x) - - toeplitz_coefficients = reduced_polynomial[-1::] + [0] * (n + 1) + reduced_polynomial[1:-1] - - # Compute the vector h from the paper using a Toeplitz matric multiplication - h = toeplitz_part3(toeplitz_part2(toeplitz_coefficients, xext_fft)) - - h = h + [P1_INF.dup() for _ in range(n)] - - # The proofs are the DFT of the h vector - return fft(h, MODULUS, get_root_of_unity(2 * n)) - - -def data_availabilty_using_fk20(polynomial: list[int], setup: tuple[list[blst.P1], list[blst.P2]]) -> list[blst.P1]: - """ - Computes all the KZG proofs for data availability checks. This involves sampling on the double domain - and reordering according to reverse bit order - """ - assert is_power_of_two(len(polynomial)) - n = len(polynomial) - extended_polynomial = polynomial + [0] * n - - all_proofs = fk20_single_data_availability_optimized(extended_polynomial, setup) - - return list_to_reverse_bit_order(all_proofs) - - -if __name__ == "__main__": - #uncomment to report time for the functions - #from timer import chrono - #generate_setup = chrono(generate_setup) - #commit_to_poly = chrono(commit_to_poly) - #eval_poly_at = chrono(eval_poly_at) - #check_proof_single = chrono(check_proof_single) - - import random - from tqdm import tqdm - - MAX_DEGREE_POLY = MODULUS-1 - N_POINTS = 512 - - polynomial = [random.randint(1, MAX_DEGREE_POLY) for _ in range(512)] - n = N_POINTS - - setup = generate_setup(random.getrandbits(256), n) - - commitment = commit_to_poly(polynomial, setup) - - # Computing the proofs on the double - all_proofs = data_availabilty_using_fk20(polynomial, setup) - print("All KZG proofs computed") - - # Now check a random position - - pos = random.randrange(0, len(polynomial), desc='Single point check') - for pos in tqdm(range(n)): - root_of_unity = get_root_of_unity(n * 2) - x = pow(root_of_unity, pos, MODULUS) - y = eval_poly_at(polynomial, x) - - assert check_proof_single(commitment, all_proofs[reverse_bit_order(pos, 2 * n)], x, y, setup) - print(f"Single point check passed for all {n} points") \ No newline at end of file diff --git a/kzg_data_availability/kzg_proofs.py b/kzg_data_availability/kzg_proofs.py deleted file mode 100644 index 42eab42..0000000 --- a/kzg_data_availability/kzg_proofs.py +++ /dev/null @@ -1,277 +0,0 @@ -import blst -from fft import fft -from multicombs import lincomb - -# Generatore for the field -PRIMITIVE_ROOT = 5 -MODULUS = 52435875175126190479447740508185965837690552500527637822603658699938581184513 #b.curve_order - -P1_INF = blst.P1(bytes.fromhex("400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")) -P2_INF = blst.P2(bytes.fromhex("400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")) - -assert pow(PRIMITIVE_ROOT, (MODULUS - 1) // 2, MODULUS) != 1 -assert pow(PRIMITIVE_ROOT, MODULUS - 1, MODULUS) == 1 - -######################################################################################### -# -# Helpers -# -######################################################################################### -def hex(i : blst.P1): - bytes = i.serialize() - return ''.join(f'{b:02x}' for b in bytes) - -def is_power_of_two(x): - return x > 0 and x & (x-1) == 0 - - -def generate_setup(s :int, size :int) -> tuple[list[blst.P1], list[blst.P2]]: - """ - # Generate trusted setup, in coefficient form. - # For data availability we always need to compute the polynomials anyway, so it makes little sense to do things in Lagrange space - """ - return( - [blst.G1().mult( pow(s, i, MODULUS) ) for i in range(size + 1)], - [blst.G2().mult( pow(s, i, MODULUS) ) for i in range(size + 1)] - ) - -######################################################################################### -# -# Field operations -# -######################################################################################### - - -def get_root_of_unity(order: int) -> int: - """ - Returns a root of unity of order "order" - """ - assert (MODULUS - 1) % order == 0 - return pow(PRIMITIVE_ROOT, (MODULUS - 1) // order, MODULUS) - -def inv(a): - """ - Modular inverse using eGCD algorithm - """ - if a == 0: - return 0 - lm, hm = 1, 0 - low, high = a % MODULUS, MODULUS - while low > 1: - r = high // low - nm, new = hm - lm * r, high - low * r - lm, low, hm, high = nm, new, lm, low - return lm % MODULUS - -def div(x, y): - return x * inv(y) % MODULUS - -######################################################################################### -# -# Polynomial operations -# -######################################################################################### - -def eval_poly_at(p: list[int], x: int) -> int: - """ - Evaluate polynomial p (coefficient form) at point x - """ - y = 0 - power_of_x = 1 - for i, p_coeff in enumerate(p): - y += power_of_x * p_coeff - power_of_x = (power_of_x * x) % MODULUS - return y % MODULUS - -def div_polys(a, b): - """ - Long polynomial difivion for two polynomials in coefficient form - """ - a = [x for x in a] - o = [] - apos = len(a) - 1 - bpos = len(b) - 1 - diff = apos - bpos - while diff >= 0: - quot = div(a[apos], b[bpos]) - o.insert(0, quot) - for i in range(bpos, -1, -1): - a[diff + i] -= b[i] * quot - apos -= 1 - diff -= 1 - return [x % MODULUS for x in o] - -######################################################################################### -# -# Utils for reverse bit order -# -######################################################################################### - - -def reverse_bit_order(n, order): - """ - Reverse the bit order of an integer n - """ - assert is_power_of_two(order) - # Convert n to binary with the same number of bits as "order" - 1, then reverse its bit order - return int(('{:0' + str(order.bit_length() - 1) + 'b}').format(n)[::-1], 2) - - -def list_to_reverse_bit_order(l): - """ - Convert a list between normal and reverse bit order. This operation is idempotent. - """ - return [l[reverse_bit_order(i, len(l))] for i in range(len(l))] - - -######################################################################################### -# -# Converting between polynomials (in coefficient form) and data (in reverse bit order) -# and extending data -# -######################################################################################### - -def get_polynomial(data): - """ - Interpolate a polynomial (coefficients) from data in reverse bit order - """ - assert is_power_of_two(len(data)) - root_of_unity = get_root_of_unity(len(data)) - return fft(list_to_reverse_bit_order(data), MODULUS, root_of_unity, True) - -def get_data(polynomial): - """ - Get data (in reverse bit order) from polynomial in coefficient form - """ - assert is_power_of_two(len(polynomial)) - root_of_unity = get_root_of_unity(len(polynomial)) - return list_to_reverse_bit_order(fft(polynomial, MODULUS, root_of_unity, False)) - -def get_extended_data(polynomial): - """ - Get extended data (expanded by 2x, reverse bit order) from polynomial in coefficient form - """ - assert is_power_of_two(len(polynomial)) - extended_polynomial = polynomial + [0] * len(polynomial) - root_of_unity = get_root_of_unity(len(extended_polynomial)) - return list_to_reverse_bit_order(fft(extended_polynomial, MODULUS, root_of_unity, False)) - -######################################################################################### -# -# Kate single proofs -# -######################################################################################### - -BLSTADDER = lambda x,y: x.dup().add(y) - -def commit_to_poly(polynomial: list[int], setup: tuple[list[blst.P1], list[blst.P2]]) -> blst.P1: - """ - Kate commitment to polynomial in coefficient form - """ - return lincomb(setup[0][:len(polynomial)], polynomial, BLSTADDER, P1_INF.dup()) - -def compute_proof_single(polynomial: list[int], x: int, setup: tuple[list[blst.P1], list[blst.P2]]) -> blst.P1: - """ - Compute Kate proof for polynomial in coefficient form at position x - """ - quotient_polynomial = div_polys(polynomial, [-x, 1]) - return lincomb(setup[0][:len(quotient_polynomial)], quotient_polynomial, BLSTADDER, P1_INF.dup()) - -def check_proof_single(commitment: blst.P1, proof: blst.P1, x: int, y: int, setup: tuple[list[blst.P1], list[blst.P2]]) -> bool: - """ - Check a proof for a Kate commitment for an evaluation f(x) = y - """ - # Verify the pairing equation - # - # e([commitment - y], [1]) = e([proof], [s - x]) - # equivalent to - # e([commitment - y]^(-1), [1]) * e([proof], [s - x]) = 1_T - # - - smx = setup[1][1].dup().add(blst.G2().neg().mult(x)) - cmy = commitment.dup().add(blst.G1().neg().mult(y)) - - pc = blst.PT(blst.G2().to_affine(), cmy.neg().to_affine()) - pc.mul(blst.PT(smx.to_affine(), proof.to_affine())) - return pc.final_exp().is_one() - -######################################################################################### -# -# Kate multiproofs on a coset -# -######################################################################################### - -def compute_proof_multi(polynomial: list[int], x: blst.P1, n:int , setup: blst.P1) -> blst.P1: - """ - Compute Kate proof for polynomial in coefficient form at positions x * w^y where w is - an n-th root of unity (this is the proof for one data availability sample, which consists - of several polynomial evaluations) - """ - quotient_polynomial = div_polys(polynomial, [-pow(x, n, MODULUS)] + [0] * (n - 1) + [1]) - return lincomb(setup[0][:len(quotient_polynomial)], quotient_polynomial, BLSTADDER, P1_INF.dup()) - -def check_proof_multi(commitment: blst.P1, proof: blst.P1, x: int, ys: list[int], setup: tuple[list[blst.P1], list[blst.P2]]) ->bool: - """ - Check a proof for a Kate commitment for an evaluation f(x w^i) = y_i - """ - n = len(ys) - root_of_unity = get_root_of_unity(n) - - # Interpolate at a coset. Note because it is a coset, not the subgroup, we have to multiply the - # polynomial coefficients by x^i - interpolation_polynomial = fft(ys, MODULUS, root_of_unity, True) - interpolation_polynomial = [div(c, pow(x, i, MODULUS)) for i, c in enumerate(interpolation_polynomial)] - - # Verify the pairing equation - # - # e([commitment - interpolation_polynomial(s)], [1]) = e([proof], [s^n - x^n]) - # equivalent to - # e([commitment - interpolation_polynomial]^(-1), [1]) * e([proof], [s^n - x^n]) = 1_T - # - - #xn_minus_yn = b.add(setup[1][n], b.multiply(b.neg(b.G2), pow(x, n, MODULUS))) - xn_minus_yn = setup[1][n].dup().add( blst.G2().neg().mult(pow(x, n, MODULUS)) ) - #commitment_minus_interpolation = b.add(commitment, b.neg(lincomb( - # setup[0][:len(interpolation_polynomial)], interpolation_polynomial, b.add, b.Z1))) - commitment_minus_interpolation = commitment.dup().add( lincomb( - setup[0][:len(interpolation_polynomial)], interpolation_polynomial, BLSTADDER, P1_INF.dup() - ).neg() ) - - pc = blst.PT(blst.G2().to_affine(), commitment_minus_interpolation.neg().to_affine()) - pc.mul(blst.PT(xn_minus_yn.to_affine(), proof.to_affine())) - return pc.final_exp().is_one() - -if __name__ == "__main__": - from timer import chrono - import random - from tqdm import tqdm - # Uncomment to report time of the functions - #generate_setup = chrono(generate_setup) - #commit_to_poly = chrono(commit_to_poly) - #eval_poly_at = chrono(eval_poly_at) - #check_proof_single = chrono(check_proof_single) - #compute_proof_multi = chrono(compute_proof_multi) - #check_proof_multi = chrono(check_proof_multi) - - MAX_DEGREE_POLY = MODULUS-1 - N_POINTS = 512 - polynomial = [random.randint(1, MAX_DEGREE_POLY) for _ in range(N_POINTS)] - n = N_POINTS - - setup = generate_setup(random.getrandbits(256), n) - - commitment = commit_to_poly(polynomial, setup) - - for i in tqdm(range(n), desc='Single point test'): - proof = compute_proof_single(polynomial, i, setup) - value = eval_poly_at(polynomial, i) - assert check_proof_single(commitment, proof, i, value, setup) - print(f"Single point check passed for all {n} points") - - root_of_unity = get_root_of_unity(8) - x = 5431 - coset = [x * pow(root_of_unity, i, MODULUS) for i in range(8)] - ys = [eval_poly_at(polynomial, z) for z in coset] - proof = compute_proof_multi(polynomial, x, 8, setup) - assert check_proof_multi(commitment, proof, x, ys, setup) - print("Coset check passed") \ No newline at end of file diff --git a/kzg_data_availability/multicombs.py b/kzg_data_availability/multicombs.py deleted file mode 100644 index 972526c..0000000 --- a/kzg_data_availability/multicombs.py +++ /dev/null @@ -1,131 +0,0 @@ -import random, time, sys, math - -# For each subset in `subsets` (provided as a list of indices into `numbers`), -# compute the sum of that subset of `numbers`. More efficient than the naive method. -def multisubset(numbers, subsets, adder=lambda x,y: x+y, zero=0): - numbers = numbers[::] - subsets = {i: {x for x in subset} for i, subset in enumerate(subsets)} - output = [zero for _ in range(len(subsets))] - - for roundcount in range(9999999): - # Compute counts of every pair of indices in the subset list - pair_count = {} - for index, subset in subsets.items(): - for x in subset: - for y in subset: - if y > x: - pair_count[(x, y)] = pair_count.get((x, y), 0) + 1 - - # Determine pairs with highest count. The cutoff parameter [:len(numbers)] - # determines a tradeoff between group operation count and other forms of overhead - pairs_by_count = sorted([el for el in pair_count.keys()], key=lambda el: pair_count[el], reverse=True)[:len(numbers)*int(math.log(len(numbers)))] - - # Exit condition: all subsets have size 1, no pairs - if len(pairs_by_count) == 0: - for key, subset in subsets.items(): - for index in subset: - output[key] = adder(output[key], numbers[index]) - return output - - # In each of the highest-count pairs, take the sum of the numbers at those indices, - # and add the result as a new value, and modify `subsets` to include the new value - # wherever possible - used = set() - for maxx, maxy in pairs_by_count: - if maxx in used or maxy in used: - continue - used.add(maxx) - used.add(maxy) - numbers.append(adder(numbers[maxx], numbers[maxy])) - for key, subset in list(subsets.items()): - if maxx in subset and maxy in subset: - subset.remove(maxx) - subset.remove(maxy) - if not subset: - output[key] = numbers[-1] - del subsets[key] - else: - subset.add(len(numbers)-1) - -# Alternative algorithm. Less optimal than the above, but much lower bit twiddling -# overhead and much simpler. -def multisubset2(numbers, subsets, adder=lambda x,y: x+y, zero=0): - # Split up the numbers into partitions - partition_size = 1 + int(math.log(len(subsets) + 1)) - # Align number count to partition size (for simplicity) - numbers = numbers[::] - while len(numbers) % partition_size != 0: - numbers.append(zero) - # Compute power set for each partition (eg. a, b, c -> {0, a, b, a+b, c, a+c, b+c, a+b+c}) - power_sets = [] - for i in range(0, len(numbers), partition_size): - new_power_set = [zero] - for dimension, value in enumerate(numbers[i:i+partition_size]): - new_power_set += [adder(n, value) for n in new_power_set] - power_sets.append(new_power_set) - # Compute subset sums, using elements from power set for each range of values - # ie. with a single power set lookup you can get the sum of _all_ elements in - # the range partition_size*k...partition_size*(k+1) that are in that subset - subset_sums = [] - for subset in subsets: - o = zero - for i in range(len(power_sets)): - index_in_power_set = 0 - for j in range(partition_size): - if i * partition_size + j in subset: - index_in_power_set += 2 ** j - o = adder(o, power_sets[i][index_in_power_set]) - subset_sums.append(o) - return subset_sums - -# Reduces a linear combination `numbers[0] * factors[0] + numbers[1] * factors[1] + ...` -# into a multi-subset problem, and computes the result efficiently -def lincomb(numbers, factors, adder=lambda x,y: x+y, zero=0): - # Maximum bit length of a number; how many subsets we need to make - maxbitlen = max((len(bin(f))-2 for f in factors), default=0) - # Compute the subsets: the ith subset contains the numbers whose corresponding factor - # has a 1 at the ith bit - subsets = [{i for i in range(len(numbers)) if factors[i] & (1 << j)} for j in range(maxbitlen+1)] - subset_sums = multisubset2(numbers, subsets, adder=adder, zero=zero) - # For example, suppose a value V has factor 6 (011 in increasing-order binary). Subset 0 - # will not have V, subset 1 will, and subset 2 will. So if we multiply the output of adding - # subset 0 with twice the output of adding subset 1, with four times the output of adding - # subset 2, then V will be represented 0 + 2 + 4 = 6 times. This reasoning applies for every - # value. So `subset_0_sum + 2 * subset_1_sum + 4 * subset_2_sum` gives us the result we want. - # Here, we compute this as `((subset_2_sum * 2) + subset_1_sum) * 2 + subset_0_sum` for - # efficiency: an extra `maxbitlen * 2` group operations. - o = zero - for i in range(len(subsets)-1, -1, -1): - o = adder(adder(o, o), subset_sums[i]) - return o - -# Tests go here -def make_mock_adder(): - counter = [0] - def adder(x, y): - if x and y: - counter[0] += 1 - return x+y - return adder, counter - -def test_multisubset(numcount, setcount): - numbers = [random.randrange(10**20) for _ in range(numcount)] - subsets = [{i for i in range(numcount) if random.randrange(2)} for i in range(setcount)] - adder, counter = make_mock_adder() - o = multisubset(numbers, subsets, adder=adder) - for output, subset in zip(o, subsets): - assert output == sum([numbers[x] for x in subset]) - -def test_lincomb(numcount, bitlength=256): - numbers = [random.randrange(10**20) for _ in range(numcount)] - factors = [random.randrange(2**bitlength) for _ in range(numcount)] - adder, counter = make_mock_adder() - o = lincomb(numbers, factors, adder=adder) - assert o == sum([n*f for n,f in zip(numbers, factors)]) - total_ones = sum(bin(f).count('1') for f in factors) - print("Naive operation count: %d" % (bitlength * numcount + total_ones)) - print("Optimized operation count: %d" % (bitlength * 2 + counter[0])) - print("Optimization factor: %.2f" % ((bitlength * numcount + total_ones) / (bitlength * 2 + counter[0]))) - -if __name__ == '__main__': - test_lincomb(int(sys.argv[1]) if len(sys.argv) >= 2 else 80) diff --git a/kzg_data_availability/timer.py b/kzg_data_availability/timer.py deleted file mode 100644 index b2c26fa..0000000 --- a/kzg_data_availability/timer.py +++ /dev/null @@ -1,23 +0,0 @@ -import time -import sys - -"Simple wrapper to measure the timer of a function. Can be used either as a decorator, or as f = chrono(f)" -def chrono(f): - def timed(*args, **kargs): - t = -time.time() - result = f(*args, **kargs) - t += time.time() - - print(f'func {f.__name__} exec in {t:2.6f}s', file=sys.stderr) - return result - return timed - -if __name__ == '__main__': - - @chrono - def testFunc(n): - from math import factorial - return factorial(n) - - testFunc(10**5) - diff --git a/py_plonk/main.plonk.vkey-58.json b/main.plonk.vkey-58.json similarity index 100% rename from py_plonk/main.plonk.vkey-58.json rename to main.plonk.vkey-58.json diff --git a/py_plonk/main.plonk.vkey-59.json b/main.plonk.vkey-59.json similarity index 100% rename from py_plonk/main.plonk.vkey-59.json rename to main.plonk.vkey-59.json diff --git a/py_plonk/main.plonk.vkey.json b/main.plonk.vkey.json similarity index 100% rename from py_plonk/main.plonk.vkey.json rename to main.plonk.vkey.json diff --git a/merkle_tree/merk.py b/merkle_tree/merk.py deleted file mode 100644 index 5395e68..0000000 --- a/merkle_tree/merk.py +++ /dev/null @@ -1,53 +0,0 @@ -from hashlib import sha256 -def hash(x): return sha256(x).digest() - -def merkle_tree(leaves): - o = [0] * len(leaves) + leaves - for i in range(len(leaves)-1, 0, -1): - o[i] = hash(o[i*2] + o[i*2+1]) - return o - -def log2(x): - return 0 if x == 1 else 1 + log2(x//2) - -def get_proof_indices(tree_indices, depth): - leaf_count = 2**depth - # Get all indices touched by the proof - maximal_indices = set({}) - for i in tree_indices: - x = leaf_count + i - while x > 1: - maximal_indices.add(x ^ 1) - x //= 2 - maximal_indices = [leaf_count + i for i in tree_indices] + sorted(list(maximal_indices))[::-1] - # Get indices that cannot be recalculated from earlier indices - redundant_indices = set({}) - proof = [] - for index in maximal_indices: - if index not in redundant_indices: - proof.append(index) - while index > 1: - redundant_indices.add(index) - if (index ^ 1) not in redundant_indices: - break - index //= 2 - return [i for i in proof if i-leaf_count not in tree_indices] - -def mk_multi_proof(tree, indices): - return [tree[i] for i in get_proof_indices(indices, log2(len(tree) // 2))] - -def verify_multi_proof(root, indices, leaves, depth, proof): - tree = {} - for index, leaf in zip(indices, leaves): - tree[2**depth + index] = leaf - for index, proofitem in zip(get_proof_indices(indices, depth), proof): - tree[index] = proofitem - indexqueue = sorted(tree.keys())[:-1] - i = 0 - while i < len(indexqueue): - index = indexqueue[i] - if index >= 2 and index^1 in tree: - tree[index//2] = hash(tree[index - index%2] + tree[index - index%2 + 1]) - indexqueue.append(index//2) - i += 1 - return (indices == []) or (1 in tree and tree[1] == root) diff --git a/merkle_tree/merktest.py b/merkle_tree/merktest.py deleted file mode 100644 index bf3c4a5..0000000 --- a/merkle_tree/merktest.py +++ /dev/null @@ -1,17 +0,0 @@ -from merk import merkle_tree, mk_multi_proof, verify_multi_proof - -def test_multi_merkle_tree(): - leaves = [i.to_bytes(32, 'big') for i in range(16)] - tree = merkle_tree(leaves) - for i in range(65536): - indices = [j for j in range(16) if (i>>j)%2 == 1] - proof = mk_multi_proof(tree, indices) - assert verify_multi_proof(tree[1], indices, [leaves[i] for i in indices], 4, proof) - if i%1024 == 1023: - print("%d of 65536 16-element proofs checked" % (i+1)) - assert not verify_multi_proof(tree[2], indices, [leaves[i] for i in indices], 4, proof) - assert not verify_multi_proof(tree[1], indices, [leaves[i][::-1] for i in indices], 4, proof) - print("Multi Merkle tree test passed") - -if __name__ == '__main__': - test_multi_merkle_tree() diff --git a/mimc_stark/README.md b/mimc_stark/README.md deleted file mode 100644 index 9642853..0000000 --- a/mimc_stark/README.md +++ /dev/null @@ -1,45 +0,0 @@ -#### Disclaimer - -DO NOT USE FOR ANYTHING IN REAL LIFE. DO NOT ASSUME THE PROTOCOL DESCRIBED HERE IS SOUND. TALK TO A SPECIALIST IF YOU'RE LOOKING TO USE STARKS IN YOUR APPLICATION. - -#### What is this? - -See main article: https://vitalik.ca/general/2018/07/21/starks_part_3.html - -This is a very basic implementation of a STARK on a MIMC computation that is probably (ie. definitely) broken in a few places but is intended as a proof of concept to show the rough level of complexity that is involved in implementing a simple STARK. A STARK is a really cool proof-of-computation scheme that allows you to create an efficiently verifiable proof that some computation was executed correctly; the verification time only rises logarithmically with the computation time, and that relies only on hashes and information theory for security. - -The STARKs are done over a finite field chosen to have `2**32`'th roots of unity (to facilitate STARKs), and NOT have 3rd roots of unity (to facilitate MIMC). The MIMC permutation in general takes the form: - - k_1 k_2 - | | - v v - x0 ---> (x->x**3) ---> xor ---> (x->x**3) ---> xor --- ... ---> output - -Where the `k_i` values are round constants. MIMC can be used as a building block in a hash function, or as a verifiable delay function; its simple arithmetic representation makes it ideal for use in STARKs, SNARKs, MPC and other "cryptography over general-purpose computation" schemes. - -The MIMC round constants used here are successive powers of 9 mod `2**256` xored with 1, though could be set to anything. The computational trace is computed over successive powers of a `2**k`'th root of unity. This allows the constraint checking polynomial to be `C(P(x), P(r*x), K(x)) = P(r*x) - P(x)**3 - K(x)`. - -For a description of how STARKs work, see: - -* [STARKs, part 1: Proofs with Polynomials](https://vitalik.ca/general/2017/11/09/starks_part_1.html) -* [STARKs, part 2: Thank Goodness it's FRI-day](https://vitalik.ca/general/2017/11/22/starks_part_2.html) - -For more discussion on MIMC, see: - -* [Zcash issue 2233](https://github.com/zcash/zcash/issues/2233) - -### How does the STARK scheme here work? - -Here are the approximate steps in the code. Note that all arithmetic is done over the finite field of integers mod `2**256 - 2**32 * 351 + 1`. - -1. Let `P[0]` equal the input, and `P[i+1] = P[i]**3 + K[i]`, up to `steps` (where `steps` must be a power of 2) -2. Construct a polynomial where `P(subroot ^ i) = P[i]` up to steps-1, where `subroot` is a steps'th root of unity (that is, `subroot**steps = 1`). Do the same with K. -3. Construct the polynomial `CP(x) = C(P(x), P(x * subroot), K(x))`. Note that since `P(x * subroot) = P(x) ^ 3 + K(x), CP(x) = 0` for any x inside the computation trace (that is, powers of subroot except the last). -4. Construct the polynomial `Z(x)`, which is the minimal polynomial that is 0 across the computation trace. Note that because Z is minimal, CP must be a multiple of Z. -5. Construct `D = CP / Z`. Because CP is a multiple of Z, D must itself be a low-degree polynomial. -6. Put D and P into Merkle trees. -7. Construct `L = D + k * x**steps * P`, where `k` is selected based on the Merkle roots of D and P. -8. Create an FRI proof that L is low-degree ((7) and (8) together are a clever way of making an aggregate low-degree proof of D and P) -9. Create probabilistic checks, using the Merkle root of L as source data, to spot-check that D(x) * Z(x) actually equal C(P(x)). - -The probabilistic checks and the FRI proof are themselves restricted to `2**precision`'th roots of unity, where `precision = 8 * steps` (so we're FRI checking that the degree of L, which equals twice the degree of P, is at most 1/4 the theoretical maximum). diff --git a/mimc_stark/better_lagrange.py b/mimc_stark/better_lagrange.py deleted file mode 100644 index bbd823e..0000000 --- a/mimc_stark/better_lagrange.py +++ /dev/null @@ -1,18 +0,0 @@ -def inv(a, modulus): - if a == 0: - return 0 - lm, hm = 1, 0 - low, high = a % modulus, modulus - while low > 1: - r = high//low - nm, new = hm-lm*r, high-low*r - lm, low, hm, high = nm, new, lm, low - return lm % modulus - -def eval_poly_at(poly, x, modulus): - o, p = 0, 1 - for coeff in poly: - o += coeff * p - p = (p * x % modulus) - return o % modulus - diff --git a/mimc_stark/fft.py b/mimc_stark/fft.py deleted file mode 100644 index 982805a..0000000 --- a/mimc_stark/fft.py +++ /dev/null @@ -1,108 +0,0 @@ -def _simple_ft(vals, modulus, roots_of_unity): - L = len(roots_of_unity) - o = [] - for i in range(L): - last = 0 - for j in range(L): - last += vals[j] * roots_of_unity[(i*j)%L] - o.append(last % modulus) - return o - -def _fft(vals, modulus, roots_of_unity): - if len(vals) <= 4: - #return vals - return _simple_ft(vals, modulus, roots_of_unity) - L = _fft(vals[::2], modulus, roots_of_unity[::2]) - R = _fft(vals[1::2], modulus, roots_of_unity[::2]) - o = [0 for i in vals] - for i, (x, y) in enumerate(zip(L, R)): - y_times_root = y*roots_of_unity[i] - o[i] = (x+y_times_root) % modulus - o[i+len(L)] = (x-y_times_root) % modulus - return o - -def expand_root_of_unity(root_of_unity, modulus): - # Build up roots of unity - rootz = [1, root_of_unity] - while rootz[-1] != 1: - rootz.append((rootz[-1] * root_of_unity) % modulus) - return rootz - -def fft(vals, modulus, root_of_unity, inv=False): - rootz = expand_root_of_unity(root_of_unity, modulus) - # Fill in vals with zeroes if needed - if len(rootz) > len(vals) + 1: - vals = vals + [0] * (len(rootz) - len(vals) - 1) - if inv: - # Inverse FFT - invlen = pow(len(vals), modulus-2, modulus) - return [(x*invlen) % modulus for x in - _fft(vals, modulus, rootz[:0:-1])] - else: - # Regular FFT - return _fft(vals, modulus, rootz[:-1]) - -# Evaluates f(x) for f in evaluation form -def inv_fft_at_point(vals, modulus, root_of_unity, x): - if len(vals) == 1: - return vals[0] - # 1/2 in the field - half = (modulus + 1)//2 - # 1/w - inv_root = pow(root_of_unity, len(vals)-1, modulus) - # f(-x) in evaluation form - f_of_minus_x_vals = vals[len(vals)//2:] + vals[:len(vals)//2] - # e(x) = (f(x) + f(-x)) / 2 in evaluation form - evens = [(f+g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - # o(x) = (f(x) - f(-x)) / 2 in evaluation form - odds = [(f-g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - # e(x^2) + coordinate * x * o(x^2) in evaluation form - comb = [(o * x * inv_root**i + e) % modulus for i, (o, e) in enumerate(zip(odds, evens))] - return inv_fft_at_point(comb[:len(comb)//2], modulus, root_of_unity ** 2 % modulus, x**2 % modulus) - -def shift_domain(vals, modulus, root_of_unity, factor): - if len(vals) == 1: - return vals - # 1/2 in the field - half = (modulus + 1)//2 - # 1/w - inv_factor = pow(factor, modulus - 2, modulus) - half_length = len(vals)//2 - # f(-x) in evaluation form - f_of_minus_x_vals = vals[half_length:] + vals[:half_length] - # e(x) = (f(x) + f(-x)) / 2 in evaluation form - evens = [(f+g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - print('e', evens) - # o(x) = (f(x) - f(-x)) / 2 in evaluation form - odds = [(f-g) * half % modulus for f,g in zip(vals, f_of_minus_x_vals)] - print('o', odds) - shifted_evens = shift_domain(evens[:half_length], modulus, root_of_unity ** 2 % modulus, factor ** 2 % modulus) - print('se', shifted_evens) - shifted_odds = shift_domain(odds[:half_length], modulus, root_of_unity ** 2 % modulus, factor ** 2 % modulus) - print('so', shifted_odds) - return ( - [(e + inv_factor * o) % modulus for e, o in zip(shifted_evens, shifted_odds)] + - [(e - inv_factor * o) % modulus for e, o in zip(shifted_evens, shifted_odds)] - ) - -def shift_poly(poly, modulus, factor): - factor_power = 1 - inv_factor = pow(factor, modulus - 2, modulus) - o = [] - for p in poly: - o.append(p * factor_power % modulus) - factor_power = factor_power * inv_factor % modulus - return o - -def mul_polys(a, b, modulus, root_of_unity): - rootz = [1, root_of_unity] - while rootz[-1] != 1: - rootz.append((rootz[-1] * root_of_unity) % modulus) - if len(rootz) > len(a) + 1: - a = a + [0] * (len(rootz) - len(a) - 1) - if len(rootz) > len(b) + 1: - b = b + [0] * (len(rootz) - len(b) - 1) - x1 = _fft(a, modulus, rootz[:-1]) - x2 = _fft(b, modulus, rootz[:-1]) - return _fft([(v1*v2)%modulus for v1,v2 in zip(x1,x2)], - modulus, rootz[:0:-1]) diff --git a/mimc_stark/fri.py b/mimc_stark/fri.py deleted file mode 100644 index ed76ad1..0000000 --- a/mimc_stark/fri.py +++ /dev/null @@ -1,146 +0,0 @@ -from permuted_tree import merkelize, mk_branch, verify_branch, mk_multi_branch, verify_multi_branch -from utils import get_power_cycle, get_pseudorandom_indices -from poly_utils import PrimeField - -# Generate an FRI proof that the polynomial that has the specified -# values at successive powers of the specified root of unity has a -# degree lower than maxdeg_plus_1 -# -# We use maxdeg+1 instead of maxdeg because it's more mathematically -# convenient in this case. - -def prove_low_degree(values, root_of_unity, maxdeg_plus_1, modulus, exclude_multiples_of=0): - f = PrimeField(modulus) - print('Proving %d values are degree <= %d' % (len(values), maxdeg_plus_1)) - - # If the degree we are checking for is less than or equal to 32, - # use the polynomial directly as a proof - if maxdeg_plus_1 <= 16: - print('Produced FRI proof') - return [[x.to_bytes(32, 'big') for x in values]] - - # Calculate the set of x coordinates - xs = get_power_cycle(root_of_unity, modulus) - assert len(values) == len(xs) - - # Put the values into a Merkle tree. This is the root that the - # proof will be checked against - m = merkelize(values) - - # Select a pseudo-random x coordinate - special_x = int.from_bytes(m[1], 'big') % modulus - - # Calculate the "column" at that x coordinate - # (see https://vitalik.ca/general/2017/11/22/starks_part_2.html) - # We calculate the column by Lagrange-interpolating each row, and not - # directly from the polynomial, as this is more efficient - quarter_len = len(xs)//4 - x_polys = f.multi_interp_4( - [[xs[i+quarter_len*j] for j in range(4)] for i in range(quarter_len)], - [[values[i+quarter_len*j] for j in range(4)] for i in range(quarter_len)] - ) - column = [f.eval_quartic(p, special_x) for p in x_polys] - m2 = merkelize(column) - - # Pseudo-randomly select y indices to sample - ys = get_pseudorandom_indices(m2[1], len(column), 40, exclude_multiples_of=exclude_multiples_of) - - # Compute the positions for the values in the polynomial - poly_positions = sum([[y + (len(xs) // 4) * j for j in range(4)] for y in ys], []) - - # This component of the proof, including Merkle branches - o = [m2[1], mk_multi_branch(m2, ys), mk_multi_branch(m, poly_positions)] - - # Recurse... - return [o] + prove_low_degree(column, f.exp(root_of_unity, 4), - maxdeg_plus_1 // 4, modulus, exclude_multiples_of=exclude_multiples_of) - -# Verify an FRI proof -def verify_low_degree_proof(merkle_root, root_of_unity, proof, maxdeg_plus_1, modulus, exclude_multiples_of=0): - f = PrimeField(modulus) - - # Calculate which root of unity we're working with - testval = root_of_unity - roudeg = 1 - while testval != 1: - roudeg *= 2 - testval = (testval * testval) % modulus - - # Powers of the given root of unity 1, p, p**2, p**3 such that p**4 = 1 - quartic_roots_of_unity = [1, - f.exp(root_of_unity, roudeg // 4), - f.exp(root_of_unity, roudeg // 2), - f.exp(root_of_unity, roudeg * 3 // 4)] - - # Verify the recursive components of the proof - for prf in proof[:-1]: - root2, column_branches, poly_branches = prf - print('Verifying degree <= %d' % maxdeg_plus_1) - - # Calculate the pseudo-random x coordinate - special_x = int.from_bytes(merkle_root, 'big') % modulus - - # Calculate the pseudo-randomly sampled y indices - ys = get_pseudorandom_indices(root2, roudeg // 4, 40, - exclude_multiples_of=exclude_multiples_of) - - # Compute the positions for the values in the polynomial - poly_positions = sum([[y + (roudeg // 4) * j for j in range(4)] for y in ys], []) - - # Verify Merkle branches - column_values = verify_multi_branch(root2, ys, column_branches) - poly_values = verify_multi_branch(merkle_root, poly_positions, poly_branches) - - # For each y coordinate, get the x coordinates on the row, the values on - # the row, and the value at that y from the column - xcoords = [] - rows = [] - columnvals = [] - for i, y in enumerate(ys): - # The x coordinates from the polynomial - x1 = f.exp(root_of_unity, y) - xcoords.append([(quartic_roots_of_unity[j] * x1) % modulus for j in range(4)]) - - # The values from the original polynomial - row = [int.from_bytes(x, 'big') for x in poly_values[i*4: i*4+4]] - rows.append(row) - - columnvals.append(int.from_bytes(column_values[i], 'big')) - - # Verify for each selected y coordinate that the four points from the - # polynomial and the one point from the column that are on that y - # coordinate are on the same deg < 4 polynomial - polys = f.multi_interp_4(xcoords, rows) - - for p, c in zip(polys, columnvals): - assert f.eval_quartic(p, special_x) == c - - # Update constants to check the next proof - merkle_root = root2 - root_of_unity = f.exp(root_of_unity, 4) - maxdeg_plus_1 //= 4 - roudeg //= 4 - - # Verify the direct components of the proof - data = [int.from_bytes(x, 'big') for x in proof[-1]] - print('Verifying degree <= %d' % maxdeg_plus_1) - assert maxdeg_plus_1 <= 16 - - # Check the Merkle root matches up - mtree = merkelize(data) - assert mtree[1] == merkle_root - - # Check the degree of the data - powers = get_power_cycle(root_of_unity, modulus) - if exclude_multiples_of: - pts = [x for x in range(len(data)) if x % exclude_multiples_of] - else: - pts = range(len(data)) - - poly = f.lagrange_interp([powers[x] for x in pts[:maxdeg_plus_1]], - [data[x] for x in pts[:maxdeg_plus_1]]) - for x in pts[maxdeg_plus_1:]: - assert f.eval_poly_at(poly, powers[x]) == data[x] - - print('FRI proof verified') - return True diff --git a/mimc_stark/merkle_tree.py b/mimc_stark/merkle_tree.py deleted file mode 100644 index 3ca2c05..0000000 --- a/mimc_stark/merkle_tree.py +++ /dev/null @@ -1,107 +0,0 @@ -try: - from hashlib import blake2s -except: - from pyblake2 import blake2s -blake = lambda x: blake2s(x).digest() - -def merkelize(L): - # L = permute4(L) - nodes = [b''] * len(L) + [x.to_bytes(32, 'big') if isinstance(x, int) else x for x in L] - for i in range(len(L) - 1, 0, -1): - nodes[i] = blake(nodes[i*2] + nodes[i*2+1]) - return nodes - -def mk_branch(tree, index): - # index = get_index_in_permuted(index, len(tree) // 2) - index += len(tree) // 2 - o = [tree[index]] - while index > 1: - o.append(tree[index ^ 1]) - index //= 2 - return o - -def verify_branch(root, index, proof, output_as_int=False): - # index = get_index_in_permuted(index, 2**len(proof) // 2) - index += 2**len(proof) - v = proof[0] - for p in proof[1:]: - if index % 2: - v = blake(p + v) - else: - v = blake(v + p) - index //= 2 - assert v == root - return int.from_bytes(proof[0], 'big') if output_as_int else proof[0] - -# Make a compressed proof for multiple indices -def mk_multi_branch(tree, indices): - # Branches we are outputting - output = [] - # Elements in the tree we can get from the branches themselves - calculable_indices = {} - for i in indices: - new_branch = mk_branch(tree, i) - index = len(tree) // 2 + i - calculable_indices[index] = True - for j in range(1, len(new_branch)): - calculable_indices[index ^ 1] = True - index //= 2 - output.append(new_branch) - # Fill in the calculable list: if we can get or calculate both children, we can calculate the parent - complete = False - while not complete: - complete = True - keys = sorted([x//2 for x in calculable_indices])[::-1] - for k in keys: - if k*2 in calculable_indices and (k*2)+1 in calculable_indices and k not in calculable_indices: - calculable_indices[k] = True - complete = False - # If for any branch node both children are calculable, or the node overlaps with a leaf, or the node - # overlaps with a previously calculated one, elide it - scanned = {} - for i, b in zip(indices, output): - index = len(tree) // 2 + i - scanned[index] = True - for j in range(1, len(b)): - if ((index^1)*2 in calculable_indices and (index^1)*2+1 in calculable_indices) or ((index^1)-len(tree)//2 in indices) or (index^1) in scanned: - b[j] = b'' - scanned[index^1] = True - index //= 2 - return output - -# Verify a compressed proof -def verify_multi_branch(root, indices, proof): - # The values in the Merkle tree we can fill in - partial_tree = {} - # Fill in elements from the branches - for i, b in zip(indices, proof): - half_tree_size = 2**(len(b) - 1) - index = half_tree_size+i - partial_tree[index] = b[0] - for j in range(1, len(b)): - if b[j]: - partial_tree[index ^ 1] = b[j] - index //= 2 - # If we can calculate or get both children, we can calculate the parent - complete = False - while not complete: - complete = True - keys = sorted([x//2 for x in partial_tree])[::-1] - for k in keys: - if k*2 in partial_tree and k*2+1 in partial_tree and k not in partial_tree: - partial_tree[k] = blake(partial_tree[k*2] + partial_tree[k*2+1]) - complete = False - # If any branch node is missing, we can calculate it - for i, b in zip(indices, proof): - index = half_tree_size + i - for j in range(1, len(b)): - if b[j] == b'': - b[j] = partial_tree[index ^ 1] - partial_tree[index^1] = b[j] - index //= 2 - # Verify the branches and output the values - return [verify_branch(root, i, b) for i,b in zip(indices, proof)] - -# Byte length of a multi proof -def bin_length(proof): - return sum([len(b''.join(x)) + len(x) // 8 for x in proof]) + len(proof) * 2 diff --git a/mimc_stark/mimc_stark.py b/mimc_stark/mimc_stark.py deleted file mode 100644 index 78e589d..0000000 --- a/mimc_stark/mimc_stark.py +++ /dev/null @@ -1,209 +0,0 @@ -from permuted_tree import merkelize, mk_branch, verify_branch, blake, mk_multi_branch, verify_multi_branch -from poly_utils import PrimeField -import time -from fft import fft -from fri import prove_low_degree, verify_low_degree_proof -from utils import get_power_cycle, get_pseudorandom_indices, is_a_power_of_2 - -modulus = 2**256 - 2**32 * 351 + 1 -f = PrimeField(modulus) -nonresidue = 7 - -spot_check_security_factor = 80 -extension_factor = 8 - -# Compute a MIMC permutation for some number of steps -def mimc(inp, steps, round_constants): - start_time = time.time() - for i in range(steps-1): - inp = (inp**3 + round_constants[i % len(round_constants)]) % modulus - print("MIMC computed in %.4f sec" % (time.time() - start_time)) - return inp - -# Generate a STARK for a MIMC calculation -def mk_mimc_proof(inp, steps, round_constants): - start_time = time.time() - # Some constraints to make our job easier - assert steps <= 2**32 // extension_factor - assert is_a_power_of_2(steps) and is_a_power_of_2(len(round_constants)) - assert len(round_constants) < steps - - precision = steps * extension_factor - - # Root of unity such that x^precision=1 - G2 = f.exp(7, (modulus-1)//precision) - - # Root of unity such that x^steps=1 - skips = precision // steps - G1 = f.exp(G2, skips) - - # Powers of the higher-order root of unity - xs = get_power_cycle(G2, modulus) - last_step_position = xs[(steps-1)*extension_factor] - - # Generate the computational trace - computational_trace = [inp] - for i in range(steps-1): - computational_trace.append( - (computational_trace[-1]**3 + round_constants[i % len(round_constants)]) % modulus - ) - output = computational_trace[-1] - print('Done generating computational trace') - - # Interpolate the computational trace into a polynomial P, with each step - # along a successive power of G1 - computational_trace_polynomial = fft(computational_trace, modulus, G1, inv=True) - p_evaluations = fft(computational_trace_polynomial, modulus, G2) - print('Converted computational steps into a polynomial and low-degree extended it') - - skips2 = steps // len(round_constants) - constants_mini_polynomial = fft(round_constants, modulus, f.exp(G1, skips2), inv=True) - constants_polynomial = [0 if i % skips2 else constants_mini_polynomial[i//skips2] for i in range(steps)] - constants_mini_extension = fft(constants_mini_polynomial, modulus, f.exp(G2, skips2)) - print('Converted round constants into a polynomial and low-degree extended it') - - # Create the composed polynomial such that - # C(P(x), P(g1*x), K(x)) = P(g1*x) - P(x)**3 - K(x) - c_of_p_evaluations = [(p_evaluations[(i+extension_factor)%precision] - - f.exp(p_evaluations[i], 3) - - constants_mini_extension[i % len(constants_mini_extension)]) - % modulus for i in range(precision)] - print('Computed C(P, K) polynomial') - - # Compute D(x) = C(P(x), P(g1*x), K(x)) / Z(x) - # Z(x) = (x^steps - 1) / (x - x_atlast_step) - z_num_evaluations = [xs[(i * steps) % precision] - 1 for i in range(precision)] - z_num_inv = f.multi_inv(z_num_evaluations) - z_den_evaluations = [xs[i] - last_step_position for i in range(precision)] - d_evaluations = [cp * zd * zni % modulus for cp, zd, zni in zip(c_of_p_evaluations, z_den_evaluations, z_num_inv)] - print('Computed D polynomial') - - # Compute interpolant of ((1, input), (x_atlast_step, output)) - interpolant = f.lagrange_interp_2([1, last_step_position], [inp, output]) - i_evaluations = [f.eval_poly_at(interpolant, x) for x in xs] - - zeropoly2 = f.mul_polys([-1, 1], [-last_step_position, 1]) - inv_z2_evaluations = f.multi_inv([f.eval_poly_at(zeropoly2, x) for x in xs]) - - b_evaluations = [((p - i) * invq) % modulus for p, i, invq in zip(p_evaluations, i_evaluations, inv_z2_evaluations)] - print('Computed B polynomial') - - # Compute their Merkle root - mtree = merkelize([pval.to_bytes(32, 'big') + - dval.to_bytes(32, 'big') + - bval.to_bytes(32, 'big') for - pval, dval, bval in zip(p_evaluations, d_evaluations, b_evaluations)]) - print('Computed hash root') - - # Based on the hashes of P, D and B, we select a random linear combination - # of P * x^steps, P, B * x^steps, B and D, and prove the low-degreeness of that, - # instead of proving the low-degreeness of P, B and D separately - k1 = int.from_bytes(blake(mtree[1] + b'\x01'), 'big') - k2 = int.from_bytes(blake(mtree[1] + b'\x02'), 'big') - k3 = int.from_bytes(blake(mtree[1] + b'\x03'), 'big') - k4 = int.from_bytes(blake(mtree[1] + b'\x04'), 'big') - - # Compute the linear combination. We don't even both calculating it in - # coefficient form; we just compute the evaluations - G2_to_the_steps = f.exp(G2, steps) - powers = [1] - for i in range(1, precision): - powers.append(powers[-1] * G2_to_the_steps % modulus) - - l_evaluations = [(d_evaluations[i] + - p_evaluations[i] * k1 + p_evaluations[i] * k2 * powers[i] + - b_evaluations[i] * k3 + b_evaluations[i] * powers[i] * k4) % modulus - for i in range(precision)] - - l_mtree = merkelize(l_evaluations) - print('Computed random linear combination') - - # Do some spot checks of the Merkle tree at pseudo-random coordinates, excluding - # multiples of `extension_factor` - branches = [] - samples = spot_check_security_factor - positions = get_pseudorandom_indices(l_mtree[1], precision, samples, - exclude_multiples_of=extension_factor) - augmented_positions = sum([[x, (x + skips) % precision] for x in positions], []) - #for pos in positions: - # branches.append(mk_branch(mtree, pos)) - # branches.append(mk_branch(mtree, (pos + skips) % precision)) - # branches.append(mk_branch(l_mtree, pos)) - print('Computed %d spot checks' % samples) - - # Return the Merkle roots of P and D, the spot check Merkle proofs, - # and low-degree proofs of P and D - o = [mtree[1], - l_mtree[1], - mk_multi_branch(mtree, augmented_positions), - mk_multi_branch(l_mtree, positions), - prove_low_degree(l_evaluations, G2, steps * 2, modulus, exclude_multiples_of=extension_factor)] - print("STARK computed in %.4f sec" % (time.time() - start_time)) - return o - -# Verifies a STARK -def verify_mimc_proof(inp, steps, round_constants, output, proof): - m_root, l_root, main_branches, linear_comb_branches, fri_proof = proof - start_time = time.time() - assert steps <= 2**32 // extension_factor - assert is_a_power_of_2(steps) and is_a_power_of_2(len(round_constants)) - assert len(round_constants) < steps - - precision = steps * extension_factor - - # Get (steps)th root of unity - G2 = f.exp(7, (modulus-1)//precision) - skips = precision // steps - - # Gets the polynomial representing the round constants - skips2 = steps // len(round_constants) - constants_mini_polynomial = fft(round_constants, modulus, f.exp(G2, extension_factor * skips2), inv=True) - - # Verifies the low-degree proofs - assert verify_low_degree_proof(l_root, G2, fri_proof, steps * 2, modulus, exclude_multiples_of=extension_factor) - - # Performs the spot checks - k1 = int.from_bytes(blake(m_root + b'\x01'), 'big') - k2 = int.from_bytes(blake(m_root + b'\x02'), 'big') - k3 = int.from_bytes(blake(m_root + b'\x03'), 'big') - k4 = int.from_bytes(blake(m_root + b'\x04'), 'big') - samples = spot_check_security_factor - positions = get_pseudorandom_indices(l_root, precision, samples, - exclude_multiples_of=extension_factor) - augmented_positions = sum([[x, (x + skips) % precision] for x in positions], []) - last_step_position = f.exp(G2, (steps - 1) * skips) - main_branch_leaves = verify_multi_branch(m_root, augmented_positions, main_branches) - linear_comb_branch_leaves = verify_multi_branch(l_root, positions, linear_comb_branches) - for i, pos in enumerate(positions): - x = f.exp(G2, pos) - x_to_the_steps = f.exp(x, steps) - mbranch1 = main_branch_leaves[i*2] - mbranch2 = main_branch_leaves[i*2+1] - l_of_x = int.from_bytes(linear_comb_branch_leaves[i], 'big') - - p_of_x = int.from_bytes(mbranch1[:32], 'big') - p_of_g1x = int.from_bytes(mbranch2[:32], 'big') - d_of_x = int.from_bytes(mbranch1[32:64], 'big') - b_of_x = int.from_bytes(mbranch1[64:], 'big') - - zvalue = f.div(f.exp(x, steps) - 1, - x - last_step_position) - k_of_x = f.eval_poly_at(constants_mini_polynomial, f.exp(x, skips2)) - - # Check transition constraints C(P(x)) = Z(x) * D(x) - assert (p_of_g1x - p_of_x ** 3 - k_of_x - zvalue * d_of_x) % modulus == 0 - - # Check boundary constraints B(x) * Q(x) + I(x) = P(x) - interpolant = f.lagrange_interp_2([1, last_step_position], [inp, output]) - zeropoly2 = f.mul_polys([-1, 1], [-last_step_position, 1]) - assert (p_of_x - b_of_x * f.eval_poly_at(zeropoly2, x) - - f.eval_poly_at(interpolant, x)) % modulus == 0 - - # Check correctness of the linear combination - assert (l_of_x - d_of_x - - k1 * p_of_x - k2 * p_of_x * x_to_the_steps - - k3 * b_of_x - k4 * b_of_x * x_to_the_steps) % modulus == 0 - - print('Verified %d consistency checks' % spot_check_security_factor) - print('Verified STARK in %.4f sec' % (time.time() - start_time)) - return True diff --git a/mimc_stark/permuted_tree.py b/mimc_stark/permuted_tree.py deleted file mode 100644 index 6e26be7..0000000 --- a/mimc_stark/permuted_tree.py +++ /dev/null @@ -1,36 +0,0 @@ -from merkle_tree import merkelize as _merkelize -from merkle_tree import mk_branch as _mk_branch -from merkle_tree import verify_branch as _verify_branch -from merkle_tree import mk_multi_branch as _mk_multi_branch -from merkle_tree import verify_multi_branch as _verify_multi_branch -from merkle_tree import blake - -def permute4_values(values): - o = [] - ld4 = len(values) // 4 - for i in range(ld4): - o.extend([values[i], values[i + ld4], values[i + ld4 * 2], values[i + ld4 * 3]]) - return o - -def permute4_index(x, L): - ld4 = L // 4 - return x//ld4 + 4 * (x % ld4) - -def permute4_indices(xs, L): - ld4 = L // 4 - return [x//ld4 + 4 * (x % ld4) for x in xs] - -def merkelize(L): - return _merkelize(permute4_values(L)) - -def mk_branch(tree, index): - return _mk_branch(tree, permute4_index(index, len(tree) // 2)) - -def verify_branch(root, index, proof, output_as_int=False): - return _verify_branch(root, permute4_index(index, 2**len(proof) // 2), proof, output_as_int) - -def mk_multi_branch(tree, indices): - return _mk_multi_branch(tree, permute4_indices(indices, len(tree) // 2)) - -def verify_multi_branch(root, indices, proof): - return _verify_multi_branch(root, permute4_indices(indices, 2**len(proof[0]) // 2), proof) diff --git a/mimc_stark/poly_utils.py b/mimc_stark/poly_utils.py deleted file mode 100644 index c29d1b5..0000000 --- a/mimc_stark/poly_utils.py +++ /dev/null @@ -1,207 +0,0 @@ -# Creates an object that includes convenience operations for numbers -# and polynomials in some prime field -class PrimeField(): - def __init__(self, modulus): - assert pow(2, modulus, modulus) == 2 - self.modulus = modulus - - def add(self, x, y): - return (x+y) % self.modulus - - def sub(self, x, y): - return (x-y) % self.modulus - - def mul(self, x, y): - return (x*y) % self.modulus - - def exp(self, x, p): - return pow(x, p, self.modulus) - - # Modular inverse using the extended Euclidean algorithm - def inv(self, a): - if a == 0: - return 0 - lm, hm = 1, 0 - low, high = a % self.modulus, self.modulus - while low > 1: - r = high//low - nm, new = hm-lm*r, high-low*r - lm, low, hm, high = nm, new, lm, low - return lm % self.modulus - - def multi_inv(self, values): - partials = [1] - for i in range(len(values)): - partials.append(self.mul(partials[-1], values[i] or 1)) - inv = self.inv(partials[-1]) - outputs = [0] * len(values) - for i in range(len(values), 0, -1): - outputs[i-1] = self.mul(partials[i-1], inv) if values[i-1] else 0 - inv = self.mul(inv, values[i-1] or 1) - return outputs - - def div(self, x, y): - return self.mul(x, self.inv(y)) - - # Evaluate a polynomial at a point - def eval_poly_at(self, p, x): - y = 0 - power_of_x = 1 - for i, p_coeff in enumerate(p): - y += power_of_x * p_coeff - power_of_x = (power_of_x * x) % self.modulus - return y % self.modulus - - # Arithmetic for polynomials - def add_polys(self, a, b): - return [((a[i] if i < len(a) else 0) + (b[i] if i < len(b) else 0)) - % self.modulus for i in range(max(len(a), len(b)))] - - def sub_polys(self, a, b): - return [((a[i] if i < len(a) else 0) - (b[i] if i < len(b) else 0)) - % self.modulus for i in range(max(len(a), len(b)))] - - def mul_by_const(self, a, c): - return [(x*c) % self.modulus for x in a] - - def mul_polys(self, a, b): - o = [0] * (len(a) + len(b) - 1) - for i, aval in enumerate(a): - for j, bval in enumerate(b): - o[i+j] += a[i] * b[j] - return [x % self.modulus for x in o] - - def div_polys(self, a, b): - assert len(a) >= len(b) - a = [x for x in a] - o = [] - apos = len(a) - 1 - bpos = len(b) - 1 - diff = apos - bpos - while diff >= 0: - quot = self.div(a[apos], b[bpos]) - o.insert(0, quot) - for i in range(bpos, -1, -1): - a[diff+i] -= b[i] * quot - apos -= 1 - diff -= 1 - return [x % self.modulus for x in o] - - def mod_polys(self, a, b): - return self.sub_polys(a, self.mul_polys(b, self.div_polys(a, b)))[:len(b)-1] - - # Build a polynomial from a few coefficients - def sparse(self, coeff_dict): - o = [0] * (max(coeff_dict.keys()) + 1) - for k, v in coeff_dict.items(): - o[k] = v % self.modulus - return o - - # Build a polynomial that returns 0 at all specified xs - def zpoly(self, xs): - root = [1] - for x in xs: - root.insert(0, 0) - for j in range(len(root)-1): - root[j] -= root[j+1] * x - return [x % self.modulus for x in root] - - # Given p+1 y values and x values with no errors, recovers the original - # p+1 degree polynomial. - # Lagrange interpolation works roughly in the following way. - # 1. Suppose you have a set of points, eg. x = [1, 2, 3], y = [2, 5, 10] - # 2. For each x, generate a polynomial which equals its corresponding - # y coordinate at that point and 0 at all other points provided. - # 3. Add these polynomials together. - - def lagrange_interp(self, xs, ys): - # Generate master numerator polynomial, eg. (x - x1) * (x - x2) * ... * (x - xn) - root = self.zpoly(xs) - assert len(root) == len(ys) + 1 - # print(root) - # Generate per-value numerator polynomials, eg. for x=x2, - # (x - x1) * (x - x3) * ... * (x - xn), by dividing the master - # polynomial back by each x coordinate - nums = [self.div_polys(root, [-x, 1]) for x in xs] - # Generate denominators by evaluating numerator polys at each x - denoms = [self.eval_poly_at(nums[i], xs[i]) for i in range(len(xs))] - invdenoms = self.multi_inv(denoms) - # Generate output polynomial, which is the sum of the per-value numerator - # polynomials rescaled to have the right y values - b = [0 for y in ys] - for i in range(len(xs)): - yslice = self.mul(ys[i], invdenoms[i]) - for j in range(len(ys)): - if nums[i][j] and ys[i]: - b[j] += nums[i][j] * yslice - return [x % self.modulus for x in b] - - # Optimized poly evaluation for degree 4 - def eval_quartic(self, p, x): - xsq = x * x % self.modulus - xcb = xsq * x - return (p[0] + p[1] * x + p[2] * xsq + p[3] * xcb) % self.modulus - - # Optimized version of the above restricted to deg-4 polynomials - def lagrange_interp_4(self, xs, ys): - x01, x02, x03, x12, x13, x23 = \ - xs[0] * xs[1], xs[0] * xs[2], xs[0] * xs[3], xs[1] * xs[2], xs[1] * xs[3], xs[2] * xs[3] - m = self.modulus - eq0 = [-x12 * xs[3] % m, (x12 + x13 + x23), -xs[1]-xs[2]-xs[3], 1] - eq1 = [-x02 * xs[3] % m, (x02 + x03 + x23), -xs[0]-xs[2]-xs[3], 1] - eq2 = [-x01 * xs[3] % m, (x01 + x03 + x13), -xs[0]-xs[1]-xs[3], 1] - eq3 = [-x01 * xs[2] % m, (x01 + x02 + x12), -xs[0]-xs[1]-xs[2], 1] - e0 = self.eval_poly_at(eq0, xs[0]) - e1 = self.eval_poly_at(eq1, xs[1]) - e2 = self.eval_poly_at(eq2, xs[2]) - e3 = self.eval_poly_at(eq3, xs[3]) - e01 = e0 * e1 - e23 = e2 * e3 - invall = self.inv(e01 * e23) - inv_y0 = ys[0] * invall * e1 * e23 % m - inv_y1 = ys[1] * invall * e0 * e23 % m - inv_y2 = ys[2] * invall * e01 * e3 % m - inv_y3 = ys[3] * invall * e01 * e2 % m - return [(eq0[i] * inv_y0 + eq1[i] * inv_y1 + eq2[i] * inv_y2 + eq3[i] * inv_y3) % m for i in range(4)] - - # Optimized version of the above restricted to deg-2 polynomials - def lagrange_interp_2(self, xs, ys): - m = self.modulus - eq0 = [-xs[1] % m, 1] - eq1 = [-xs[0] % m, 1] - e0 = self.eval_poly_at(eq0, xs[0]) - e1 = self.eval_poly_at(eq1, xs[1]) - invall = self.inv(e0 * e1) - inv_y0 = ys[0] * invall * e1 - inv_y1 = ys[1] * invall * e0 - return [(eq0[i] * inv_y0 + eq1[i] * inv_y1) % m for i in range(2)] - - # Optimized version of the above restricted to deg-4 polynomials - def multi_interp_4(self, xsets, ysets): - data = [] - invtargets = [] - for xs, ys in zip(xsets, ysets): - x01, x02, x03, x12, x13, x23 = \ - xs[0] * xs[1], xs[0] * xs[2], xs[0] * xs[3], xs[1] * xs[2], xs[1] * xs[3], xs[2] * xs[3] - m = self.modulus - eq0 = [-x12 * xs[3] % m, (x12 + x13 + x23), -xs[1]-xs[2]-xs[3], 1] - eq1 = [-x02 * xs[3] % m, (x02 + x03 + x23), -xs[0]-xs[2]-xs[3], 1] - eq2 = [-x01 * xs[3] % m, (x01 + x03 + x13), -xs[0]-xs[1]-xs[3], 1] - eq3 = [-x01 * xs[2] % m, (x01 + x02 + x12), -xs[0]-xs[1]-xs[2], 1] - e0 = self.eval_quartic(eq0, xs[0]) - e1 = self.eval_quartic(eq1, xs[1]) - e2 = self.eval_quartic(eq2, xs[2]) - e3 = self.eval_quartic(eq3, xs[3]) - data.append([ys, eq0, eq1, eq2, eq3]) - invtargets.extend([e0, e1, e2, e3]) - invalls = self.multi_inv(invtargets) - o = [] - for (i, (ys, eq0, eq1, eq2, eq3)) in enumerate(data): - invallz = invalls[i*4:i*4+4] - inv_y0 = ys[0] * invallz[0] % m - inv_y1 = ys[1] * invallz[1] % m - inv_y2 = ys[2] * invallz[2] % m - inv_y3 = ys[3] * invallz[3] % m - o.append([(eq0[i] * inv_y0 + eq1[i] * inv_y1 + eq2[i] * inv_y2 + eq3[i] * inv_y3) % m for i in range(4)]) - # assert o == [self.lagrange_interp_4(xs, ys) for xs, ys in zip(xsets, ysets)] - return o diff --git a/mimc_stark/recovery.py b/mimc_stark/recovery.py deleted file mode 100644 index ddf1b17..0000000 --- a/mimc_stark/recovery.py +++ /dev/null @@ -1,112 +0,0 @@ -from fft import fft, mul_polys - -# Calculates modular inverses [1/values[0], 1/values[1] ...] -def multi_inv(values, modulus): - partials = [1] - for i in range(len(values)): - partials.append(partials[-1] * values[i] % modulus) - inv = pow(partials[-1], modulus - 2, modulus) - outputs = [0] * len(values) - for i in range(len(values), 0, -1): - outputs[i-1] = partials[i-1] * inv % modulus - inv = inv * values[i-1] % modulus - return outputs - -# Generates q(x) = poly(k * x) -def p_of_kx(poly, modulus, k): - o = [] - power_of_k = 1 - for x in poly: - o.append(x * power_of_k % modulus) - power_of_k = (power_of_k * k) % modulus - return o - -# Return (x - root**positions[0]) * (x - root**positions[1]) * ... -# possibly with a constant factor offset -def _zpoly(positions, modulus, roots_of_unity): - # If there are not more than 4 positions, use the naive - # O(n^2) algorithm as it is faster - if len(positions) <= 4: - root = [1] - for pos in positions: - x = roots_of_unity[pos] - root.insert(0, 0) - for j in range(len(root)-1): - root[j] -= root[j+1] * x - return [x % modulus for x in root] - else: - # Recursively find the zpoly for even indices and odd - # indices, operating over a half-size subgroup in each - # case - left = _zpoly([x//2 for x in positions if x%2 == 0], - modulus, roots_of_unity[::2]) - right = _zpoly([x//2 for x in positions if x%2 == 1], - modulus, roots_of_unity[::2]) - invroot = roots_of_unity[-1] - # Offset the result for the odd indices, and combine - # the two - o = mul_polys(left, p_of_kx(right, modulus, invroot), - modulus, roots_of_unity[1]) - # Deal with the special case where mul_polys returns zero - # when it should return x ^ (2 ** k) - 1 - if o == [0] * len(o): - return [1] + [0] * (len(o) - 1) + [modulus - 1] - else: - return o - -def zpoly(positions, modulus, root_of_unity): - # Precompute roots of unity - rootz = [1, root_of_unity] - while rootz[-1] != 1: - rootz.append((rootz[-1] * root_of_unity) % modulus) - return _zpoly(positions, modulus, rootz[:-1]) - -def erasure_code_recover(vals, modulus, root_of_unity): - # Generate the polynomial that is zero at the roots of unity - # corresponding to the indices where vals[i] is None - import poly_utils - z = zpoly([i for i in range(len(vals)) if vals[i] is None], - modulus, root_of_unity) - zvals = fft(z, modulus, root_of_unity) - - # Pointwise-multiply (vals filling in zero at missing spots) * z - # By construction, this equals vals * z - vals_with_zeroes = [x or 0 for x in vals] - p_times_z_vals = [x*y % modulus for x,y in zip(vals_with_zeroes, zvals)] - p_times_z = fft(p_times_z_vals, modulus, root_of_unity, inv=True) - - # Keep choosing k values until the algorithm does not fail - # Check only with primitive roots of unity - for k in range(2, modulus): - if pow(k, (modulus - 1) // 2, modulus) == 1: - continue - invk = pow(k, modulus - 2, modulus) - # Convert p_times_z(x) and z(x) into new polynomials - # q1(x) = p_times_z(k*x) and q2(x) = z(k*x) - # These are likely to not be 0 at any of the evaluation points. - p_times_z_of_kx = [x * pow(k, i, modulus) % modulus - for i, x in enumerate(p_times_z)] - p_times_z_of_kx_vals = fft(p_times_z_of_kx, modulus, root_of_unity) - z_of_kx = [x * pow(k, i, modulus) for i, x in enumerate(z)] - z_of_kx_vals = fft(z_of_kx, modulus, root_of_unity) - - # Compute q1(x) / q2(x) = p(k*x) - inv_z_of_kv_vals = multi_inv(z_of_kx_vals, modulus) - p_of_kx_vals = [x*y % modulus for x,y in - zip(p_times_z_of_kx_vals, inv_z_of_kv_vals)] - p_of_kx = fft(p_of_kx_vals, modulus, root_of_unity, inv=True) - - # Given q3(x) = p(k*x), recover p(x) - p_of_x = [x * pow(invk, i, modulus) % modulus - for i, x in enumerate(p_of_kx)] - output = fft(p_of_x, modulus, root_of_unity) - - # Check that the output matches the input - success = True - for inpd, outd in zip(vals, output): - success *= (inpd is None or inpd == outd) - if not success: - continue - - # Output the evaluations if all good - return output diff --git a/mimc_stark/test.py b/mimc_stark/test.py deleted file mode 100644 index 557b32c..0000000 --- a/mimc_stark/test.py +++ /dev/null @@ -1,53 +0,0 @@ -from fft import fft -from mimc_stark import mk_mimc_proof, modulus, mimc, verify_mimc_proof -from merkle_tree import merkelize, mk_branch, verify_branch, bin_length -from fri import prove_low_degree, verify_low_degree_proof - -def test_merkletree(): - t = merkelize([x.to_bytes(32, 'big') for x in range(128)]) - b = mk_branch(t, 59) - assert verify_branch(t[1], 59, b, output_as_int=True) == 59 - print('Merkle tree works') - -def fri_proof_bin_length(fri_proof): - return sum([32 + bin_length(x[1]) + bin_length(x[2]) for x in fri_proof[:-1]]) + len(b''.join(fri_proof[-1])) - -def test_fri(): - # Pure FRI tests - poly = list(range(4096)) - root_of_unity = pow(7, (modulus-1)//16384, modulus) - evaluations = fft(poly, modulus, root_of_unity) - proof = prove_low_degree(evaluations, root_of_unity, 4096, modulus) - print("Approx proof length: %d" % fri_proof_bin_length(proof)) - assert verify_low_degree_proof(merkelize(evaluations)[1], root_of_unity, proof, 4096, modulus) - - try: - fakedata = [x if pow(3, i, 4096) > 400 else 39 for x, i in enumerate(evaluations)] - proof2 = prove_low_degree(fakedata, root_of_unity, 4096, modulus) - assert verify_low_degree_proof(merkelize(fakedata)[1], root_of_unity, proof, 4096, modulus) - raise Exception("Fake data passed FRI") - except: - pass - try: - assert verify_low_degree_proof(merkelize(evaluations)[1], root_of_unity, proof, 2048, modulus) - raise Exception("Fake data passed FRI") - except: - pass - -def test_stark(): - INPUT = 3 - import sys - LOGSTEPS = int(sys.argv[1]) if len(sys.argv) > 1 else 13 - # Full STARK test - import random - #constants = [random.randrange(modulus) for i in range(64)] - constants = [(i**7) ^ 42 for i in range(64)] - proof = mk_mimc_proof(INPUT, 2**LOGSTEPS, constants) - m_root, l_root, main_branches, linear_comb_branches, fri_proof = proof - L1 = bin_length(main_branches) + bin_length(linear_comb_branches) - L2 = fri_proof_bin_length(fri_proof) - print("Approx proof length: %d (branches), %d (FRI proof), %d (total)" % (L1, L2, L1 + L2)) - assert verify_mimc_proof(3, 2**LOGSTEPS, constants, mimc(3, 2**LOGSTEPS, constants), proof) - -if __name__ == '__main__': - test_stark() diff --git a/mimc_stark/test_multi_merkle.py b/mimc_stark/test_multi_merkle.py deleted file mode 100644 index c18a0cf..0000000 --- a/mimc_stark/test_multi_merkle.py +++ /dev/null @@ -1,14 +0,0 @@ -from merkle_tree import merkelize, mk_multi_branch, verify_multi_branch - -def test_multi_merkle_tree(): - tree = merkelize(list(range(16))) - for i in range(65536): - indices = [j for j in range(16) if (i>>j)%2 == 1] - branch = mk_multi_branch(tree, indices) - assert verify_multi_branch(tree[1], indices, branch) == [tree[16+j] for j in indices] - if i%1024 == 1023: - print("%d of 65536 16-element proofs checked" % (i+1)) - print("Multi Merkle tree test passed") - -if __name__ == '__main__': - test_multi_merkle_tree() diff --git a/mimc_stark/test_recovery.py b/mimc_stark/test_recovery.py deleted file mode 100644 index 41f8fe0..0000000 --- a/mimc_stark/test_recovery.py +++ /dev/null @@ -1,72 +0,0 @@ -import recovery, fft -import random -import time - -def test_zpoly(): - for i in range(255): - indices = [] - for j in range(8): - if (i >> j) % 2: - indices.append(j) - z = recovery.zpoly(indices, 337, 111) - evals = fft.fft(z, 337, 111) - for x in range(8): - if x in indices: - assert evals[x] == 0 - else: - assert evals[x] != 0 - print("Passed exhaustive test at size 8") - modulus = 2**256 - 2**32 * 351 + 1 - nonresidue = 7 - for L in range(3, 13): - indices = list(set([random.randrange(2**L) for i in range(2**(L-1))])) - root_of_unity = pow(nonresidue, (modulus-1)//(2**L), modulus) - a = time.time() - z = recovery.zpoly(indices, modulus, root_of_unity) - print('Zpoly of size %d done in time %.4f' % (2**L, time.time() - a)) - evals = fft.fft(z, modulus, root_of_unity) - for x in range(L): - if x in indices: - assert evals[x] == 0 - else: - assert evals[x] != 0 - print("Passed expansive test") - -def test_recovery(): - for i in range(256): - indices = [] - for j in range(8): - if (i >> j) % 2: - indices.append(j) - if len(indices) > 4: - continue - data = fft.fft([random.randrange(337) for i in range(4)], 337, 111) - erased_data = [data[i] if i not in indices else None - for i in range(8)] - outdata = recovery.erasure_code_recover(erased_data, 337, 111) - assert data == outdata - print("Passed exhaustive test at size 8") - modulus = 2**256 - 2**32 * 351 + 1 - nonresidue = 7 - for L in range(3, 13): - root_of_unity = pow(nonresidue, (modulus-1)//(2**L), modulus) - data = fft.fft([random.randrange(modulus) for i in range(2**(L-1))], - modulus, root_of_unity) - indices = {} - while len(indices) < (2**L * 3 // 8): - indices[random.randrange(2**L)] = True - indices = sorted(list(indices)) - erased_data = [data[i] if i not in indices else None - for i in range(2**L)] - a = time.time() - outdata = recovery.erasure_code_recover( - erased_data, modulus, root_of_unity - ) - assert outdata == data - print("Recovery in dataset of size %i done in time %.4f" % - (2**L, time.time() - a)) - print("Passed expansive test") - -if __name__ == '__main__': - test_zpoly() - test_recovery() diff --git a/mimc_stark/utils.py b/mimc_stark/utils.py deleted file mode 100644 index 1c67b3f..0000000 --- a/mimc_stark/utils.py +++ /dev/null @@ -1,25 +0,0 @@ -from merkle_tree import blake - -# Get the set of powers of R, until but not including when the powers -# loop back to 1 -def get_power_cycle(r, modulus): - o = [1, r] - while o[-1] != 1: - o.append((o[-1] * r) % modulus) - return o[:-1] - -# Extract pseudorandom indices from entropy -def get_pseudorandom_indices(seed, modulus, count, exclude_multiples_of=0): - assert modulus < 2**24 - data = seed - while len(data) < 4 * count: - data += blake(data[-32:]) - if exclude_multiples_of == 0: - return [int.from_bytes(data[i: i+4], 'big') % modulus for i in range(0, count * 4, 4)] - else: - real_modulus = modulus * (exclude_multiples_of - 1) // exclude_multiples_of - o = [int.from_bytes(data[i: i+4], 'big') % real_modulus for i in range(0, count * 4, 4)] - return [x+1+x//(exclude_multiples_of-1) for x in o] - -def is_a_power_of_2(x): - return True if x==1 else False if x%2 else is_a_power_of_2(x//2) diff --git a/py_plonk/mini_poseidon.py b/mini_poseidon.py similarity index 100% rename from py_plonk/mini_poseidon.py rename to mini_poseidon.py diff --git a/minimal_utxo/utxo_tester.py b/minimal_utxo/utxo_tester.py deleted file mode 100644 index f6d1ad6..0000000 --- a/minimal_utxo/utxo_tester.py +++ /dev/null @@ -1,26 +0,0 @@ -from ethereum.tools import tester as t -from ethereum import utils as u -c = t.Chain() -x = c.contract(open('utxos.v.py').read(), language='viper', sender=t.k0) -assert u.normalize_address(x.get_utxos__owner(u.encode_int32(1))) == t.a0 -assert x.get_utxos__value(u.encode_int32(1)) == 2**32 - -sigdata = u.encode_int32(1) + u.encode_int32(0) + b'\x00' * 12 + t.a2 + \ - u.encode_int32(2**30) + b'\x00' * 12 + t.a2 + u.encode_int32(3 * 2**30) -sighash = u.sha3(sigdata) - -v, r, s = u.ecsign(sighash, t.k0) - -assert x.tx(u.encode_int32(1), u.encode_int32(0), t.a2, 2**30, t.a2, 3 * 2**30, v, r, s) == sighash -assert u.normalize_address(x.get_utxos__owner(sighash)) == t.a2 -assert x.get_utxos__value(sighash) == 2**30 - -sigdata2 = sighash + u.encode_int32(0) + b'\x00' * 12 + t.a3 + \ - u.encode_int32(2**29) + b'\x00' * 12 + t.a3 + u.encode_int32(2**29) -sighash2 = u.sha3(sigdata2) - -v, r, s = u.ecsign(sighash2, t.k2) - -assert x.tx(sighash, u.encode_int32(0), t.a3, 2**29, t.a3, 2**29, v, r, s) == sighash2 - -print('Tests passed') diff --git a/minimal_utxo/utxos.v.py b/minimal_utxo/utxos.v.py deleted file mode 100644 index 828998a..0000000 --- a/minimal_utxo/utxos.v.py +++ /dev/null @@ -1,19 +0,0 @@ -utxos: public({owner: address, value: num}[bytes32]) - -def __init__(): - self.utxos[as_bytes32(1)] = {owner: msg.sender, value: 4294967296} - -def tx(in1: bytes32, in2: bytes32, out1: address, value1: num, - out2: address, value2: num, v: num256, r: num256, s: num256) -> bytes32: - sighash = sha3(concat(in1, in2, as_bytes32(out1), as_bytes32(value1), as_bytes32(out2), as_bytes32(value2))) - sender = ecrecover(sighash, v, r, s) - assert self.utxos[in1].owner == sender or not in1 - assert self.utxos[in2].owner == sender or not in2 - value = self.utxos[in1].value + self.utxos[in2].value - assert value == value1 + value2 - self.utxos[in1] = {owner: None, value: None} - self.utxos[in2] = {owner: None, value: None} - self.utxos[sighash] = {owner: out1, value: value1} - self.utxos[as_bytes32(bitwise_xor(as_num256(sighash), as_num256(1)))] = \ - {owner: out2, value: value2} - return sighash diff --git a/mining/arpow_miner.py b/mining/arpow_miner.py deleted file mode 100644 index 8720cc9..0000000 --- a/mining/arpow_miner.py +++ /dev/null @@ -1,104 +0,0 @@ -from pyethereum import utils -import random - - -def sha3(x): - return utils.decode_int(utils.zunpad(utils.sha3(x))) - - -class SeedObj(): - def __init__(self, seed): - self.seed = seed - self.a = 3**160 - self.c = 7**80 - self.n = 2**256 - 4294968273 # secp256k1n, why not - - def rand(self, r): - self.seed = (self.seed * self.a + self.c) % self.n - return self.seed % r - - -def encode_int(x): - o = '' - for _ in range(8): - o = chr(x % 256) + o - x //= 256 - return o - - -ops = { - "plus": lambda x, y: (x + y) % 2**64, - "times": lambda x, y: (x * y) % 2**64, - "xor": lambda x, y: x ^ y, - "and": lambda x, y: x & y, - "or": lambda x, y: x | y, - "not": lambda x, y: 2**64-1-x, - "nxor": lambda x, y: (2**64-1-x) ^ y, - "rshift": lambda x, y: x >> (y % 64) -} - - -def gentape(W, H, SEED): - s = SeedObj(SEED) - tape = [] - for i in range(H): - op = ops.keys()[s.rand(len(ops))] - r = s.rand(100) - if r < 20 and i > 20: - x1 = tape[-r]["x1"] - else: - x1 = s.rand(W) - x2 = s.rand(W) - tape.append({"op": op, "x1": x1, "x2": x2}) - return tape - - -def runtape(TAPE, SEED, params): - s = SeedObj(SEED) - # Fill up tape inputs - mem = [0] * params["w"] - for i in range(params["w"]): - mem[i] = s.rand(2**64) - # Direction variable (run forwards or backwards) - dir = 1 - # Run the tape on the inputs - for i in range(params["h"] // 100): - for j in (range(100) if dir == 1 else range(99, -1, -1)): - t = TAPE[i * 100 + j] - mem[t["x1"]] = ops[t["op"]](mem[t["x1"]], mem[t["x2"]]) - # 16% of the time, we flip the order of the next 100 ops; - # this adds in conditional branching - if 2 < mem[t["x1"]] % 37 < 9: - dir *= -1 - return sha3(''.join(encode_int(x) for x in mem)) - - -def PoWVerify(header, nonce, params): - tape = gentape(params["w"], params["h"], - sha3(header + encode_int(nonce // params["n"]))) - h = runtape(tape, sha3(header + encode_int(nonce)), params) - print h - return h < 2**256 / params["diff"] - - -def PoWRun(header, params): - # actual randomness, so that miners don't overlap - nonce = random.randrange(2**50) * params["n"] - tape = None - while 1: - print nonce - if nonce % params["n"] == 0: - tape = gentape(params["w"], params["h"], - sha3(header + encode_int(nonce // params["n"]))) - h = runtape(tape, sha3(header + encode_int(nonce)), params) - if h < 2**256 / params["diff"]: - return nonce - else: - nonce += 1 - -params = { - "w": 100, - "h": 15000, # generally, w*log(w) at least - "diff": 2**24, # initial - "n": 1000 -} diff --git a/mining/compute_probabilities_of_finality.py b/mining/compute_probabilities_of_finality.py deleted file mode 100644 index c6e31c2..0000000 --- a/mining/compute_probabilities_of_finality.py +++ /dev/null @@ -1,27 +0,0 @@ -import math -BLKTIME = 17 -X = 0.28 - -faclog = [1] -for i in range(5000): - faclog.append(faclog[-1] * len(faclog)) - -def fac(x): - return faclog[x] - -def poisson(expected, actual): - if expected == 0: - return 1 if actual == 0 else 0 - return 2.718281828 ** (-expected + actual * math.log(expected) - math.log(fac(actual))) - -def p_we_win(k, x): - return 1 - (x / (1.0 - x)) ** k - -def p_we_win_after(s): - p = 0 - for i in range(4000): - p += poisson(s * 1.0 / BLKTIME, i) * p_we_win(i, X) - return p - -for i in range(0, 7200, 12): - print i, p_we_win_after(i) diff --git a/mining/finality_probability_sim.py b/mining/finality_probability_sim.py deleted file mode 100644 index 470d8f0..0000000 --- a/mining/finality_probability_sim.py +++ /dev/null @@ -1,52 +0,0 @@ -import random -BLKTIME = 600 -LATENCY = 10 -TEST_MAX = 1200 -TEST_INTERVAL = 6 - -class Block(): - def __init__(self, parent, txstate): - self.parent = parent - self.score = 1 if parent is None else parent.score + 1 - if parent is None or parent.txstate is None: - self.txstate = txstate - else: - self.txstate = parent.txstate - - -results = {} - - -for double_spend_delay in range(0, TEST_MAX, TEST_INTERVAL): - results[double_spend_delay] = 0 - for _ in range(1000): - a_head = None - b_head = None - recvqueue = {} - for time_elapsed in range(5000): - txstate = 1 if time_elapsed < double_spend_delay else 2 - # Miner A mines and sends (has 50% network share) - if random.random() * BLKTIME < 0.5: - a_head = Block(a_head, txstate) - if time_elapsed + LATENCY not in recvqueue: - recvqueue[time_elapsed + LATENCY] = [] - recvqueue[time_elapsed + LATENCY].append(a_head) - # Miner B mines and sends (has 50% network share) - if random.random() * BLKTIME < 0.5: - b_head = Block(b_head, txstate) - if time_elapsed + LATENCY not in recvqueue: - recvqueue[time_elapsed + LATENCY] = [] - recvqueue[time_elapsed + LATENCY].append(b_head) - # Receive blocks - if time_elapsed in recvqueue: - for b in recvqueue[time_elapsed]: - if not a_head or b.score > a_head.score or (b.score == a_head.score and random.random() < 0.5): - a_head = b - if not b_head or b.score > b_head.score or (b.score == b_head.score and random.random() < 0.5): - b_head = b - # Check which transaction "made it" - if a_head and a_head.txstate == 1: - results[double_spend_delay] += 0.001 - print (double_spend_delay, results[double_spend_delay]) - -print(results) diff --git a/mining/hashimoto.py b/mining/hashimoto.py deleted file mode 100644 index 03a3eb5..0000000 --- a/mining/hashimoto.py +++ /dev/null @@ -1,257 +0,0 @@ -#!/usr/bin/env python -# -*- coding: utf-8 -*- -""" -Requirements: -- I/O bound: cycles spent on I/O ≫ cycles spent in cpu -- no sharding: impossible to implement data locality strategy -- easy verification - -Thoughts: - -Efficient implementations will not switch context (threading) when waiting for data. -But they would leverage all fill buffers and have concurrent memory accesses. -It can be assumed, that code can be written in a way to calculate N (<10) -nonces in parallel (on a single core). - -So, after all maybe memory bandwidth rather than latency is the actual bottleneck. -Can this be solved in a way that aligns with hashing nonces and allows -for a quick verification? Probably not. - -Loop unrolling: -Initially proposed dagger sets offer data locality which allows to scale the algo -on multiple cores/l2chaches. 320MB / 40sets = 8MB (< L2 cache) -A solution is to make accessed mem location depended on the value of the -previous access. - -Partitial Memory: -If a users only keeps e.g. one third of each DAG in memory (i.e. to -have in L3 cache), he still can answer ~0.5**k of accesses by substituting -them through previous node lookups. -This can be mitigated by -a) making each node deterministically depend on the value of at -least one close high memory node. Optionally for quick validation, select -the 2nd dependency for the lower (cached) memory. see produce_dag_k2dr -b) for DAG creation, using a hashing function which needs more cycles -than multiple memory lookups would - even for GPUs/FPGAs/ASICs. -""" - - -import time - -from pyethereum import utils - - -def decode_int(s): - o = 0 - for i in range(len(s)): - o = o * 256 + ord(s[i]) - return o - - -def encode_int(x): - o = '' - for _ in range(64): - o = chr(x % 256) + o - x //= 256 - return o - - -def sha3(x): - return decode_int(utils.sha3(x)) - - -def cantor_pair(x, y, p): - return ((x+y) * (x+y+1) / 2 + y) % p - - -def get_daggerset(params, seedset): - return [produce_dag(params, i) for i in seedset] - - -def update_daggerset(params, daggerset, seedset, seed): - idx = decode_int(seed) % len(daggerset) - seedset[idx] = seed - daggerset[idx] = produce_dag(params, seed) - - -def produce_dag(params, seed): - k, hk, w, hw, n, p, t = params.k, params.hk, params.w, \ - params.hw, params.dag_size, params.p, params.h_threshold - print 'Producing dag of size %d (%d memory)' % (n, n * params.wordsz) - o = [sha3(seed)] - init = o[0] - picker = 1 - for i in range(1, n): - x = 0 - picker = (picker * init) % p - curpicker = picker - if i < t: - for j in range(k): # can be flattend if params are known - x ^= o[curpicker % i] - curpicker >>= 10 - else: - for j in range(hk): - x ^= o[curpicker % t] - curpicker >>= 10 - o.append(pow(x, w if i < t else hw, p)) # use any "hash function" here - return o - - -def quick_calc(params, seed, pos, known=None): - k, hk, w, hw, p, t = params.k, params.hk, params.w, \ - params.hw, params.p, params.h_threshold - init = sha3(seed) % p - if known is None: - known = {} - known[0] = init - - def calc(i): - if i not in known: - curpicker = pow(init, i, p) - x = 0 - if i < t: - for j in range(k): - x ^= calc(curpicker % i) - curpicker >>= 10 - known[i] = pow(x, w, p) - else: - for j in range(hk): - x ^= calc(curpicker % t) - curpicker >>= 10 - known[i] = pow(x, hw, p) - return known[i] - o = calc(pos) - print 'Calculated index %d in %d lookups' % (pos, len(known)) - return o - - -def hashimoto(params, daggerset, header, nonce): - """ - Requirements: - - I/O bound: cycles spent on I/O ≫ cycles spent in cpu - - no sharding: impossible to implement data locality strategy - - # I/O bound: - e.g. lookups = 16 - sha3: 12 * 32 ~384 cycles - lookups: 16 * 160 ~2560 cycles # if zero cache - loop: 16 * 3 ~48 cycles - I/O / cpu = 2560/432 = ~ 6/1 - - # no sharding - lookups depend on previous lookup results - impossible to route computation/lookups based on the initial sha3 - """ - rand = sha3(header + encode_int(nonce)) % params.p - mix = rand - # loop, that can not be unrolled - # dag and dag[pos] depended on previous lookup - for i in range(params.lookups): - v = mix if params.is_serial else rand >> i - dag = daggerset[v % params.num_dags] # modulo - pos = v % params.dag_size # modulo - mix ^= dag[pos] # xor - # print v % params.num_dags, pos, dag[pos] - print header, nonce, mix - return mix - - -def light_hashimoto(params, seedset, header, nonce): - rand = sha3(header + encode_int(nonce)) % params.p - mix = rand - - for i in range(params.lookups): - v = mix if params.is_serial else rand >> i - seed = seedset[v % len(seedset)] - pos = v % params.dag_size - qc = quick_calc(params, seed, pos) - # print v % params.num_dags, pos, qc - mix ^= qc - print 'Calculated %d lookups' % \ - (params.lookups) - print header, nonce, mix - return mix - - -def light_verify(params, seedset, header, nonce): - h = light_hashimoto(params, seedset, header, nonce) - return h <= 256**params.wordsz / params.diff - - -def mine(daggerset, params, header, nonce=0): - orignonce = nonce - origtime = time.time() - while 1: - h = hashimoto(params, daggerset, header, nonce) - if h <= 256**params.wordsz / params.diff: - noncediff = nonce - orignonce - timediff = time.time() - origtime - print 'Found nonce: %d, tested %d nonces in %.2f seconds (%d per sec)' % \ - (nonce, noncediff, timediff, noncediff / timediff) - return nonce - nonce += 1 - - -class params(object): - """ - === tuning === - memory: memory requirements ≫ L2/L3/L4 cache sizes - lookups: hashes_per_sec(lookups=0) ≫ hashes_per_sec(lookups_mem_hard) - k: ? - d: higher values enfore memory availability but require more quick_calcs - num_dags: so that a dag can be updated in reasonable time - """ - p = (2 ** 256 - 4294968273)**2 # prime modulus - wordsz = 64 # word size - memory = 10 * 1024**2 # memory usage - num_dags = 2 # number of dags - dag_size = memory/num_dags/wordsz # num 64byte values per dag - lookups = 40 # memory lookups per hash - diff = 2**14 # higher is harder - k = 2 # num dependecies of each dag value - hk = 8 # dependencies for final nodes - d = 8 # max distance of first dependency (1/d=fraction of size) - w = 2 # work factor on node generation - hw = 8 # work factor on final node generation - h_threshold = dag_size*2/5 # cutoff between final and nonfinal nodes - is_serial = False # hashimoto is serial - - -if __name__ == '__main__': - print dict((k, v) for k, v in params.__dict__.items() - if isinstance(v, int)) - - # odds of a partitial storage attack - missing_mem = 0.01 - P_partitial_mem_success = (1-missing_mem) ** params.lookups - print 'P success per hash with %d%% mem missing: %d%%' % \ - (missing_mem*100, P_partitial_mem_success*100) - - # which actually only results in a slower mining, - # as more hashes must be tried - slowdown = 1 / P_partitial_mem_success - print 'x%.1f speedup required to offset %d%% missing mem' % \ - (slowdown, missing_mem*100) - - # create set of DAGs - st = time.time() - seedset = [str(i) for i in range(params.num_dags)] - daggerset = get_daggerset(params, seedset) - print 'daggerset with %d dags' % len(daggerset), 'size:', \ - 64*params.dag_size*params.num_dags / 1024**2, 'MB' - print 'creation took %.2fs' % (time.time() - st) - - # update DAG - st = time.time() - update_daggerset(params, daggerset, seedset, seed='qwe') - print 'updating 1 dag took %.2fs' % (time.time() - st) - - # Mine - for i in range(1): - header = 'test%d' % i - print '\nmining', header - nonce = mine(daggerset, params, header) - # verify - st = time.time() - assert light_verify(params, seedset, header, nonce) - print 'verification took %.2fs' % (time.time() - st) diff --git a/mining/mining.go b/mining/mining.go deleted file mode 100644 index 08738a3..0000000 --- a/mining/mining.go +++ /dev/null @@ -1,366 +0,0 @@ -package main - -import ( - "fmt" - "math" - "math/big" - "encoding/hex" - "github.com/obscuren/sha3" - "testing" - "strconv" -) - -//For use in benchmarking -const tree_depth = 5 -const tape_width = 32 //int(math.Pow(2,tree_depth)) < would be nice, but go won't recognize as const -const tape_depth = 100 - -//Number of operations that are drawn from to form the tape and the tree -const num_ops = 9 -//This is the number of times the PoW algorithm is run -const sample_size = 100 - -func Bytes2Hex(d []byte) string { - return hex.EncodeToString(d) -} - -func Hex2Bytes(str string) []byte { - h, _ := hex.DecodeString(str) - return h -} - -func plus(z *big.Int, x *big.Int, y *big.Int) *big.Int { - var lim big.Int - lim.Exp(big.NewInt(2),big.NewInt(256), big.NewInt(0)) - z.Add(x,y) - return z.Mod(z,&lim) - -} - -func times(z *big.Int, x *big.Int, y *big.Int) *big.Int { - var lim, x1, y1 big.Int - lim.Exp(big.NewInt(2),big.NewInt(256), big.NewInt(0)) - x1.Set(x) - y1.Set(y) - z.Mul(x,y) - z.Mod(z,&lim) - return z -} - -func mod(z *big.Int, x *big.Int, y *big.Int) *big.Int { - - if (x.Cmp(big.NewInt(0)) == 0 || y.Cmp(big.NewInt(0)) == 0) { - return big.NewInt(0) - } - if x.Cmp(y) == -1 { //if x < y - z.Mod(y,x) - } else if x.Cmp(y) == 1 { //if x > y - z.Mod(x,y) - } - return z -} - -func xor(z *big.Int, x *big.Int, y *big.Int) *big.Int {return z.Xor(x,y)} - -func nxor(z *big.Int, x *big.Int, y *big.Int) *big.Int { - z.Xor(x,y) - return z.Not(z) -} - -func and(z *big.Int, x *big.Int, y *big.Int) *big.Int {return z.And(x,y)} - -func not(z *big.Int, x *big.Int, y *big.Int) *big.Int { - _ = y - return z.Not(x) -} - -func or(z *big.Int, x *big.Int, y *big.Int) *big.Int {return z.Or(x,y)} - -func rshift(z *big.Int, x *big.Int, y *big.Int) *big.Int { - var lim big.Int - lim.Exp(big.NewInt(2),big.NewInt(256), big.NewInt(0)) - z.Rsh(x,7) - return z.Mod(z,&lim) -} - - -func GetOp(i int) func(z *big.Int, x *big.Int, y *big.Int) *big.Int{ - switch i { - case 0: - return plus - case 1: - return xor - case 2: - return not - case 3: - return times - case 4: - return mod - case 5: - return rshift - case 6: - return or - case 7: - return and - case 8: - return nxor - } - return plus -} - -//the tapelink is used to t -type Tapelink struct { - I int64 - J int64 - op func(z *big.Int, x *big.Int, y *big.Int) *big.Int -} - -func Sha3Bin(data []byte) []byte { - d := sha3.NewKeccak256() - d.Write(data) - return d.Sum(nil) -} - -func BenchmarkSha3Bin(b *testing.B){ - for i:= 0; i < b.N; i++ { - Sha3Bin([]byte(string(i))) - } -} - -//generates a tape of operations that is w*d long -func gen_tape(seed int64, w int, d int) []Tapelink { - var X = big.NewInt(0) - var Y = big.NewInt(0) - Y.Exp(big.NewInt(2),big.NewInt(80), nil) - var M = big.NewInt(0) - var T []Tapelink - for i := 0; i < w*d; i++{ - // add empty link to tape - T = append(T, *new(Tapelink)) - - // generate new entropy as needed - if (int64(X.Cmp(Y)) == -1) {X.SetBytes(Sha3Bin([]byte(strconv.FormatInt(seed + int64(i), 10))))} - - // Pick random index I - T[i].I = M.Mod(X,big.NewInt(int64(w))).Int64() - M = big.NewInt(int64(w)) - X = X.Div(X,M) - - // Pick random index J - mm := big.NewInt(M.Mod(X,big.NewInt(int64(w-1))).Int64() + int64(1) + T[i].I) - T[i].J = M.Mod(mm, big.NewInt(int64(w))).Int64() - M = big.NewInt(int64(w-1)) - X = X.Div(X,M) - - // Pick random operation - T[i].op = GetOp(int(M.Mod(X, big.NewInt(int64(num_ops))).Int64())) - M = big.NewInt(int64(num_ops)) - X = X.Div(X,M) - } - return T -} - -func BenchmarkGen_tape(b *testing.B){ - var X big.Int - var s int64 - b.ResetTimer() - for i := 0; i < b.N; i++ { - b.StopTimer() - X.SetBytes(Sha3Bin([]byte(string(i)))) - s = X.Int64() - b.StartTimer() - gen_tape(s, tape_width, tape_depth) - } - -} - -func gen_inputs(seed int64, w int) []big.Int { - var A []big.Int - for i := 0; i < w; i++ { - A = append(A, *new(big.Int)) - if (i % 256 == 0) { - A[i].SetBytes(Sha3Bin([]byte(strconv.FormatInt(seed + int64(i), 10)))) - } else { - A[i].Lsh(&A[i-1], 1) - } - } - return A -} - -func BenchmarkGen_inputs(b *testing.B){ - var X big.Int - var s int64 - b.ResetTimer() - for i := 0; i < b.N; i++ { - b.StopTimer() - X.SetBytes(Sha3Bin([]byte(string(i)))) - s = X.Int64() - b.StartTimer() - gen_inputs(s, tape_width) - } -} - -//this changes the inputs as it goes through a tape with d links -func run_tape(tape []Tapelink, inputs []big.Int, d int) { - var X *big.Int - X = big.NewInt(0) - for i := 0; i < d; i++ { - X = tape[i].op(X, &inputs[tape[i].I], &inputs[tape[i].J]) - inputs[tape[i].I].Set(X) - } -} - -func BenchmarkRun_tape(b *testing.B){ - b.ResetTimer() - for i := 0; i < b.N; i++ { - b.StopTimer() - T := gen_tape(int64(i), tape_width, tape_depth) - I := gen_inputs(int64(i), tape_width) - b.StartTimer() - run_tape(T,I,tape_width*tape_depth) - } -} - - -//returns a 2^d - 1 length tape of operations (no I or J's in the Tapelinks) -func gen_tree(seed int64, d int) []Tapelink { - M := big.NewInt(0) // dummy variable - X := big.NewInt(0) // entropy variable - Y := big.NewInt(0) // entropy buffer size - Y.Exp(big.NewInt(2),big.NewInt(80), nil) - var T []Tapelink // the tree will be stored here - - for i := 0; i < int(math.Pow(2, float64(d))) - 1; i++{ - - T = append(T, *new(Tapelink)) - - //giving it more entropy, if X < 2^32 - if (X.Cmp(Y) == -1) {X.SetBytes(Sha3Bin([]byte(strconv.FormatInt(seed + int64(i),10))))} - - //filling the tape with random ops - T[i].op = GetOp(int(M.Mod(X, big.NewInt(num_ops)).Int64())) - M = big.NewInt(num_ops) - X = X.Div(X,M) - } - return T -} - -func BenchmarkGen_tree(b *testing.B) { - var X big.Int - var s int64 - b.ResetTimer() - for i := 0; i < b.N; i++ { - b.StopTimer() - X.SetBytes(Sha3Bin([]byte(string(i)))) - s = X.Int64() - b.StartTimer() - gen_tree(s, tree_depth) - } -} - -//there should be 2^d inputs and 2^d - 1 links in the tape. not complying is an unhandled exception -func run_tree(inputs []big.Int, tree []Tapelink, d int) *big.Int { - X := big.NewInt(0) - counter := 0 - for j := 0; j < d; j++ { - for i := 0; i < int(math.Pow(2,float64(d - j - 1))); i++ { - X = tree[counter].op(X, &inputs[2*i], &inputs[2*i + 1]) - inputs[i].Set(X) - counter += 1 - } - } - - return &inputs[0] -} - -func BenchmarkRun_tree(b *testing.B) { - var X big.Int - b.ResetTimer() - for i := 0; i < b.N; i++ { - b.StopTimer() - var inputs []big.Int - for j := 0; j < tape_width; j++ { - X.SetBytes(Sha3Bin([]byte(string(j + i*tape_width)))) - inputs = append(inputs, X) - } - tree := gen_tree(X.Int64(), tree_depth) - b.StartTimer() - run_tree(inputs, tree, tree_depth) - } -} - -func sha_cap(s []string, n int) []byte{ - var feed string - feed = "" - for i := 0; i < n; i++ { - feed += s[i] - } - return Sha3Bin([]byte(feed)) -} - - -func BenchmarkSha_cap(b *testing.B){ - var X big.Int - var s []string - b.ResetTimer() - for i := 0; i < b.N; i++ { - b.StopTimer() - X.SetBytes(Sha3Bin([]byte(string(i)))) - s = append(s, X.String()) - b.StartTimer() - sha_cap(s,1) - } -} - -func main(){ - var seed int64 - var sample []big.Int - - - seed = int64(13300331) - - for i := 0; i < sample_size; i++ { - - Tape := gen_tape(seed, tape_width, tape_depth) - Tree := gen_tree(seed, tree_depth) - - seed += int64(i*i) - if i%10 == 0 { - fmt.Printf("i: %d\n",i) - } - I := gen_inputs(seed, tape_width) - run_tape(Tape, I, tape_depth*tape_width) - - - output := *run_tree(I, Tree, tree_depth) - if output.Cmp(big.NewInt(0)) == 0 { - fmt.Printf("We have a zero from the tree, form operation: \n") - fmt.Println(Tree[len(Tree)-1]) - - } - - - var blockhashes []string - blockhashes = append(blockhashes, output.String()) - - sample = append(sample, output) - H := sha_cap(blockhashes, 1) - - output.SetBytes(H) - //sample = append(sample, output) - } - - var collisions int = 0 - for i := 0; i < sample_size; i++ { - //fmt.Println(sample[i]) - for j:=0; j < i; j++ { - //if sample[i] == sample[j] { - if sample[i].Cmp(&sample[j]) == 0 { - collisions += 1 - //fmt.Printf("collision on i, j: %d, %d", i, j) - //fmt.Println(sample[i]) - } - } - } - fmt.Printf("number of outputs with same value: %d out of %d\n", (1+int(math.Pow(float64(1+8*collisions),0.5)))/2, sample_size) -} diff --git a/mining/mining.py b/mining/mining.py deleted file mode 100644 index f49d067..0000000 --- a/mining/mining.py +++ /dev/null @@ -1,95 +0,0 @@ -import pyethereum -u = pyethereum.utils -import time - -#These are the operations that will end up in the tape -ops = [ - lambda x, y: x+y % 2**256, - lambda x, y: x*y % 2**256, - lambda x, y: x % y if y > 0 else x+y, - lambda x, y: x & y, - lambda x, y: x | y, - lambda x, y: x ^ y -] - - -''' -the tape will be 'w' wide and 'd' operations deep -it is a list of triples [i, j, op], later used -in the tape's execution: xi = xi op xj -''' -def gen_tape(seed, w, d): - tape = [] - h = 0 - #Getting as much entropy out of a hash as possible - for i in range(d): - if h < 2**32: - h = u.big_endian_to_int(u.sha3(seed+str(i))) - v1 = h % w - h /= w - v2 = h % w - h /= w - op = ops[h % len(ops)] - h /= len(ops) - tape.append([v1, v2, op]) - return tape - - -def lshift(n): - return 2**255 * (n % 2) + (n / 2) - -#Generates the inputs to and evaluates the tape, the mining nonce can be taken to be in the seed -def gen_inputs(seed,w): - #generating the tape's inputs - v = [] - h = 0 - for i in range(w): - if i % 1 == 0: - h = u.big_endian_to_int(u.sha3(seed+str(i))) - else: - h = lshift(h) - v.append(h) - return v - -#Evaluate tape on inputs (incorrect dimension of v is an unhandled exception) -def run_tape(v, tape): - for t in tape: - v[t[0]] = t[2](v[t[0]], v[t[1]]) - #Implemented in a blockchain, any additional hashes or timestamp would be added in the sha - return str(v) - - -# This times the various parts of the hashing function - you can make the tape longer to make tape evaluation dominate -#num_iterations is the number of tapes that are used -#num_tape_evals is the number of nonces allowed, per tape -#tape_w is the width of the tape -#tape_d is the depth of the tape - -def test(num_iterations = 10, num_tape_evals = 1000, tape_w = 100, tape_d = 1000): - time_generating_tape = 0. - time_generating_inputs = 0. - time_evaluating_tape = 0. - time_sha_capping = 0. - for i in range(num_iterations): - t = time.time() - tape = gen_tape(str(i), tape_w, tape_d) - time_generating_tape += time.time() - t - - for j in xrange(num_tape_evals): - t = time.time() - v = gen_inputs(str(j), tape_w) - time_generating_inputs += time.time() - t - - t = time.time() - x = run_tape(v,tape) - time_evaluating_tape += time.time() - t - - t = time.time() - h = u.sha3(x) - time_sha_capping += time.time() - t - - total_time = time_generating_tape + time_generating_inputs + time_evaluating_tape + time_sha_capping - print "% of time generating tape:", time_generating_tape/total_time - print "% of time generating inputs:", time_generating_inputs/total_time - print "% of time evaluating tape:", time_evaluating_tape/total_time - print "% of time sha-capping:", time_sha_capping/total_time diff --git a/mining/python_sha3.py b/mining/python_sha3.py deleted file mode 100644 index fa72032..0000000 --- a/mining/python_sha3.py +++ /dev/null @@ -1,411 +0,0 @@ -#! /usr/bin/env python -# coding: utf-8 - -# The Keccak sponge function was designed by Guido Bertoni, Joan Daemen, -# Michaël Peeters and Gilles Van Assche. For more information, feedback or -# questions, please refer to their website: http://keccak.noekeon.org/ -# -# Based on the implementation by Renaud Bauvin, -# from http://keccak.noekeon.org/KeccakInPython-3.0.zip -# -# Modified by Moshe Kaplan to be hashlib-compliant -# -# To the extent possible under law, the implementer has waived all copyright -# and related or neighboring rights to the source code in this file. -# http://creativecommons.org/publicdomain/zero/1.0/ - - -import math - - -def sha3_224(data=None): - return Keccak(c=448, r=1152, n=224, data=data) - - -def sha3_256(data=None): - return Keccak(c=512, r=1088, n=256, data=data) - - -def sha3_384(data=None): - return Keccak(c=768, r=832, n=384, data=data) - - -def sha3_512(data=None): - return Keccak(c=1024, r=576, n=512, data=data) - - -class KeccakError(Exception): - """Custom error Class used in the Keccak implementation""" - - def __init__(self, value): - self.value = value - - def __str__(self): - return repr(self.value) - - -class Keccak: - def __init__(self, r, c, n, data=None): - # Initialize the constants used throughout Keccak - # bitrate - self.r = r - # capacity - self.c = c - # output size - self.n = n - - self.b = r + c - # b = 25*w - self.w = self.b // 25 - # 2**l = w - self.l = int(math.log(self.w, 2)) - - self.n_r = 12 + 2 * self.l - - self.block_size = r - self.digest_size = n - - # Initialize the state of the sponge - # The state is made up of 25 words, each word being w bits. - self.S = [[0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0]] - - # A string of hexchars, where each char represents 4 bits. - self.buffered_data = "" - - # Store the calculated digest. - # We'll only apply padding and recalculate the hash if it's modified. - self.last_digest = None - - if data: - self.update(data) - - # Constants - - ## Round constants - RC = [0x0000000000000001, - 0x0000000000008082, - 0x800000000000808A, - 0x8000000080008000, - 0x000000000000808B, - 0x0000000080000001, - 0x8000000080008081, - 0x8000000000008009, - 0x000000000000008A, - 0x0000000000000088, - 0x0000000080008009, - 0x000000008000000A, - 0x000000008000808B, - 0x800000000000008B, - 0x8000000000008089, - 0x8000000000008003, - 0x8000000000008002, - 0x8000000000000080, - 0x000000000000800A, - 0x800000008000000A, - 0x8000000080008081, - 0x8000000000008080, - 0x0000000080000001, - 0x8000000080008008] - - ## Rotation offsets - r = [[0, 36, 3, 41, 18], - [1, 44, 10, 45, 2], - [62, 6, 43, 15, 61], - [28, 55, 25, 21, 56], - [27, 20, 39, 8, 14]] - - @staticmethod - def Round(A, RCfixed, w): - """Perform one round of computation as defined in the Keccak-f permutation - - A: current state (5x5 matrix) - RCfixed: value of round constant to use (integer) - """ - - #Initialization of temporary variables - B = [[0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0]] - C = [0, 0, 0, 0, 0] - D = [0, 0, 0, 0, 0] - - #Theta step - for x in range(5): - C[x] = A[x][0] ^ A[x][1] ^ A[x][2] ^ A[x][3] ^ A[x][4] - - for x in range(5): - D[x] = C[(x - 1) % 5] ^ _rot(C[(x + 1) % 5], 1, w) - - for x in range(5): - for y in range(5): - A[x][y] = A[x][y] ^ D[x] - - #Rho and Pi steps - for x in range(5): - for y in range(5): - B[y][(2 * x + 3 * y) % 5] = _rot(A[x][y], Keccak.r[x][y], w) - - #Chi step - for x in range(5): - for y in range(5): - A[x][y] = B[x][y] ^ ((~B[(x + 1) % 5][y]) & B[(x + 2) % 5][y]) - - #Iota step - A[0][0] = A[0][0] ^ RCfixed - - return A - - @staticmethod - def KeccakF(A, n_r, w): - """Perform Keccak-f function on the state A - - A: 5x5 matrix containing the state, where each entry is a string of hexchars that is 'w' bits long - n_r: number of rounds - w: word size - """ - - for i in xrange(n_r): - A = Keccak.Round(A, Keccak.RC[i] % (1 << w), w) - - return A - - ### Padding rule - # This is a disgusting piece of code. Clean it. - @staticmethod - def pad10star1(M, n): - """Pad M with the pad10*1 padding rule to reach a length multiple of r bits - - M: message pair (length in bits, string of hex characters ('9AFC...') - n: length in bits (must be a multiple of 8) - Example: pad10star1([60, 'BA594E0FB9EBBD30'],8) returns 'BA594E0FB9EBBD93' - """ - - [my_string_length, my_string] = M - - # Check the parameter n - if n % 8 != 0: - raise KeccakError.KeccakError("n must be a multiple of 8") - - # Check the length of the provided string - if len(my_string) % 2 != 0: - #Pad with one '0' to reach correct length (don't know test - #vectors coding) - my_string += '0' - if my_string_length > (len(my_string) // 2 * 8): - raise KeccakError.KeccakError("the string is too short to contain the number of bits announced") - - nr_bytes_filled = my_string_length // 8 - nbr_bits_filled = my_string_length % 8 - l = my_string_length % n - if ((n - 8) <= l <= (n - 2)): - if (nbr_bits_filled == 0): - my_byte = 0 - else: - my_byte = int(my_string[nr_bytes_filled * 2:nr_bytes_filled * 2 + 2], 16) - my_byte = (my_byte >> (8 - nbr_bits_filled)) - my_byte = my_byte + 2 ** (nbr_bits_filled) + 2 ** 7 - my_byte = "%02X" % my_byte - my_string = my_string[0:nr_bytes_filled * 2] + my_byte - else: - if (nbr_bits_filled == 0): - my_byte = 0 - else: - my_byte = int(my_string[nr_bytes_filled * 2:nr_bytes_filled * 2 + 2], 16) - my_byte = (my_byte >> (8 - nbr_bits_filled)) - my_byte = my_byte + 2 ** (nbr_bits_filled) - my_byte = "%02X" % my_byte - my_string = my_string[0:nr_bytes_filled * 2] + my_byte - while((8 * len(my_string) // 2) % n < (n - 8)): - my_string = my_string + '00' - my_string = my_string + '80' - - return my_string - - def update(self, arg): - # Update the hash object with the string arg. Repeated calls are equivalent to a single call with the concatenation of all the arguments: m.update(a); m.update(b) is equivalent to m.update(a+b). arg is a normal bytestring. - - self.last_digest = None - # Convert the data into a workable format, and add it to the buffer - self.buffered_data += arg.encode('hex') - - # Absorb any blocks we can: - if len(self.buffered_data) * 4 >= self.r: - extra_bits = len(self.buffered_data) * 4 % self.r - - # An exact fit! - if extra_bits == 0: - P = self.buffered_data - self.buffered_data = "" - else: - # Slice it up into the first r*a bits, for some constant a>=1, and the remaining total-r*a bits. - P = self.buffered_data[:-extra_bits // 4] - self.buffered_data = self.buffered_data[-extra_bits // 4:] - - #Absorbing phase - for i in xrange((len(P) * 8 // 2) // self.r): - to_convert = P[i * (2 * self.r // 8):(i + 1) * (2 * self.r // 8)] + '00' * (self.c // 8) - P_i = _convertStrToTable(to_convert, self.w, self.b) - - # First apply the XOR to the state + block - for y in xrange(5): - for x in xrange(5): - self.S[x][y] = self.S[x][y] ^ P_i[x][y] - # Then apply the block permutation, Keccak-F - self.S = Keccak.KeccakF(self.S, self.n_r, self.w) - - def digest(self): - """Return the digest of the strings passed to the update() method so far. - - This is a string of digest_size bytes which may contain non-ASCII - characters, including null bytes.""" - - if self.last_digest: - return self.last_digest - - # UGLY WARNING - # Handle bytestring/hexstring conversions - M = _build_message_pair(self.buffered_data.decode('hex')) - - # First finish the padding and force the final update: - self.buffered_data = Keccak.pad10star1(M, self.r) - self.update('') - # UGLY WARNING over - - assert len(self.buffered_data) == 0, "Why is there data left in the buffer? %s with length %d" % (self.buffered_data, len(self.buffered_data) * 4) - - # Squeezing time! - Z = '' - outputLength = self.n - while outputLength > 0: - string = _convertTableToStr(self.S, self.w) - # Read the first 'r' bits of the state - Z = Z + string[:self.r * 2 // 8] - outputLength -= self.r - if outputLength > 0: - S = KeccakF(S, verbose) - - self.last_digest = Z[:2 * self.n // 8].decode('hex') - return self.last_digest - - def hexdigest(self): - """Like digest() except the digest is returned as a string of hex digits - - This may be used to exchange the value safely in email or other - non-binary environments.""" - return self.digest().encode('hex') - - def copy(self): - # First initialize whatever can be done normally - duplicate = Keccak(c=self.c, r=self.r, n=self.n) - # Then copy over the state. - for i in xrange(5): - for j in xrange(5): - duplicate.S[i][j] = self.S[i][j] - # and any other stored data - duplicate.buffered_data = self.buffered_data - duplicate.last_digest = self.last_digest - return duplicate - - -## Generic utility functions - -def _build_message_pair(data): - hex_data = data.encode('hex') - size = len(hex_data) * 4 - return (size, hex_data) - - -def _rot(x, shift_amount, length): - """Rotate x shift_amount bits to the left, considering the \ - string of bits is length bits long""" - - shift_amount = shift_amount % length - return ((x >> (length - shift_amount)) + (x << shift_amount)) % (1 << length) - -### Conversion functions String <-> Table (and vice-versa) - - -def _fromHexStringToLane(string): - """Convert a string of bytes written in hexadecimal to a lane value""" - - #Check that the string has an even number of characters i.e. whole number of bytes - if len(string) % 2 != 0: - raise KeccakError.KeccakError("The provided string does not end with a full byte") - - #Perform the conversion - temp = '' - nrBytes = len(string) // 2 - for i in xrange(nrBytes): - offset = (nrBytes - i - 1) * 2 - temp += string[offset:offset + 2] - return int(temp, 16) - - -def _fromLaneToHexString(lane, w): - """Convert a lane value to a string of bytes written in hexadecimal""" - - laneHexBE = (("%%0%dX" % (w // 4)) % lane) - #Perform the conversion - temp = '' - nrBytes = len(laneHexBE) // 2 - for i in xrange(nrBytes): - offset = (nrBytes - i - 1) * 2 - temp += laneHexBE[offset:offset + 2] - return temp.upper() - - -def _convertStrToTable(string, w, b): - """Convert a string of hex-chars to its 5x5 matrix representation - - string: string of bytes of hex-coded bytes (e.g. '9A2C...')""" - - # Check that the input paramaters are expected - if w % 8 != 0: - raise KeccakError("w is not a multiple of 8") - - # Each character in the string represents 4 bits. - # The string should have exactly 'b' bits. - if len(string) * 4 != b: - raise KeccakError.KeccakError("string can't be divided in 25 blocks of w bits\ - i.e. string must have exactly b bits") - - #Convert - output = [[0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0]] - - bits_per_char = 2 * w // 8 - for x in xrange(5): - for y in xrange(5): - # Each entry will have b/25=w bits. - offset = (5 * y + x) * bits_per_char - # Store the data into the associated word. - hexstring = string[offset:offset + bits_per_char] - output[x][y] = _fromHexStringToLane(hexstring) - return output - - -def _convertTableToStr(table, w): - """Convert a 5x5 matrix representation to its string representation""" - - #Check input format - if w % 8 != 0: - raise KeccakError.KeccakError("w is not a multiple of 8") - if (len(table) != 5) or any(len(row) != 5 for row in table): - raise KeccakError.KeccakError("table must be 5x5") - - #Convert - output = [''] * 25 - for x in xrange(5): - for y in xrange(5): - output[5 * y + x] = _fromLaneToHexString(table[x][y], w) - output = ''.join(output).upper() - return output diff --git a/bulletproofs/multicombs.py b/multicombs.py similarity index 100% rename from bulletproofs/multicombs.py rename to multicombs.py diff --git a/newssz/foo.py b/newssz/foo.py deleted file mode 100644 index f233b05..0000000 --- a/newssz/foo.py +++ /dev/null @@ -1,120 +0,0 @@ -def get_default_value(typ): - if typ == int: - return 0 - else: - return typ.default() - -def type_check(typ, value): - if typ == int: - return isinstance(value, int) - else: - return typ.value_check(value) - -class AbstractListMeta(type): - def __new__(cls, class_name, parents, attrs): - out = type.__new__(cls, class_name, parents, attrs) - if 'elem_type' in attrs and 'length' in attrs: - setattr(out, 'elem_type', attrs['elem_type']) - setattr(out, 'length', attrs['length']) - return out - - def __getitem__(self, params): - if not isinstance(params, tuple) or len(params) != 2: - raise Exception("List must be instantiated with two args: elem type and length") - o = self.__class__(self.__name__, (self,), {'elem_type': params[0], 'length': params[1]}) - o._name = 'AbstractList' - return o - - def __instancecheck__(self, obj): - if obj.__class__.__name__ != self.__name__: - return False - if hasattr(self, 'elem_type') and obj.__class__.elem_type != self.elem_type: - return False - if hasattr(self, 'length') and obj.__class__.length != self.length: - return False - return True - -class ValueCheckError(Exception): - pass - -class AbstractList(metaclass=AbstractListMeta): - def __init__(self, *args): - items = self.extract_args(args) - - if not self.value_check(items): - raise ValueCheckError("Bad input for class {}: {}".format(self.__class__, items)) - self.items = items - - def value_check(self, value): - for v in value: - if not isinstance(v, self.__class__.elem_type): - return False - return True - - def extract_args(self, args): - return list(args) if len(args) > 0 else self.default() - - def default(self): - raise Exception("Not implemented") - - def __getitem__(self, i): - return self.items[i] - - def __setitem__(self, k, v): - self.items[k] = v - - def __len__(self): - return len(self.items) - - def __repr__(self): - return repr(self.items) - - def __iter__(self): - return iter(self.items) - - def __eq__(self, other): - return self.items == other.items - -class List(AbstractList, metaclass=AbstractListMeta): - def value_check(self, value): - return len(value) <= self.__class__.length and super().value_check(value) - - def default(self): - return [] - -class Vector(AbstractList, metaclass=AbstractListMeta): - def value_check(self, value): - return len(value) == self.__class__.length and super().value_check(value) - - def default(self): - return [get_default_value(self.__class__.elem_type) for _ in range(self.__class__.length)] - -class BytesMeta(AbstractListMeta): - def __getitem__(self, params): - if not isinstance(params, int): - raise Exception("Bytes must be instantiated with one arg: length") - o = self.__class__(self.__name__, (self,), {'length': params}) - o._name = 'Bytes' - return o - -def single_item_extractor(cls, args): - assert len(args) < 2 - return args[0] if len(args) > 0 else cls.default() - -class Bytes(AbstractList, metaclass=BytesMeta): - def value_check(self, value): - return len(value) <= self.__class__.length and isinstance(value, bytes) - - extract_args = single_item_extractor - - def default(self): - return b'' - -class BytesN(AbstractList, metaclass=BytesMeta): - def value_check(self, value): - return len(value) == self.__class__.length and isinstance(value, bytes) - - extract_args = single_item_extractor - - def default(self): - return b'\x00' * self.__class__.length diff --git a/newssz/test_foo.py b/newssz/test_foo.py deleted file mode 100644 index 7f26d7b..0000000 --- a/newssz/test_foo.py +++ /dev/null @@ -1,50 +0,0 @@ -from foo import List, Vector, Bytes, BytesN, ValueCheckError - -def assert_pass(typ, value): - x = typ(*value) if issubclass(typ, List) or issubclass(typ, Vector) else typ(value) - for i in range(len(value)): - assert x[i] == value[i] - -def assert_invalid(typ, value): - try: - x = typ(*value) if issubclass(typ, List) or issubclass(typ, Vector) else typ(value) - passed = True - except ValueCheckError: - passed = False - assert not passed - -assert isinstance(List[int, 3](10, 20, 30), List[int, 3]) -assert not isinstance(List[int, 3](10, 20, 30), List[int, 5]) -assert not isinstance(List[int, 3](10, 20, 30), List[bool, 3]) -assert isinstance(List[int, 3](10, 20, 30), List) -assert isinstance(Vector[int, 3](10, 20, 30), Vector[int, 3]) -assert not isinstance(Vector[int, 3](10, 20, 30), List[int, 3]) -assert isinstance(Bytes[3](b"cow"), Bytes[3]) -assert not isinstance(Bytes[3](b"cow"), Bytes[5]) -assert isinstance(Bytes[3](b"cow"), Bytes) -assert_pass(List[int, 3], []) -assert_pass(List[int, 3], [10]) -assert_pass(List[int, 3], [10, 20]) -assert_pass(List[int, 3], [10, 20, 30]) -assert_invalid(List[int, 3], [10, 20, 30, 40]) -assert_invalid(List[int, 3], ["dog", 20, 30]) -assert_pass(Vector[int, 3], [10, 20, 30]) -assert_invalid(Vector[int, 3], [10]) -assert_invalid(Vector[int, 3], [10, 20, 30, 40]) -assert_invalid(Vector[int, 3], [10, "cow", 30]) -assert_pass(Vector[Vector[int, 2], 2], [Vector[int, 2](10, 20), Vector[int, 2](30, 40)]) -assert_invalid(Vector[Vector[int, 2], 2], [Vector[int, 2](10, 20), Vector[int, 3](30, 40, 50)]) -assert_invalid(Vector[Vector[int, 2], 2], [Vector[int, 2](10, 20), Vector[int, 2](30, 40), Vector[int, 2](50, 60)]) -assert_invalid(Vector[Vector[int, 2], 2], [Vector[int, 2](10, 20), List[int, 2](30, 40)]) -assert_pass(Bytes[3], b'ow') -assert_pass(Bytes[3], b'cow') -assert_invalid(Bytes[3], b'crow') -assert_invalid(Bytes[3], [10, 20, 30]) -assert_invalid(BytesN[3], b'ow') -assert_pass(BytesN[3], b'cow') -assert_invalid(BytesN[3], b'crow') -assert_invalid(BytesN[3], [10, 20, 30]) -x = List[int, 3](10, 20, 30) -x[2] = 100 -assert x == List[int, 3](10, 20, 100) -print("Tests passed") diff --git a/old_consensus_by_bet/README.md b/old_consensus_by_bet/README.md deleted file mode 100644 index 548979e..0000000 --- a/old_consensus_by_bet/README.md +++ /dev/null @@ -1,40 +0,0 @@ -### Casper proof of stake algorithm - -Casper is a new proof of stake algorithm being developed by Vitalik Buterin, Vlad Zamfir et al, which tries to resolve, or optimally compromise between, several of the outstanding issues in previous proof of stake algorithms. Proof of stake has many benefits, chief among which is the potential for massive reductions in electricity costs as well as more rapid convergence toward a state of "finality" where transactions cannot be reverted no matter what, but so far some of these issues have caused concern among developers and users, and led to a reduced willingness to adopt proof-of-stake protocols. - -The three primary issues with existing proof of stake algorithms can be described as follows. - -* **Nothing at stake**: if there are multiple "forks" of a blockchain, there is no incentive for validators not to register a vote on _every_ fork of the chain. This may end up a fatal problem even without any attackers, but if an attacker is present then they can, in theory, bribe everyone $0.001 to do this, and themselves mine only on their own fork, and thus revert an arbitrarily long chain at near-zero cost. - -Some blockchains (eg. [Tendermint](http://tendermint.com/)) solve the first problem via a "slashing" mechanic where validators are required to post security bonds, which can be taken away if a user double-votes. This insight can even be taken much further and provide a very strong robustness property where a double spend _cannot_ happen without a very large quantity of security bonds getting destroyed. However, to make this work, a requirement must be added where some portion `x > 0.5` of validators must either sign every block or sign the chain after some height, so that a successful double spend requires at least `2x - 1` of validators to sign two blocks (as `x` signed the original chain, `x` signed the new chain, and `2x - 1` signing both chains is the mathematically smallest possible overlap; you can see this yourself via Venn diagrams). Hence, `2x - 1` of all security deposits (eg. at `x = 2/3` this means one third) must be destroyed for a fork to happen. However, tis itself introduces two new problems: - -* **Sudden dropout ice age**: what if more than `1-x` of nodes suddenly drop dead? Then the blockchain may "freeze" forever. -* **Stuck scenario**: what if, somehow, half of nodes sign one block and the other half sign the other block, so the chain cannot proceed further without a large quantity of deposits being destroyed? This is arguably as fatal a scenario as a successful double spend, and so getting to this point too should not be possible without a large quantity of security bond slashing. - -Casper introduces a proof of stake model which solves this using a similar (arguably cop-out) approach as Bitcoin: rather then trying to go from zero to finality in one step, we make it a gradual process, where validators progressively put more and more "stake" behind blocks until these blocks reach finality. The fundamental approach relies on a mechanism known as **consensus-by-bet**: essentially, instead of simply voting on which answer to give when the consensus mechanism requires a choice to be made, validators bet on the answer, and the bets themselves determine the answer. - -More precisely, at every block height, validators must achieve binary consensus (ie. all agree either 0 or 1) on the question: has a block been submitted at this height, and if so what block hash? We can model this by imagining a ball which starts off at the top of a hill, where there are multiple ramps down the hill that the ball can take: one ramp representing "no block" and one ramp representing "yes there is a block" (in the special malicious case where a validator submits two blocks, there may be two ramps representing "yes, there is a block and it's X" and "yes, there is a block and it's Y". The simple intuition behind the consensus algorithm is that each voter's strategy is: - -* Take the median position that everyone else is on (or, more precisely, mode by orientation and 33rd percentile by latitude) -* Apply one step of "gravity" from this position. Randomly jiggle a bit to prevent "stuck" scenarios -* Make this your new position, and publicly create a vote announcing this - -In the case that no block has been submitted, the "yes there is a block" ramp is closed off, and so there is only one ramp to go down. Once a block has fully gone down one particular ramp from the point of view of 2/3 of validators, consider it "finalized". This process takes place in parallel for every block height, and is continuous; validators can update their votes on every height every time a new block comes in. - -This algorithm can be analyzed from two perspectives: BFT analysis and economic analysis. From a BFT analysis perspective, the 33rd percentile rule makes the algorithm equivalent to a highly multi-round version of DLS-like pre-commit/commit/finalize algorithms. From an economic analysis perspective, the algorithm is much more interesting, and in fact borrows more from prediction market and scoring rule theory than it does from consensus theory. Every vote is a bet, and the bets are incentivized via a [scoring rule](https://en.wikipedia.org/wiki/Scoring_rule). The "altitude" on the ramps can be thought of as a probability estimate, where the top of the hill is 50% and the bottom of the hill is 99.99%; if you bet 97% on a particular outcome then that means that you are willing to accept a penalty of 97 if the result does NOT converge toward that outcome in exchange for a reward of 3 if the result does converge in that direction. The closer your bet gets to 100%, the more you gain if you are right, but the more you lose if you are wrong, until at 99.99% if you are wrong you lose your entire deposit. The idea is that validators get progressively more and more confident about a particular outcome as they see other validators getting more confident, and thus the system eventually (and in fact, logarithmically quickly) does converge on one outcome. - -The exact formula for this contains two functions, `s(p)` (which determines the payout given a bet `p` if you are right) and `f(p)` (which determines the payout given a bet `p` if you are wrong). To simplify things, we can also express the probability in terms of odds (which we'll denote `q`); for example, odds of 5:1 imply that something is five times more likely to happen than not happen, and in general we define `q = p/(1-p)`. In order for the formula to be incentive-compatible, we need (in probability form) `s'(p) * p = -f'(p) * (1-p)`, or (in odds form) `s'(q) * q = -f'(q)`. I propose the following functions: - - s(q) = q - f(q) = -q^2 / 2 - -As `q` gets high, you may notice that the penalties get high very quickly, though the rewards also increase albeit less drastically. For example, if your belief is that the odds of a given state (either 0 or 1) succeeding are 500:1, then if you bet `q = 400`, your expected return is `500/501 * s(400) + 1/501 * f(400) = 500/501 * 400 - 1/501 * 80000 = 239.52`, if you bet `q = 500` your expected return is 249.50, and if you bet `q = 600` your expected return is 239.52; if you bet `q = 1000` your expected return drops to zero and if you bet even more confidently your expected return becomes negative. In general, we expect risk aversion to lead to a bias where users converge toward an outcome more slowly than they "should" but this effect should only be moderately large; the "take the median of everyone else and apply one step of gravity" model is a good first approximation, and particularly ensures that you are not taking bets which are more than ~2.7x as risky/confident as bets that have already been taken by other validators. - -"Stuck" scenarios are impossible, as no one will vote confidently for a particular block unless a majority has already gone most of the way along the same direction; the worst outcome that may happen is one where the ball "remains at the top of the hill" for an extended period of time due to a combination of bad strategy selection and perhaps some malicious betting that tries to counteract any movements along any of the "ramps" going down. A possible counteraction is creating a default strategy that pushes harder and harder toward the "no block" outcome as time goes on. - -The sudden dropout ice age risk is dealt with via a compromise: if 67% of validators _are_ present, then the system converges; however, if fewer than 67% of validators are present then the system continues to produce blocks, but simply without agreeing on finality for any of them. Hence, in such a situation the system will simply have roughly the same level of security as systems like NXT. - -Ongoing research questions: - -* Do we detect such ice ages? If so, do we respond to them in a particular way (eg. reducing the 67% threshold over time)? Perhaps do we eventually switch to requiring only 67% of recently online nodes to agree on a block? Perhaps a proof of work backstop? -* What is the most efficient way to express a signature? This algorithm carries a high data overhead, and so any reduction in the overhead would be highly appreciated. diff --git a/old_consensus_by_bet/casper.py b/old_consensus_by_bet/casper.py deleted file mode 100644 index f15a04e..0000000 --- a/old_consensus_by_bet/casper.py +++ /dev/null @@ -1,335 +0,0 @@ -import copy, random, hashlib -from distributions import normal_distribution -import networksim -from voting_strategy import vote, default_vote -import math - -# Number of validators -NUM_VALIDATORS = 20 -# Block time -BLKTIME = 40 -# 0 for no netsplits -# 1 for simulating a netsplit where 20% of validators jump off -# the network -# 2 for simulating the above netsplit, plus a 50-50 netsplit, -# plus reconvergence -NETSPLITS = 2 -# Check the equality of finalized states -CHECK_INTEGRITY = True -# The genesis state root -GENESIS_STATE = 0 - -logging_level = 0 - - -def log(s, lvl): - if logging_level >= lvl: - print(s) - - -# A signture specifies an initial height ("sign_from"), a finalized -# state from all blocks before that height and a list of probability -# bets from that height up to the latest height -class Signature(): - def __init__(self, signer, probs, finalized_state, sign_from): - # The ID of the signer - self.signer = signer - # List of probability bets, expressed in log odds - self.probs = probs - # Hash of the signature (for db storage purposes) - self.hash = random.randrange(10**14) - # Finalized state - self.finalized_state = finalized_state - # Finalized height - self.sign_from = sign_from - - def get_height(self): - return self.sign_from + len(self.probs) - - -# Right now, a block simply specifies a proposer and a height. -class Block(): - def __init__(self, maker, height): - # The producer of the block - self.maker = maker - # The height of the block - self.height = height - # Hash of the signature (for db storage purposes) - self.hash = random.randrange(10**20) + 10**21 + 10**23 * self.height - - -# A request to receive a block at a particular height -class BlockRequest(): - def __init__(self, sender, height): - self.sender = sender - self.ask_height = height - self.hash = random.randrange(10**14) - - -# Toy state transition function (in production, do sequential -# apply_transaction here) -def state_transition(state, block): - return state if block is None else (state ** 3 + block.hash ** 5) % 10**40 - - -# A validator -class Validator(): - def __init__(self, pos, network): - # Map from height to {node_id: latest_bet} - self.received_signatures = [] - # List of received blocks - self.received_blocks = [] - # Own probability estimates - self.probs = [] - # All objects that this validator has received; basically a database - self.received_objects = {} - # Time when the object was received - self.time_received = {} - # The validator's ID, and its position in the queue - self.pos = self.id = pos - # The offset of this validator's clock vs. real time - self.time_offset = normal_distribution(0, 100)() - # The highest height that this validator has seen - self.max_height = 0 - # The validator's hash chain - self.finalized_hashes = [] - # Finalized states - self.finalized_states = [] - # The highest height that the validator has finalized - self.max_finalized_height = -1 - # The network object - self.network = network - # Last time signed - self.last_time_signed = 0 - # Next height to mine - self.next_height = self.pos - - # Get the local time from the point of view of this validator, using the - # validator's offset from real time - def get_time(self): - return self.network.time + self.time_offset - - # Broadcast an object to the network - def broadcast(self, obj): - self.network.broadcast(self, obj) - - # Create a signature - def sign(self): - # Initialize the probability array, the core of the signature - best_guesses = [None] * len(self.received_blocks) - sign_from = max(0, self.max_finalized_height - 30) - for i, b in list(enumerate(self.received_blocks))[sign_from:]: - # Compute this validator's own initial vote based on when the block - # was received, compared to what time the block should have arrived - received_time = self.time_received[b.hash] if b is not None else None - my_opinion = default_vote(BLKTIME * i, received_time, self.get_time(), blktime=BLKTIME) - # Get others' bets on this height - votes = self.received_signatures[i].values() if i < len(self.received_signatures) else [] - votes = [x for x in votes if x != 0] - # Fill in the not-yet-received votes with this validator's default bet - votes += [my_opinion] * (NUM_VALIDATORS - len(votes)) - vote_from_signatures = int(vote(votes)) - # Add the bet to the list - bg = min(vote_from_signatures, 10 if self.received_blocks[i] is not None else my_opinion) - best_guesses[i] = bg - # Request a block if we should have it, and should have had it for - # a long time, but don't - if vote_from_signatures > 3 and self.received_blocks[i] is None: - self.broadcast(BlockRequest(self.id, i)) - elif i < len(self.received_blocks) - 50 and self.received_blocks[i] is None: - if random.random() < 0.05: - self.broadcast(BlockRequest(self.id, i)) - # Block finalized - if best_guesses[i] >= 10: - while len(self.finalized_hashes) <= i: - self.finalized_hashes.append(None) - self.finalized_hashes[i] = self.received_blocks[i].hash - # Absense of the block finalized - elif best_guesses[i] <= -10: - while len(self.finalized_hashes) <= i: - self.finalized_hashes.append(None) - self.finalized_hashes[i] = False - # Add to the list of finalized states - while self.max_finalized_height < len(self.finalized_hashes) - 1 \ - and self.finalized_hashes[self.max_finalized_height + 1] is not None: - self.max_finalized_height += 1 - last_state = self.finalized_states[-1] if len(self.finalized_states) else GENESIS_STATE - self.finalized_states.append(state_transition(last_state, self.received_blocks[self.max_finalized_height])) - - self.probs = self.probs[:sign_from] + best_guesses[sign_from:] - log('Making signature: %r' % self.probs[-10:], lvl=1) - sign_from_state = self.finalized_states[sign_from - 1] if sign_from > 0 else GENESIS_STATE - s = Signature(self.pos, self.probs[sign_from:], sign_from_state, sign_from) - all_signatures.append(s) - return s - - def on_receive(self, obj): - # Ignore objects that we already know about - if obj.hash in self.received_objects: - return - # When receiving a block - if isinstance(obj, Block): - log('received block: %d %d' % (obj.height, obj.hash), lvl=2) - while len(self.received_blocks) <= obj.height: - self.received_blocks.append(None) - self.received_blocks[obj.height] = obj - self.time_received[obj.hash] = self.get_time() - # Upon receiving a new block, make a new signature - s = self.sign() - self.network.broadcast(self, s) - self.on_receive(s) - self.network.broadcast(self, obj) - # When receiving a signature - elif isinstance(obj, Signature): - while len(self.received_signatures) <= len(obj.probs) + obj.sign_from: - self.received_signatures.append({}) - for i, p in enumerate(obj.probs): - self.received_signatures[i + obj.sign_from][obj.signer] = p - self.network.broadcast(self, obj) - # Received a block request, respond if we have it - elif isinstance(obj, BlockRequest): - if obj.ask_height < len(self.received_blocks): - if self.received_blocks[obj.ask_height] is not None: - self.network.direct_send(obj.sender, self.received_blocks[obj.ask_height]) - self.received_objects[obj.hash] = obj - self.time_received[obj.hash] = self.get_time() - - # Run every tick - def tick(self): - mytime = self.get_time() - target_time = BLKTIME * self.next_height - if mytime >= target_time: - o = Block(self.pos, self.next_height) - self.next_height += NUM_VALIDATORS - log('making block: %d %d' % (o.height, o.hash), lvl=1) - if random.random() < 0.9: - self.network.broadcast(self, o) - while len(self.received_blocks) <= o.height: - self.received_blocks.append(None) - self.received_blocks[o.height] = o - self.received_objects[o.hash] = o - self.time_received[o.hash] = mytime - return o - -validator_list = [] -future = {} -discarded = {} -finalized_blocks = {} -all_signatures = [] -now = [0] - - -def who_heard_of(h, n): - o = '' - for x in n.agents: - o += '1' if h in x.received_objects else '0' - return o - - -def get_opinions(n): - o = [] - maxheight = 0 - for x in n.agents: - maxheight = max(maxheight, len(x.probs)) - for h in range(maxheight): - p = '' - q = '' - for x in n.agents: - if len(x.probs) <= h: - p += '_' - elif x.probs[h] <= -10: - p += '-' - elif x.probs[h] >= 10: - p += '+' - else: - p += str(x.probs[h])+',' - q += 'n' if len(x.received_blocks) <= h or x.received_blocks[h] is None else 'y' - o.append((h, p, q)) - return o - - -def get_finalization_heights(n): - o = [] - for x in n.agents: - o.append(x.max_finalized_height) - return o - - -# Check how often blocks that are assigned particular probabilities of -# finalization by our algorithm are actually finalized -def calibrate(finalized_hashes): - thresholds = range(-10, 11) - signed = [0] * (len(thresholds) - 1) - _finalized = [0] * (len(thresholds) - 1) - _discarded = [0] * (len(thresholds) - 1) - for s in all_signatures: - for i, prob in enumerate(s.probs): - if i + s.sign_from >= len(finalized_hashes): - continue - actual_result = 1 if finalized_hashes[i + s.sign_from] else 0 - index = 0 - while index + 2 < len(thresholds) and prob > thresholds[index + 1]: - index += 1 - signed[index] += 1 - if actual_result == 1: - _finalized[index] += 1 - elif actual_result == 0: - _discarded[index] += 1 - for i in range(len(thresholds) - 1): - if _finalized[i] + _discarded[i]: - print 'Probability from %f to %f: %f (%d of %d)' % (thresholds[i], thresholds[i+1], _finalized[i] * 1.0 / (_finalized[i] + _discarded[i]), _finalized[i], _finalized[i] + _discarded[i]) - print 'Percentage of block heights filled: %f%%' % (len([x for x in finalized_hashes if x]) * 100.0 / len(finalized_hashes)) - - -def run(steps=4000): - n = networksim.NetworkSimulator() - for i in range(NUM_VALIDATORS): - n.agents.append(Validator(i, n)) - n.generate_peers(3) - while len(all_signatures): - all_signatures.pop() - for x in future.keys(): - del future[x] - for x in finalized_blocks.keys(): - del finalized_blocks[x] - for x in discarded.keys(): - del discarded[x] - for i in range(steps): - n.tick() - if i % 500 == 0: - minmax = 99999999999999999 - for x in n.agents: - minmax = min(minmax, x.max_finalized_height - 10) - print get_opinions(n)[max(minmax, 0):] - finalized0 = [(v.max_finalized_height, v.finalized_hashes) for v in n.agents] - if CHECK_INTEGRITY: - finalized = sorted(finalized0, key=lambda x: len(x[1])) - for j in range(len(n.agents) - 1): - for k in range(len(finalized[j][1])): - if finalized[j][1][k] is not None and finalized[j+1][1][k] is not None: - if finalized[j][1][k] != finalized[j+1][1][k]: - print finalized[j] - print finalized[j+1] - raise Exception("Finalization mismatch: %r %r" % (finalized[j][1][k], finalized[j+1][1][k])) - print 'Finalized status: %r' % [x[0] for x in finalized0] - _all = finalized0[0][1] - _pos = len([x for x in _all if x]) - _neg = len([x for x in _all if not x]) - print 'Finalized blocks: %r (%r positive, %r negaitve)' % (len(_all), _pos, _neg) - if i == 10000 and NETSPLITS >= 1: - print "###########################################################" - print "Knocking off 20% of the network!!!!!" - print "###########################################################" - n.knock_offline_random(NUM_VALIDATORS // 5) - if i == 20000 and NETSPLITS >= 2: - print "###########################################################" - print "Simluating a netsplit!!!!!" - print "###########################################################" - n.generate_peers() - n.partition() - if i == 30000 and NETSPLITS >= 1: - print "###########################################################" - print "Network health back to normal!" - print "###########################################################" - n.generate_peers() - calibrate(n.agents[0].finalized_hashes[:n.agents[0].max_finalized_height + 1]) diff --git a/old_consensus_by_bet/distributions.py b/old_consensus_by_bet/distributions.py deleted file mode 100644 index 6412e3d..0000000 --- a/old_consensus_by_bet/distributions.py +++ /dev/null @@ -1,37 +0,0 @@ -import random, sys - - -def normal_distribution(mean, standev): - def f(): - return int(random.normalvariate(mean, standev)) - - return f - - -def exponential_distribution(mean): - def f(): - total = 0 - while 1: - total += 1 - if not random.randrange(32): - break - return int(total * 0.03125 * mean) - - return f - - -def convolve(*args): - def f(): - total = 0 - for arg in args: - total += arg() - return total - - return f - - -def transform(dist, xformer): - def f(): - return xformer(dist()) - - return f diff --git a/old_consensus_by_bet/networksim.py b/old_consensus_by_bet/networksim.py deleted file mode 100644 index 301cd65..0000000 --- a/old_consensus_by_bet/networksim.py +++ /dev/null @@ -1,75 +0,0 @@ -from distributions import transform, normal_distribution -import random - - -class NetworkSimulator(): - - def __init__(self): - self.agents = [] - self.latency_distribution_sample = transform(normal_distribution(50, 20), lambda x: max(x, 0)) - self.time = 0 - self.objqueue = {} - self.peers = {} - self.reliability = 0.9 - - def generate_peers(self, num_peers=5): - self.peers = {} - for a in self.agents: - p = [] - while len(p) <= num_peers // 2: - p.append(random.choice(self.agents)) - if p[-1] == a: - p.pop() - self.peers[a.id] = self.peers.get(a.id, []) + p - for peer in p: - self.peers[peer.id] = self.peers.get(peer.id, []) + [a] - - def tick(self): - if self.time in self.objqueue: - for recipient, obj in self.objqueue[self.time]: - if random.random() < self.reliability: - recipient.on_receive(obj) - del self.objqueue[self.time] - for a in self.agents: - a.tick() - self.time += 1 - - def run(self, steps): - for i in range(steps): - self.tick() - - def broadcast(self, sender, obj): - for p in self.peers[sender.id]: - recv_time = self.time + self.latency_distribution_sample() - if recv_time not in self.objqueue: - self.objqueue[recv_time] = [] - self.objqueue[recv_time].append((p, obj)) - - def direct_send(self, to_id, obj): - for a in self.agents: - if a.id == to_id: - recv_time = self.time + self.latency_distribution_sample() - if recv_time not in self.objqueue: - self.objqueue[recv_time] = [] - self.objqueue[recv_time].append((a, obj)) - - def knock_offline_random(self, n): - ko = {} - while len(ko) < n: - c = random.choice(self.agents) - ko[c.id] = c - for c in ko.values(): - self.peers[c.id] = [] - for a in self.agents: - self.peers[a.id] = [x for x in self.peers[a.id] if x.id not in ko] - - def partition(self): - a = {} - while len(a) < len(self.agents) / 2: - c = random.choice(self.agents) - a[c.id] = c - for c in self.agents: - if c.id in a: - self.peers[c.id] = [x for x in self.peers[c.id] if x.id in a] - else: - self.peers[c.id] = [x for x in self.peers[c.id] if x.id not in a] diff --git a/old_consensus_by_bet/run.py b/old_consensus_by_bet/run.py deleted file mode 100644 index 37906f7..0000000 --- a/old_consensus_by_bet/run.py +++ /dev/null @@ -1,5 +0,0 @@ -import casper -import sys - -casper.logging_level = int(sys.argv[1]) if len(sys.argv) > 1 else 0 -casper.run(50000) diff --git a/old_consensus_by_bet/voting_strategy.py b/old_consensus_by_bet/voting_strategy.py deleted file mode 100644 index ba8be3b..0000000 --- a/old_consensus_by_bet/voting_strategy.py +++ /dev/null @@ -1,31 +0,0 @@ -import random - -# The voting strategy. Validators see what every other validator votes, -# and return their vote. -# -# Votes are log odds, ie. ln(p / (1-p)) -# -# Remember, 0 and 1 are not probabilities! -# http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ !) - -def default_vote(scheduled_time, received_time, now, **kwargs): - if received_time is None: - time_delta = now - scheduled_time - my_opinion_prob = 1 if time_delta < kwargs["blktime"] * 4 else 4.0 / (4 + time_delta * 1.0 / kwargs["blktime"]) - return 0 if random.random() < my_opinion_prob else -1 - else: - time_delta = received_time * 0.9 + now * 0.1 - scheduled_time - my_opinion_prob = 1 if abs(time_delta) < kwargs["blktime"] * 4 else 4.0 / (4 + abs(time_delta) * 1.0 / kwargs["blktime"]) - return 1 if random.random() < my_opinion_prob else -1 - - -def vote(probs): - if len(probs) == 0: - return 0 - probs = sorted(probs) - if probs[len(probs)/3] >= 1: - return probs[len(probs)/3] + 1 - elif probs[len(probs)*2/3] <= -1: - return probs[len(probs)*2/3] - 1 - else: - return probs[len(probs)/2] diff --git a/papers/CasperTFG/CasperTFG.pdf b/papers/CasperTFG/CasperTFG.pdf deleted file mode 100644 index 05b41bb355b3ee3189d619414864357ea970704d..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 715385 zcma&NQ+p=+%}HaoU$+fF*RZQI`SoW1Ynx>$8lPyK@$?-*5- zN@5a>tV|qml(UP&t8kp$BrGI$MwW1Vd~nQirnctJ79?!kESx0&f59K|k7F(@L|hg~=-PkAXAZ0QK!dJD=E(CU7$dN|*L(3C%YFnt zmd)sDtCfO58%CWqYJc!z@ZF!K-4TeW;^23Vw7z~}fv z2qUlV9P}5TM`nNL0#44)7EAvDM1Y?r-@3kYoAn^@0R+rkF- zp%AwqR_KE7xl_b2l(H${-nds2kcEBdbns7awgK`w>m$s?T4YdYB;S6lYVnP)_m3g8 zU|MrxxL_!D-gvMy(Y29A7a-nb*;BRx`mj{eb3M$t^=TD3w`HlmmOf}FRK++!UVVSb z8j^WGm#V1t>)A(iNF`SBqAc6?ymzV+{Pik8pm0aV8Ldm)T0~vd4!$O$4_26Jyp@(b<7Vbr9~cngkRR4In~2*zm?}%iI9{eoDZ;Wi zhac(j*Lo^`xEt|n<~bJkFI0T|uQ=xC?())#QH(w;R=-&I)S&2^Q;ij3iyH$v6`fA+ znoep6ner4NNgfy}KW+v{o~}|v>w3@{fJWW0aD|KKF~N4>Yl!_H(lOjaaZE?MDd0IZ zpvRGplB*DbOgN>Enx5~kCNq}I@I&Ju^($;%C!*PhncXIT>@mHJ6BSy!z`m@ExomNS 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\mathcal{E}(M) &= 1 &\text{ if } \text{Score}(1, M) > \text{Score}(0, M), \\ - \mathcal{E}(M) &= \emptyset &\text{ if } \text{Score}(1, M) = \text{Score}(0, M) -\end{align} -\end{defn} - -At this stage we have protocol messages and an estimator. If we can define a method for counting Byzantine faults from a set of protocol messages, then we can give the set of protocol states with their state transitions for a binary consensus protocol that tolerates $t$ Byzantine faults. - -Each protocol message $m$ is supposed to represent a record of messages that were seen by validator $V(m)$. Any ``correct'' node has a growing record of messages that they have received and sent. Specifically, a correct node is never the sender of a pair of messages $m_1$ and $m_2$ such that neither $m_1 \prec m_2$ nor $m_1 \succ m_2$. We call such a pair of messages ``an equivocation''. - - -\begin{defn}[Equivocation] -\begin{align} -Eq(m_1, m_2) \iff V(m_1) = V(m_2) \text{ and } m_1 \nsucc m_2 \text{ and } m_1 \nprec m_2 -\end{align} -\end{defn} - -A sender $v$ with an equivocation in a set of protocol messages $M$, is said to be ``Byzantine'', or to have exhibited a ``Byzantine fault'' in $M$. - -\begin{defn}[Byzantine faulty node] -\begin{align} -B(v,M) \iff \exists m_1, m_2 \in D(M) : v = V(m_1) \land Eq(m_1, m_2) -\end{align} -\end{defn} - -We then define the Byzantine nodes visible in $M$ as - -$$ -B(M) = \{v \in \mathcal{V}: B(v,M)\} -$$ - -The weight of Byzantine faults evidenced in a set of messages $M$ is the sum of the weights of validators who are Byzantine in $M$. - -\begin{defn}[Fault weight] -\begin{align} -F(M) = \sum_{v \in B(M)} W(v) -\end{align} -\end{defn} - -We now define our protocol states $\Sigma_t \subset \mathcal{P}(\mathcal{M})$ as the sets of protocol messages that exhibit less than $t$ faults, by weight: - -\begin{defn}[Protocol States] -\begin{align} -\Sigma_t = \left\{\sigma \subseteq \mathcal{M}: F(\sigma) \leq t \right\} -\end{align} -\end{defn} - -And we also define ``protocol executions'' as directed paths between states in $\Sigma_t$ such that an execution from $\sigma \in \Sigma_t$ to $\sigma' \in \Sigma_t$ exists if and only if $\sigma \subseteq \sigma'$. We write the existence of such a state transition as $\sigma \to \sigma'$. - -\begin{defn}[Protocol Executions] -\begin{align} -\forall \sigma, \sigma' \in \Sigma_t \hspace{3mm} : \sigma \to \sigma' \iff \sigma \subseteq \sigma' -\end{align} -\end{defn} - -Protocol executions compose ($\sigma \to \sigma' \land \sigma' \to \sigma'' \implies \sigma \to \sigma''$) because the improper subset relation ($\subseteq$) composes. - -We can now give the definition of estimate safety for the Binary Consensus, for an estimate $e$ in a protocol state $\sigma$. - -\begin{defn}[Binary Estimate Safety] -$$ -S_t(e, \sigma) \iff \forall \sigma' \in \Sigma_t: \sigma \to \sigma',\hspace{1.5mm} e = \mathcal{E}(\sigma') -$$ -\end{defn} - -Because this construction satisfies the terms of our consensus safety proof, we know that decisions on such safe estimates in this protocol are consensus safe (if there are less than $t$ Byzantine faults (by weight)). - -We have yet to discuss how nodes running the binary consensus protocol can detect when they are in a state with a safe estimate. We discuss this following the specification of the blockchain consensus protocol because we detect estimate safety in the same way for both protocols. - -Now that we've covered the binary consensus protocol, it is much simpler to specify the blockchain consensus protocol. - - -\section{Casper the Friendly Ghost} - -The specification of Casper the Friendly Ghost proceeds along \emph{very} similar lines as Casper the Friendly Binary Consensus. In fact, we are able to reuse most of our definitions without any modification. - -We again first define the set of all protocol messages and then the estimator, which this time is the Greedy Heaviest-observed Sub-tree (GHOST) ``fork choice rule''. Then, we define protocol states as sets of messages which exhibit up to $t$ Byzantine faults (by weight), and then we define the protocol's ``state transitions''. Finally, we define block estimate safety. These definitions satisfy those in the consensus safety proof for decisions on safe estimates. - -Protocol messages are called ``blocks'' and have the same three components as the messages in the binary consensus protocol; an estimate, a sender and a justification. The estimate is a block, called ``the prevblock'' or ``the parent block''. For valid messages, the estimate is the block on the head of the blockchain chosen by the GHOST fork choice rule in the justification. The ``sender'' (a validator name) field is defined precisely as before. Finally, the justification is again simply a set of protocol messages. - -Formally, in Casper the Friendly Ghost we have protocol messages, $\mathcal{M}$, with the following form (again parametric in a set of validator names, $\mathcal{V}$): - - -\begin{defn}[Blocks] -\begin{equation*} -\begin{split} - &\text{Genesis Block} = \{\emptyset\}\\ - &\mathcal{M}_0 = \{\text{Genesis Block}\} \times \mathcal{V} \times \{\text{Genesis Block}\}\\ - &\mathcal{M}_n = \bigcup_{i=0}^{n-1} \mathcal{M}_i \times \mathcal{V} \times \mathcal{P}(\bigcup_{i=0}^{n-1} \mathcal{M}_i)\\ - &\mathcal{M} = \{\text{Genesis Block}\} \cup \lim_{n \to \infty} \bigcup_{i=0}^{n} \mathcal{M}_i -\end{split} -\end{equation*} -\end{defn} - -The definitions of the ``helper functions'' ($E$, $V$, and $J$), ``dependency'', ``later'', ``latest messages'', and ``validator weights'' given in the previous section binary consensus are defined \emph{precisely} in the same way here. We therefore use them without giving the definitions again. - -We do need a couple of new terms, though, to define the fork choice rule. We write $b_1 \downarrow b_2$ and say that block $b_1$ is ``in the blockchain'' of block $b_2$, if - -\begin{defn}[Blockchain membership, $b_1 \downarrow b_2$] -\begin{align} - b_1 \downarrow b_2 &\iff b_1 = b_2 \text{ or } b_1 \downarrow E(b_2) -\end{align} -\end{defn} - -We define the ``score'' of a block $b$ given a set of protocol messages $M$ as the total weight of validators with latest blocks $b'$ such that $b \downarrow b'$. - -\begin{defn}[Score of a block] -\begin{align} -\text{Score}(b, M) = \sum_{\substack{v \in \mathcal{V} : \\ m \in L(v,M) \\ b \downarrow E(m)}} W(v) -\end{align} -\end{defn} - -The ``children'' of a block $b$ in a set of protocol messages $M$ are the blocks with $b$ as their prevblock. - -$$ -C(b,M) = \{b' \in M : E(b') = b\} -$$ - -We now have the language required to define the estimator for the blockchain consensus, the Greedy Heaviest-Observed Sub-Tree rule! -\begin{defn}[The Greedy Heaviest-Observed Sub-Tree (GHOST) fork-choice rule, $\mathcal{E}$] -\end{defn} - -\begin{algorithm}[H] - \KwData{A set of blocks, $M$} - \KwResult{The block at the head of the fork choice} - $b$ = Genesis Block - - \While{$b$ has children ($C(b,M)$ is nonempty)}{ - scores = dict() - - \For{each child of block $b$, $b' \in C(b,M)$}{ - scores[$b'$] = $\text{Score}(b', M)$ - } - \eIf{scores has a unique maximum}{ - $b$ = argmax(scores) - }{ - $b$ = the max score block with the lowest hash - } -} -\Return{b} - -\caption{The Greedy Heaviest-Observed Sub-tree Fork-choice rule, $\mathcal{E}$} -\end{algorithm} - -We assume that ``hash'' has the property that out of any set of blocks, only one has the lowest hash. Using the hashes of blocks to eliminate ``ties'' means that the estimator for the blockchain consensus never outputs an exception. Previously the binary estimator returned $\emptyset$ when $0$ and $1$ had the same score. This means that a message $m$ is valid if $E(m) = \mathcal{E}(J(m))$, and just as in the binary consensus we insist that all the blocks are valid. \footnote{Following the process described in the footnote about excluding invalid messages from the binary consensus.} - -``Equivocation'', ``Byzantine faulty'', ``fault weight'', ``protocol states'', and ``protocol executions'' are defined here in \emph{precisely} the same way as in the binary consensus. We therefore do not give the definitions again. - -We can now give the definition of estimate safety for Casper the Friendly Ghost, for a block $b$ in a protocol state $\sigma$. - -\begin{defn}[Blockchain Estimate Safety] -$$ -S_t(b, \sigma) \iff \forall \sigma' \in \Sigma_t: \sigma \to \sigma',\hspace{1.5mm} b \downarrow \mathcal{E}(\sigma') -$$ -\end{defn} - -Because this construction satisfies the terms of our consensus safety proof, we know that decisions on safe estimates in this protocol are consensus safe (if there are less than $t$ Byzantine faults (by weight)). - -We now present a mechanism that nodes can use to detect which of their estimates are safe in both the binary and the blockchain consensus. - -\section{A Simple Safety Oracle} - -Estimate safety is parametric in some protocol state $\sigma$ and is a property of all its future protocol states. The challenge with estimate safety is that there are (at least in our cases) an infinite number of possible future protocol states, yet nodes somehow need to make a determination about whether or not an estimate is safe in a finite (ideally very short) amount of time. - -Estimate safety is also parametric in a value of the estimate which is somehow invariant in the estimator $\mathcal{E}$ over these future states. We refer to the estimate whose safety is being determined as ``the candidate estimate.'' - -An ``ideal adversary'' returns an ``attack'', a future protocol state $\sigma'$ such that $\sigma \to \sigma'$, with an estimator $\mathcal{E}(\sigma')$ that ``disagrees'' with the candidate estimate if and only if such a protocol state exists in $\Sigma_t$. We might imagine that such an adversary would be strategic about which possible future states they search. An ``ideal safety oracle'' would indicate safety whenever the ideal adversary fails to find an attack. - -If we can detect \emph{only some} of the circumstances in which the ideal adversary fails to find an attack, then we can construct a safety oracle which is able to detect safety in some of the states with estimate safety. Due to efficiency considerations, the cases may be available enough for it to be useful in an implementation even though it may not be an ideal safety oracle. - -We identify such a set of circumstances. To discuss more generally, we denote ``agreement'' between estimate $e$ and estimate $e'$ as $e \equiv e'$. This corresponds to $e = e'$ in the binary consensus, and $e \downarrow e'$ in the blockchain consensus. Disagreement will be denoted with $\not\equiv$. - -We say that validator $v_i$ ``sees validator $v_j$ agreeing with estimate $e$ in a set of protocol messages $M$'' if: -\begin{itemize} -\item $v_i$ has exactly one latest message in $M$ (we are denoting this message as $L(v_i, M)$) -\item $v_j$ has exactly one latest message in the justification of $v_i$'s latest message, $J(L(v_i, M))$ (which we denote as $L(v_j, J(L(v_i, M)))$ -\item This message's estimate agrees with $e$, i.e. $E(L(v_j, J(L(v_i, M)))) \equiv e$ -\end{itemize} - -\begin{defn}[$v_i$ sees $v_j$ agreeing with $e$ in $M$] -$$ -v_i \xrightarrow[\text{$M$}]{\text{$\equiv, e$}} v_j \iff E(L(v_j, J(L(v_i, M)))) \equiv e -$$ -\end{defn} - -And we say that a validator $v_i$ ``can eventually see $v_j$ disagreeing with estimate $e$ in a set of protocol messages $M$'' if: -\begin{itemize} -\item $v_i$ has exactly one latest message in $M$, $L(v_i, M)$ -\item $v_j$ has exactly one latest message in the justification of $v_i$'s latest message, $J(L(v_i, M))$ (which we denote as $L(v_j, J(L(v_i, M))))$ -\item $v_j$ has a message $m \in M$ that is undelivered to $v_i$ : $m \succ L(v_j, J(L(v_i, M))))$ -\item And this $m$ disagrees with $e$, $E(m) \not\equiv e$ -\end{itemize} - -\begin{defn}[$v_i$ can see $v_j$ disagreeing with $e$ in $M$] -$$ -v_i \xRightarrow[\text{$M$}]{\text{$\not\equiv, e$}} v_j \iff \exists m \in M : V(m) = v_j \land m \succ L(v_j, J(L(v_i, M))) \land E(m) \not\equiv e -$$ -\end{defn} - -A set of non-Byzantine nodes in $M$ \emph{who each mutually see each other agreeing with $e$ in $M$ and also mutually can't see each other disagreeing with $e$ in $M$} are called an ``$e$-clique'' in $M$. - -Our aim is to show that if there is an $e$-clique in $M$ with total weight $W'$, and $2*W' > \sum_{v\in \mathcal{V}} W(v)$, then $e$ is safe for the protocol with states $\Sigma_t$ for $t = 0$. We won't give a rigorous proof, but the idea is simple enough. If nodes in an $e$-clique see each other agreeing on $e$ and can't see each other disagreeing on $e$, then there does not exist any new message from inside the clique that will cause them to assign lower scores to $e$. Further, if the clique has more than half of the validators by weight, then no messages external to the clique can raise the scores these validators assign to a competing estimate to be higher than the score they assign to $e$. Messages from senders who are inside or outside the clique therefore cannot change the estimates of senders inside the clique, and the ideal adversary will necessarily fail. - -We can also show that if $e$-clique in $M$ with total weight $W'$, then $e$ is safe as long as $2*W' - \sum_{v\in \mathcal{V}} W(v) > t - F(M)$, but we leave this for a future draft of this work. - -We present the pseudocode for the ``clique oracle'' that uses this result to detect estimate safety: - -\begin{algorithm}[H] - \KwData{An estimate $e$, a set of messages $M \in \Sigma_t$} - \KwResult{True or False, an indicator when $e$ is safe in $M \in \Sigma_t$} - - - - $N$ = a fully connected network with undirected edges and validator names $\mathcal{V}$ as nodes - - \For{each non-Byzantine validator, $v_i \in \mathcal{V}$}{ - \For{each non-Byzantine validator, $v_j \in \mathcal{V}$}{ - \If{$v_i$ doesn't see $v_j$ agreeing with $e$ in $M$ (not $v_i \xrightarrow[\text{$M$}]{\text{$\equiv, e$}} v_j$)}{ - $N$.remove\_edge($(v_i, v_j)$) - } - \If{$v_i$ can see $v_j$ disagreeing with $e$ in $M$ ($v_i \xRightarrow[\text{$M$}]{\text{$\not\equiv, e$}} v_j$)}{ - $N$.remove\_edge($(v_i, v_j)$) - } - } - } - - $N'$ = $N$.maximum\_weight\_fully\_connected\_subcomponent(weights=$W$) - - clique\_weight = $\sum_{v \in N'.nodes} W(v)$ - - total\_weight = $\sum_{v \in \mathcal{V}} W(v)$ - - \If{2*clique\_weight $\leq$ total\_weight}{ - \Return{False} - } - - \If{2*clique\_weight $>$ total\_weight}{ - initial\_fault\_weight = $F(M)$ (this will be $\leq t$ because $M \in \Sigma_t$) - - fault\_tolerance = 2*clique\_weight - total\_weight - - \eIf{fault\_tolerance + initial\_fault\_weight $>$ $t$} - { - \Return{True} - }{ - \Return{False} - } - } - -\caption{The ``Clique Oracle'', $S_t$} -\end{algorithm} - -Now that we have an implementable safety oracle, we can equip nodes in both Casper the Friendly Binary Consensus and in Casper the Friendly Ghost with the ability to detect estimate safety. This allows nodes to \emph{actually} rather than \emph{only hypothetically} make (consensus safe) decisions on safe estimates. - - -\section{Subjective Fault Tolerance Thresholds} - -The consensus safety proof can be adapted to discuss the consensus safety of decisions on safe estimates by nodes who are running any of these ``correct-by-construction'' consensus protocols \emph{at different levels of fault tolerance}. - -One node can execute the protocol in $\Sigma_{t_1}$ while another node can execute in $\Sigma_{t_2}$. Their decisions (which happen only on safe estimates, of course) have consensus safety as long as the union of their states exhibits less than the smallest of $t_1$ and $t_2$ faults (by weight). - -This is because the protocol states in these different protocols are identical, except for the fact that one of them also includes protocol states that exhibit even more Byzantine faults than the other. If for example $t_1 < t_2$, then $\Sigma_{t_1} \subset \Sigma_{t_2}$. This means a node at $\sigma_2 \in \Sigma_{t_2}$ shares a common future with a node at $\sigma_1 \in \Sigma_{t_1}$ as long as it is not in a state $\sigma_2$ such that $F(\sigma_1 \cup \sigma_2) > t_1$. - -Removing fault tolerance thresholds from the protocol and making them, instead, a setting that each node can configure independently has a number of attractive properties. For one, an attacker may not know the fault tolerance threshold of its targets. There are also economic benefits, but these are out of scope of this paper.\footnote{Briefly, removing in-protocol fault tolerance thresholds allows every node to marginally contribute to consensus (since more fault tolerance may allow more nodes to find safety) and therefore have a positive contribution to any cartel (and thus it would not be in the cartel's interest to censor them). It also removes focal points for cartelization.} - -\section{Casper the Friendly Ghost with Validator Rotation} - -We can define a modified version of Casper the Friendly Ghost which allows for dynamically changing sets of consensus forming nodes (and/or their weights). The protocol specification works as normal, so we are lighter on the details. - -Block structures are modified so that the justifications also include a weights map. - -\begin{defn}[Blocks] -\begin{equation*} -\begin{split} - &\text{Genesis Block} = \{\emptyset\} \times \{\emptyset\} \times (\{\emptyset\} \times \{W_{genesis}\})\\ - &\mathcal{M}_0 = \{\text{Genesis Block}\} \times \mathcal{V} \times (\{\text{Genesis Block}\} \times \mathcal{W})\\ - &\mathcal{M}_n = \bigcup_{i=0}^{n-1} \mathcal{M}_i \times \mathcal{V} \times (\mathcal{P}(\bigcup_{i=0}^{n-1} \mathcal{M}_i) \times \mathcal{W}))\\ - &\mathcal{M} = \{\text{Genesis Block}\} \cup \lim_{n \to \infty} \bigcup_{i=0}^{n} \mathcal{M}_i -\end{split} -\end{equation*} -\end{defn} - -We use $\mathcal{W}$ to represent the set of all weights mappings $W:\mathcal{V} \to \mathbb{R}_+$ - -We redefine a block's ``score'' to use the weights in the parent block. The score, remember, is used to by the GHOST fork choice rule to choose between children of some block. Those children (naturally) have the same parent, and therefore will have scores determined by the latest messages from the same validators. - -\begin{defn}[Score of a block, for Casper the Friendly Ghost with validator rotation] -\begin{align} -\text{Score}(b, M) = \sum_{\substack{v \in \mathcal{V} \\ m \in L(v,M) \\ b \downarrow E(m)}} J(E(b)).W(v) -\end{align} -\end{defn} - -Using ```$J(m).W$'' to pick out the weights from the justification of $m$. - -The rest of the definitions in the protocol remain completely identical (including the estimator, the protocol states/transitions, and the safety oracle), and therefore are not restated. We have therefore specified Casper the Friendly Ghost with validator rotation, a consensus protocol which tolerates up to $t$ Byzantine faults.\footnote{We allowed completely unrestrained changes in the validator set between any block and any of its children. This means that while we always have estimate safety unless there are $t$ or more faults for nodes running $\Sigma_t$, we have not restricted the total sum of the weights to be constant (or even greater than $t$). In practice, we either restrict the sum of the weights to be constant or redefine $t$ so that it refers to a proportion of the weight.} - - -\section{Liveness Considerations} - -Traditionally, we would like to show that the protocol ``has liveness'', i.e. that nodes running the consensus protocol \emph{eventually} decide on a value. For us, the corresponding guarantee is that nodes \emph{eventually} detect that they have a safe estimate. - -The FLP impossibility (where FLP refers to the authors of \cite{Fischer_Lynch_Paterson_FLP_Impossibility_1985}) shows that it is impossible for consensus protocols like ours (which don't use non-determinism or cryptography) to be live in an ``asynchronous network,'' which is to say, without making assumptions about the timing of message propagation (or the order of message arrival). - -We have not yet made any synchrony assumptions of any kind, which is why the consensus protocols given here are asynchronously safe. Moreover, we have not said anything about when nodes \emph{should} send protocol messages. We have instead imposed relatively loose constraints on the protocol executions that nodes can take (they can receive messages and move to any state $\sigma' \supset \sigma$ from $\sigma$, as long as $\sigma'$ does not evidence too many Byzantine faults). - -This absence of a specified strategy for how validators should make blocks means that we cannot at the moment give a liveness proof. However, we present see some experimental observations where estimate safety is accomplished in the following section. These protocol executions correspond to message arrival orders which are live, and we can therefore construct reliable strategies for achieving liveness as long as nodes can coordinate timeouts in order to (eventually) produce the desired ``shape'' of protocol messages. In a synchronous or partially synchronous network (i.e. one where there's a known or unknown bound on the message arrival time) timeout coordination is (at least eventually) possible. - -Nonetheless, liveness considerations are considered largely out of scope, and should be treated in future work. - -\pagebreak -\section{Experimental Observations} - -Early prototypes of both Casper the Friendly Binary Consensus and Casper the Friendly Ghost have been implemented, and the following graphics represent observations of executions of these protocols with various message passing orders.\footnote{The code is available at https://github.com/ethereum/cbc-casper} - -In all of these representations, each message is represented by a node in the graph. Messages from the same validator are vertically aligned. And later messages are always displayed higher than their dependencies. - -\begin{figure}[h!] -\centering -\includegraphics[width=0.5\textwidth]{3binary} -\caption{A Binary consensus protocol execution. Dotted lines are messages included in the justification of the later message. The label on the nodes represents the estimate of the message. A message is coloured if it has achieved some amount of Byzantine fault tolerant estimate safety, accoring to a clique oracle given its justification. The darker the colour, the more faults are tolerated by the estimate.} -\end{figure} - - -\begin{figure}[h!] -\centering -\includegraphics[width=0.5\textwidth]{3nodeblockchain-fix} -\caption{Blockchain protocol execution with 3 validators, $v_0, v_1, v_2$. Each node labeled $0$ is the first message from that validator, and the nodes vertically aligned above each validator represent messages made by that validator. Dotted black lines are messages included in the justification of the later message. Blue lines represent the forkchoices of the validators given by their latest blocks. Solid grey lines are prevblock pointers (that aren't blue because they are no longer the validator's forkchoice). The red line is the result of applying GHOST to the set of messages displayed here.} -\end{figure} - - -\begin{figure}[h!] -\centering -\includegraphics[width=0.5\textwidth]{blockchainsafety} -\caption{In this execution of the blockchain consensus protocol, we observe some safe blocks. They are colour coded the same way as in the earlier, however this time they represent the blocks that are seen to be safe from the view that includes all of the nodes. In contrast, in the binary consensus we displayed safety that was detected locally.} -\end{figure} - - -\begin{figure}[h!] -\centering -\includegraphics[width=0.5\textwidth]{roundrobin} -\caption{Finally, in this execution of the blockchain consensus protocol where the validators are able to pass blocks around in a ``round-robin'' configuration, we observe the $\mathcal{O}(1)$ messages received per (finalized) block. This is possible because each block contributes to the consensus safety of many blocks.} -\end{figure} - -\section{Conclusion} - -We gave a brief overview of the consensus safety proof that Casper the Friendly Ghost has been derived to satisfy (in a ``correct-by-construction'' manner). Then we defined a binary consensus protocol (Casper the Friendly Binary Consensus) that satisfies the terms of the proof and therefore benefits from the results. We then remarkably slightly modified the binary consensus protocol to give the blockchain based consensus protocol (which can be adopted for, or even termed as sequential state machine replication). - -Then we further witnessed the power of the safety proof when we showed that we can remove the fault tolerance threshold from the protocol and implement validator rotation without making significant changes to the protocol. Finally, we saw (as advertised) that it is possible for Casper the Friendly Ghost to decide on blocks with consensus safety that tolerates $t$ Byzantine faults (in an asynchronous network) with $\mathcal{O}(1)$ messages per block. - -We hope this work has been educational and will lead to the development of many interesting and useful consensus protocols. - -\section{Acknowledgements} - -I would like to thank Nate Rush and Danny Ryan for their hard work on getting the codebase ready for release at Devcon3, for their help on this (draft) paper. Thanks to Karl Floersch, who was the first developer to work on the codebase. I'd like to thank Greg Meredith for an introduction to the ``correct-by-construction'' approach to protocol design, as well as for helping formalize a lot of the ideas. Finally, I'd like to thank Vitalik Buterin, with whom I have collaborated on this research from its very early stages over three years ago. - -\bibliographystyle{naturemag} -\bibliography{ethereum} - -\end{document} diff --git a/papers/CasperTFG/eth_header.tex b/papers/CasperTFG/eth_header.tex deleted file mode 100644 index 4b1e122..0000000 --- a/papers/CasperTFG/eth_header.tex +++ /dev/null @@ -1,144 +0,0 @@ -% make in the latest NIPS format (as of this writing, 2017) - -\usepackage[nonatbib,final]{nips_2017} -%\usepackage[nonatbib,final]{nips_2017} - -\usepackage{color} -\usepackage{graphicx} -\DeclareGraphicsExtensions{.pdf,.eps,.png,.jpg} % search for .pdf, then .eps, then .pngs, then .jpg - -% look in these subdirectories for graphics referenced by \includegraphics -% each entry must end with a / -\graphicspath{{figs/}{figures/}{images/}{./}} - -\newcommand*{\red}[1]{ \color{red} #1} - -%\usepackage{tabularx} -\usepackage{url} -\usepackage{amsmath} - -% this is for environments \subfigure and \subtable -\usepackage{subcaption} - -% These packages are FORBIDDEN -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\usepackage{lmodern} % messes up \textsc -%\usepackage{cite} % messes up NIPS -%\usepackage{fullpage} % messes up NIPS -%\usepackage{natbib} % messes up NIPS -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\usepackage{array} % replacement for eqnarray. 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Then in text you only type \figref{myfig} and LaTeX -% will do the rest. -\newcommand{\tblref}[1]{Table~\ref{#1}} -%\renewcommand*{\figref}[1]{Fig.~\ref{#1}} -\renewcommand{\eqref}[1]{eq.~(\ref{#1})} -\newcommand{\Subref}[1]{(\subref{#1})} - - -\newcommand{\figref}[1]{Figure~\ref{#1}} -\newcommand{\Figref}[1]{Figure~\ref{#1}} -\newtheorem{theorem}{Theorem} -\newtheorem{lemma}[theorem]{Lemma} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% for \sout{} for strikeout -% \usepackage[normalem]{ulem} - - -% for better manipulation of tables -\usepackage{makecell} -\renewcommand\theadfont{\bfseries} - - -%----------------------------------------------------------------------------- -% Misc symbols that I like -%----------------------------------------------------------------------------- -\newcommand*{\opname}[1]{\operatorname{#1}} - - -\renewcommand*{\to}{\rightarrow} - - -%%%% - - diff --git a/papers/CasperTFG/ethereum.bib b/papers/CasperTFG/ethereum.bib deleted file mode 100644 index ac866fd..0000000 --- a/papers/CasperTFG/ethereum.bib +++ /dev/null @@ -1,637 +0,0 @@ -@misc{orphanBitcoin, - title = {{Orphan Blocks}}, - url = "https://bitcoin.org/en/developer-guide#orphan-blocks", - year = "2017", - month = "September", -} - -@inproceedings{Castro_Liskov_1999_pbft, - title = {{Practical Byzantine Fault Tolerance}}, - author = {{Miguel Castro and Barbara Liskov}}, - url = "http://pmg.lcs.mit.edu/papers/osdi99.pdf", - year = "1999", - month = "February", - booktitle = {{Proceedings of the Third Symposium on Operating Systems Design and Implementation}}, - address = "New Orleans, USA", -} - -@article{Fischer_Lynch_Paterson_FLP_Impossibility_1985, - title = {{Impossibility of Distributed Consensus with One Faulty Process}}, - author = "Michael J. 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automatically; this can be suppressed with the -% [nonatbib] package option -% - adds foot line to first page identifying the conference -% -% Roman Garnett (garnett@wustl.edu) and the many authors of -% nips15submit_e.sty, including MK and drstrip@sandia -% -% last revision: March 2017 - -\NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{nips_2017}[2017/03/20 NIPS 2017 submission/camera-ready style file] - -% declare final option, which creates camera-ready copy -\newif\if@nipsfinal\@nipsfinalfalse -\DeclareOption{final}{ - \@nipsfinaltrue -} - -% declare nonatbib option, which does not load natbib in case of -% package clash (users can pass options to natbib via -% \PassOptionsToPackage) -\newif\if@natbib\@natbibtrue -\DeclareOption{nonatbib}{ - \@natbibfalse -} - -\ProcessOptions\relax - -% fonts -\renewcommand{\rmdefault}{ptm} -\renewcommand{\sfdefault}{phv} - -% change this every year for notice string at bottom -\newcommand{\@nipsordinal}{31st} -\newcommand{\@nipsyear}{2017} -\newcommand{\@nipslocation}{Long Beach, CA, USA} - -% handle tweaks for camera-ready copy vs. submission copy -\if@nipsfinal - \newcommand{\@noticestring}{% - \@nipsordinal\/ Conference on Neural Information Processing Systems - (NIPS \@nipsyear), \@nipslocation.% - } -\else - \newcommand{\@noticestring}{% - Submitted to \@nipsordinal\/ Conference on Neural Information - Processing Systems (NIPS \@nipsyear). 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Repurposing BFT algorithms for proof of stake was first introduced by Tendermint\cite{kwon2014tendermint}, and has modern inspirations such as \cite{algorand}. Casper follows this BFT tradition, though with some modifications. - -\subsection{Our Work} -Casper the Friendly Finality Gadget is an overlay atop a \emph{proposal mechanism}---a mechanism which proposes blocks\footnote{This functionality serves a similar role to the common abstraction of ``leader election'' used in traditional BFT algorithms, but is adapted to accomodate Casper's construction of being a finality overlay atop an existing blockchain.}. Casper is responsible for finalizing these blocks, essentially selecting a -unique chain which represents the canonical transactions of the ledger. Casper provides safety, but liveness depends on the chosen proposal mechanism. That is, if attackers wholly control the proposal mechanism, Casper protects against finalizing two conflicting checkpoints, but the attackers could prevent Casper from finalizing any future checkpoints. - -Casper introduces several new features that BFT algorithms do not necessarily support: -\begin{itemize} -\item \textbf{Accountability}. If a validator violates a rule, we can detect the violation and know which validator violated the rule. Accountability allows us to penalize malfeasant validators, solving the ``nothing at stake'' problem that plagues chain-based PoS. The penalty for violating a rule is a validator's entire deposit. This maximal penalty is the defense against violating the protocol. Because proof of stake security is based on the size of the penalty, which can be set to greatly exceed the gains from the mining reward, proof of stake provides strictly stronger security incentives than proof of work. - -\item \textbf{Dynamic validators}. We introduce a safe way for the validator set to change over time (Section \ref{sect:join_and_leave}). - -\item \textbf{Defenses}. We introduce defenses against long range revision attacks as well as attacks where more than $\frac{1}{3}$ of validators drop offline, at the cost of a very weak tradeoff synchronicity assumption (Section \ref{sect:attacks}). - -\item \textbf{Modular overlay}. Casper's design as an overlay makes it easier to implement as an upgrade to an existing proof of work chain. -\end{itemize} - -We describe Casper in stages, starting with a simple version (Section \ref{sect:protocol}) and then progressively adding validator set changes (Section \ref{sect:join_and_leave}) and finally defenses against attacks (Section \ref{sect:attacks}). - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\section{The Casper Protocol} -\label{sect:protocol} - -Within Ethereum, the proposal mechanism will initially be the existing proof of work chain, making the first version of Casper a hybrid PoW/PoS system. In future versions the PoW proposal mechanism will be replaced with something more efficient. For example, we can imagine converting the block proposal into a some kind of PoS round-robin block signing scheme. - - - -In this simple version of Casper, we assume there is a fixed set of validators and a proposal mechanism (e.g., the familiar proof of work proposal mechanism) which produces child blocks of existing blocks, forming an ever-growing \emph{block tree}. From \cite{nakamoto} the root of the tree is typically called the ``genesis block''. - -%Note that for an individual block, there will often be multiple blocks added as new children by this mechanism, so the block tree will have many branches. - - -Under normal circumstances, we expect that the proposal mechanism will typically propose blocks one after the other in a linked list (i.e., each ``parent'' block having exactly one ``child'' block). But in the case of network latency or deliberate attacks, the proposal mechanism will inevitably occassionally produce multiple children of the same parent. Casper's job is to choose a single child from each parent, thus choosing one canonical chain from the block tree. - - -Rather than deal with the full block tree, for efficiency purposes\footnote{A long distance between checkpoints reduces the overhead of the algorithm, but also increases the time it takes to come to consensus. We choose a spacing of 100 blocks between checkpoints as a middle ground.} Casper only considers the subtree of \emph{checkpoints} forming the \emph{checkpoint tree} (\figref{fig:2a}). The genesis block is a checkpoint, and every block whose height in the block tree (or “block number”) is an exact multiple of 100 is also a checkpoint. The ``checkpoint height'' of a block with block height $100 * k$ is simply $k$; equivalently, the height $\h(c)$ of a checkpoint $c$ is the number of elements in the checkpoint chain stretching from $c$ all the way back to root along the parent links (\figref{fig:2b}).\footnote{Specifically, the height of a checkpoint is \emph{not} the same as the number of ancestors in the checkpoint tree all the way back to root along the supermajority links (defined in the next section).} - - -\begin{figure}[htb] -\centering - \begin{subfigure}[b]{0.90\textwidth} - \centering - \includegraphics[width=2.8in]{checkpoints_checkpoints.pdf} - \caption{The checkpoint tree. The dashed line represents 100 blocks between the checkpoints, which are represented by rounded rectangles. The root of the tree is denoted ``r''.} - \label{fig:2a} - \end{subfigure} - \vspace{0.2in} - -\begin{subfigure}[b]{0.45\textwidth} - \centering - \includegraphics[height=2.8in]{checkpoints_lengths.pdf} - \caption{The height function} - \label{fig:2b} - \end{subfigure} \hspace{0.05\textwidth} \begin{subfigure}[b]{0.45\textwidth} - \centering - \includegraphics[height=2.8in]{checkpoints_justifiedchain.pdf} -% \caption{The justified chain $(r, b_1, b_2, b_3)$} - \caption{The justified chain $r \to b_1 \to b_2 \to b_3$} - \label{fig:2c} - \end{subfigure} - -\caption{Illustrating a checkpoint tree, the height function, and a justified chain within the checkpoint tree.} -\label{fig:conflicting_checkpoints} -\end{figure} - - - -Each validator has a \emph{deposit}; when a validator joins, its deposit is the number of deposited coins. After joining, each validator's deposit rises and falls with rewards and penalties. Proof of stake's security derives from the size of the deposits, not the number of validators, so for the rest of this paper, when we say ``$\frac{2}{3}$ of validators'', we are referring to the \emph{deposit-weighted} fraction; that is, a set of validators whose sum deposit size equals to $\frac{2}{3}$ of the total deposit size of the entire set of validators. - -Validators can broadcast a \textit{vote} message containing four pieces of information (Table \ref{tbl:messages}): two checkpoints $s$ and $t$ together with their heights $\h(s)$ and $\h(t)$. We require that $s$ be an ancestor of $t$ in the checkpoint tree, otherwise the vote is considered invalid. If the public key of the validator $\upnu$ is not in the validator set, the vote is considered invalid. Together with the signature of the validator, we will write these votes in the form $\left\langle \upnu, s, t, \h(s), \h(t) \right\rangle$. - - -\begin{table}[bth] -\centering - - \begin{tabular}{l l} - \toprule - \textbf{Notation} & \textbf{Description} \\ - \midrule - $s$ & the hash of any justified checkpoint (the ``source'') \\ - $t$ & any checkpoint hash that is a descendent of $s$ (the ``target'') \\ - $\h(s)$ & the height of checkpoint $s$ in the checkpoint tree \\ - $\h(t)$ & the height of checkpoint $t$ in the checkpoint tree \\ - \signature & signature of $\left\langle s, t, \h(s), \h(t) \right\rangle$ from the validator $\upnu$'s private key \\ - \bottomrule - \end{tabular} - - -\vspace{0.15in} -\caption{The schematic of a single \msgVOTE message denoted $\left\langle \upnu, s, t, \h(s), \h(t) \right\rangle$.} -\label{tbl:messages} -\end{table} - - - -We define the following terms: -\begin{itemize} -\item A \emph{supermajority link} is an ordered pair of checkpoints $(a, b)$, also written $a \rightarrow b$, such that at least $\frac{2}{3}$ of validators (by deposit) have published votes with source $a$ and target $b$. Supermajority links \emph{can skip checkpoints}, i.e., it's perfectly okay for $\h(b) > \h(a) + 1$. \figref{fig:2c} shows three distinct supermajority links in red: $r \to b_1$, $b_1 \to b_2$, and $b_2 \to b_3$. - -\item Two checkpoints $a$ and $b$ are called \emph{conflicting} if and only if they are nodes in distinct branches, i.e., neither is an ancestor or descendant of the other. - -\item A checkpoint $c$ is called \emph{justified} if (1) it is the root, or (2) there exists a supermajority link $c^\prime \to c$ where $c^\prime$ is justified. \figref{fig:2c} shows a chain of four justified blocks. - -\item A checkpoint $c$ is called \emph{finalized} if it is justified and there is a supermajority link $c \to c^\prime$ where $c^\prime$ is a \emph{direct child} of $c$. Equivalently, checkpoint $c$ is finalized if and only if: checkpoint $c$ is justified, there exists a supermajority link $c \to c^\prime$, checkpoints $c$ and $c^\prime$ are not conflicting, and $\h(c^\prime) = \h(c) + 1$. -\end{itemize} - - - -The most notable property of Casper is that it is impossible for two conflicting checkpoints to be finalized without $\geq \frac{1}{3}$ of the validators violating one of the two\footnote{Earlier versions of Casper had two types of messages and four slashing conditions\cite{minslashing}, but we have reduced this to one message type and two slashing conditions. We removed the conditions: (i) Committed hashes must already be justified, and (ii) prepare messages must point to an already justified ancestor. This is a design choice. We made this choice so that slashing violations are independent of the state of the chain.} Casper Commandments/slashing conditions (\figref{fig:commandments}). - - - -%\clearpage - -\begin{figure} -\begin{mdframed} -\textsc{An individual validator $\upnu$ must not publish two distinct votes,} -\begin{equation*} -\left\langle \upnu, s_1, t_1, \h(s_1), \h(t_1)\right\rangle \hspace{0.5in} \textsc{and} \hspace{0.5in} \left\langle \upnu, s_2, t_2, \h(s_2), \h(t_2)\right\rangle \; , -\end{equation*} -\textsc{such that either:} - -\begin{enumerate} - \item[\textbf{I.}] $\h(t_1) = \h(t_2)$. - - Equivalently, a validator must not publish two distinct votes for the same target height. -\end{enumerate} -\vspace{-0.15in} -\textsc{or} - -\begin{enumerate} - \item[\textbf{II.}] $\h(s_1) < \h(s_2) < \h(t_2) < \h(t_1)$. - - Equivalently, a validator must not vote within the span of its other votes. -\end{enumerate} -\end{mdframed} -\caption{The two Casper Commandments. Any validator who violates either of these commandments gets their deposit slashed.} -\label{fig:commandments} -\end{figure} - - -If a validator violates either slashing condition, the evidence of the violation can be included into the blockchain as a transaction, at which point the validator's entire deposit is taken away with a small ``finder's fee'' given to the submitter of the evidence transaction. In current Ethereum, stopping the enforcement of a slashing condition requires a successful $51\%$ attack on Ethereum's proof-of-work block proposer. - - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Proving Safety and Plausible Liveness} -\label{sect:theorems} - -We prove Casper's two fundamental properties: \textit{accountable safety} and \textit{plausible liveness}. Accountable safety means that two conflicting checkpoints cannot both be finalized unless $\geq \frac{1}{3}$ of validators violate a slashing condition (meaning at least one third of the total deposit is lost). Plausible liveness means that, regardless of any previous events (e.g., slashing events, delayed blocks, censorship attacks, etc.), if $\geq \frac{2}{3}$ of validators follow the protocol, then it's always possible to finalize a new checkpoint without any validator violating a slashing condition. - -\emph{Under the assumption that $\frac{2}{3}$ of the validators by weight do not violate a slashing condition}, we have the following properties: - -\begin{enumerate} - \item[(i)] If $s_1 \rightarrow t_1$ and $s_2 \rightarrow t_2$ are distinct supermajority links, then $\h(t_1) \not= \h(t_2)$. - \item[(ii)] If $s_1 \rightarrow t_1$ and $s_2 \rightarrow t_2$ are distinct supermajority links, then the inequality $\h(s_1)~<~\h(s_2)~<~\h(t_2)~<~\h(t_1)$ cannot hold. -\end{enumerate} - -From these two properties, we can immediately see that, for any height $n$: -\begin{enumerate} -\item[(iii)] there exists at most one supermajority link $s \to t$ with $\h(t) = n$. -\item[(iv)] there exists at most one justified checkpoint with height $n$. -\end{enumerate} - -With these four properties in hand, we move to the main theorems. - -\begin{theorem}[Accountable Safety] -\label{theorem:safety} -Two conflicting checkpoints $a_m$ and $b_n$ cannot both be finalized. -\begin{proof} -Let $a_m$ (with justified direct child $a_{m+1}$) and $b_n$ (with justified direct child $b_{n+1}$) be distinct finalized checkpoints as in \figref{fig:proof1}. Now suppose $a_m$ and $b_n$ conflict, and without loss of generality $\h(a_m) < \h(b_n)$ (if $\h(a_m) = \h(b_n)$, then it is clear that $\frac{1}{3}$ of validators violated condition \textbf{I}). Let $r \rightarrow b_1 \rightarrow b_2 \rightarrow \cdots \rightarrow b_n$ be a chain of checkpoints, such that there exists a supermajority link $r \to b_1$, $\ldots$, $b_i \to b_{i+1}, \ldots, b_{n} \to b_{n+1}$. We know that no $\h(b_i)$ equals either $\h(a_m)$ or $\h(a_{m+1})$, because that violates property (iv). Let $j$ be the lowest integer such that $\h(b_j) > \h(a_{m+1})$; then $\h(b_{j-1}) < \h(a_m)$. However, this implies the existence of a supermajority link from a checkpoint with an epoch number less than $\h(a_m)$ to a checkpoint with an epoch number greater than $\h(a_{m+1})$, which is incompatible with the supermajority link from $a_m$ to $a_{m+1}$. -\end{proof} -\end{theorem} -% $(r, b_1, b_2, \ldots, b_n)$ - -\begin{theorem}[Plausible Liveness] -\label{theorem:liveness} -Supermajority links can always be added to produce new finalized checkpoints, provided there exist children extending the finalized chain. -\begin{proof} -Let $a$ be the justified checkpoint with the greatest height, and $b$ be the target checkpoint with the greatest height for which any validator has made a vote. Any checkpoint $a^\prime$ which is a descendant of $a$ with height $\h(a^\prime) = \h(b) + 1$ can be justified without violating either commandments \textbf{I} or \textbf{II}, and then $a^\prime$ can be finalized by adding a supermajority link from $a^\prime$ to a direct child of $a^\prime$, also without violating either \textbf{I} or \textbf{II}. -\end{proof} - - -\end{theorem} - - -\begin{figure}[h!tb] -\centering - \includegraphics[width=4in]{checkpoints_proof1.pdf} -\caption{Figure for Theorem \ref{theorem:safety} (Accountable Safety).} -\label{fig:proof1} -\end{figure} - - - -\subsection{Casper's Fork Choice Rule} -\label{sect:forkchoice} - -Casper is more complicated than standard PoW designs. As such, the fork-choice must be adjusted. Our modified fork-choice rule should be followed by all users, validators, and even the underlying block proposal mechanism. If the users, validators, or block-proposers instead follow the standard PoW fork-choice rule of ``always build atop the longest chain'', there are pathological scenarios where Casper gets ``stuck'' and any blocks built atop the longest chain cannot be finalized (or even justified) without some validators altruistically sacrificing their deposit. To avoid this, we introduce a novel, correct by construction, fork choice rule: \textsc{Follow the chain containing the justified checkpoint of the greatest height}. This fork choice rule is correct by construction because it follows from the plausible liveness proof (Theorem \ref{theorem:liveness}), which precisely states that it's always possible to finalize a new checkpoint on top of the justified checkpoint with the greatest height. This fork choice rule will be tweaked in Sections \ref{sect:join_and_leave} and \ref{sect:attacks}. - -\section{Enabling Dynamic Validator Sets} -\label{sect:join_and_leave} - -The set of validators needs to be able to change. New validators must be able to join, and existing validators must be able to leave. To accomplish this, we define the \textit{dynasty} of a block. The \emph{dynasty of block $b$} is the number of finalized checkpoints in the chain from root to the parent of block $b$. When a would-be validator's \emph{deposit message} is included in a block with dynasty $d$, then the validator $\upnu$ will join the validator set at first block with dynasty $d+2$. We call $d+2$ this validator's \textit{start dynasty}, $\DS(\upnu)$. - - -To leave the validator set, a validator must send a ``withdraw'' message. If validator $\upnu$'s withdraw message is included in a block with dynasty $d$, it similarly leaves the validator set at the first block with dynasty $d+2$; we call $d+2$ the validator's \textit{end dynasty}, $\DE(\upnu)$. If a withdraw message has not yet been included, then $\DE(\upnu) = \infty$. Once validator $\upnu$ leaves the validator set, the validator's public key is forever forbidden from rejoining the validator set. This removes the need to handle multiple start/end dynasties for a single identifier. - - -At the start of the end dynasty, the validator's deposit is locked for a long period of time, called the \textit{withdrawal delay} (think ``four months' worth of blocks''), before the deposit is withdrawn. If, during the withdrawal delay, the validator violates any commandment, the deposit is slashed. - -%We define $\mathbf{V}$ as the set of all validators who have sever joined the validator set. Then, -We define two functions that generate two subsets of validators for any given dynasty $d$, the \emph{forward validator set} and the \emph{rear validator set}. They are defined as, - -\begin{align*} - \mathcal{V}_{\operatorname{f}}(d) &\equiv \left\{ \upnu : \DS(\upnu) \leq d < \DE(\upnu) \right\} \\ - \mathcal{V}_{\operatorname{r}}(d) &\equiv \left\{ \upnu : \DS(\upnu) < d \leq \DE(\upnu) \right\} \; . -\end{align*} - - -Note this means that the forward validator set of dynasty $d$ is the rear validator set of dynasty $d+1$. - -Note that in order for the chain to be able to ``know'' its own current dynasty, we need to restrict our definition of ``finalization'' slightly: -Before, a checkpoint $c$ is called \emph{finalized} if it is justified and there is a supermajority link from $c$ to any of its direct children in the checkpoint tree. Now, finalization has one additional condition---$c$ is finalized only if the votes for the supermajority link $c \rightarrow c^\prime$, as well as all of the supermajority links recursively justifying $c$, are included in the block chain before the child of $c^\prime$, i.e., before block number $\h(c^\prime) * 100$. -To support dynamic validator sets, we redefine a supermajority link and finalization as follows: -\begin{itemize} - -\item An ordered pair of checkpoints $(s, t)$, where $t$ is in dynasty $d$, has a \emph{supermajority link} if both at least $\frac{2}{3}$ of the forward validator set of dynasty $d$ have published votes $s \rightarrow t$ and at least $\frac{2}{3}$ of the rear validator set of dynasty $d$ have published votes $s \rightarrow t$. - -\item A checkpoint $c$ is called currently \emph{finalized} if $c$ is justified and there is a supermajority link from $c \to c^\prime$ where $c^\prime$ is a child of $c$. We add the condition that $c$ is finalized only if the votes for the supermajority link $c \rightarrow c^\prime$, as well as the supermajority link justifying $c$, are included in $c^\prime$'s block chain and before the child of $c^\prime$---i.e., before block number $\h(c^\prime) * 100$. -\end{itemize} - - - -The forward and rear validator sets will usually greatly overlap; but if the two validator sets substantially differ, this ``stitching'' mechanism prevents safety failure in the case when two grandchildren of a finalized checkpoint have different dynasties because the evidence was included in one chain but not the other. For an example of this, see \figref{fig:DYN}. - -\begin{figure}[htb] -\centering -\includegraphics[height=3in]{dynamic_validator_sets.pdf} -\caption{\textbf{Attack from dynamic validator sets}. Without the validator set stitching mechanism, it's possible for two conflicting checkpoints $c$ and $c^\prime$ to both be finalized without any validator getting slashed. In this case $c$ and $c^\prime$ are the same height thus violating commandment \textbf{I}, but because the validator sets finalizing $c$ and $c^\prime$ are disjoint, no one gets slashed.} -\label{fig:DYN} -\end{figure} - - -\section{Stopping attacks} -\label{sect:attacks} -There are two well-known attacks against proof-of-stake systems: \emph{long range revisions} and \emph{catastrophic crashes}. We discuss each in turn. - -\subsection{Long Range Revisions} -The withdrawal delay after a validator's end dynasty introduces a synchronicity assumption between validators and clients. Once a coalition of validators has withdrawn their deposits, if that coalition had more than $\frac{2}{3}$ of deposits \emph{long ago in the past}, they can use their historical supermajority to finalize conflicting checkpoints without fear of getting slashed (because they have already withdrawn their money). This is called the \emph{long-range revision attack}, see in \figref{fig:longrange}. - -In simple terms, long-range attacks are prevented by a fork choice rule to never revert a finalized block, as well as an expectation that each client will ``log on'' and gain a complete up-to-date view of the chain at some regular frequency (e.g., once per 1--2 months). A ``long range revision'' fork that finalizes blocks older than that will simply be ignored, because all clients will have already seen a finalized block at that height and will refuse to revert it. - - - -We make an informal proof of the mechanism as follows. Suppose that: - -\begin{itemize} - -\item There is a maximum communication delay $\delta$ between two clients, so if one client hears some message at time $t$, all other clients are guaranteed to have heard it by time $t + \delta$. This means that we can talk about the ``time window'' $[t_{\min}, t_{\max}]$ during which a block was received by the network, with width $t_{\max} - t_{\min}$ at most $\delta$. -\item We assume all clients have local clocks are perfectly synchronized (any discrepancy can be treated as being part of the communication delay $\delta$). -\item Blocks are required to have timestamps. If a client has local time $T_L$, then it will reject blocks whose timestamp $T_B$ satisfies $T_B > T_L$ (i.e., in the future), and they will refuse to accept as finalized (but may still accept as part of the chain) blocks where $T_B < T_L - \delta$ (i.e., too far in the past) -\item If a validator sees a slashing violation at time $t$ (that's the time they hear the \emph{later} of the two votes), then they reject blocks with timestamps $> t + 2\delta$ that are part of chains that have not yet included this slashing evidence. -\end{itemize} - -Suppose that a large set of slashing violations results in two conflicting finalized checkpoints, $c_1$ and $c_2$. If the two time windows do not intersect, then all validators agree which checkpoint came first and everyone follows the rule to not revert finalized checkpoints then there is no issue. - -If the two time windows \emph{do} intersect, then we can handle the case as follows. Let $c_1$'s time window be $[0, \delta]$ and $c_2$'s time window be $[\delta - \epsilon, 2\delta - \epsilon]$. Then the timestamps of both are at least $0$. By time $2\delta$ it is guaranteed that all clients have seen the slashing violation, so they reject blocks with timestamp $> 4\delta$ whose chains that have not yet included the evidence transaction. Hence, as long as $\omega > 4\delta$, it's guaranteed that malfeasant validators will lose their deposits in all chains that any client accepts, where $\omega$ is the ``withdraw delay'' (\figref{fig:longrange}), the delay between the end-epoch and when validators actually receive their deposits back. - -Due to network delays, it's possible that clients will disagree whether a given piece of slashing evidence was submitted into a given chain ``on time'' or as having accepted it too late. However, this is only a liveness failure, not a safety failure, and this possibility does not weaken our security claims because it is already known that a corrupted proposal mechanism (which would be required to prevent evidence inclusion) can prevent finality. - -We can also sidestep the issue of evidence inclusion timeouts by informally arguing that attacks will be short-lived, because the validators will perceive a long-running chain without including slashing evidence as an attack and switch to another branch supported by an honest minority of validators that are not part of the attack (see Section \ref{sect:leak}) thus stopping the attack and slashing the attacker. - -\begin{figure}[tb] -\centering -\includegraphics[width=3in]{longrange.pdf} -\caption{\textbf{The long range attack}. As long as a client gains complete knowledge of the justified chain at a regular interval, it will not be susceptible to a long range attack.} -\label{fig:longrange} -\end{figure} - - - -\subsection{Castastrophic Crashes} -\label{sect:leak} - -Suppose that $>\frac{1}{3}$ of validators crash-fail at the same time---i.e., they are no longer connected to the network due to a network partition, computer failure, or the validators themselves are malicious. Intuitively, from this point on, no supermajority links can be created, and thus no future checkpoints can be finalized. - -We can recover from this by instituting an ``inactivity leak'' which slowly drains the deposit of any validator that does not vote for checkpoints, until eventually its deposit sizes decrease low enough that the validators who \emph{are} voting are a supermajority. The simplest formula is something like ``in every epoch a validator with deposit size $D$ fails to vote, it loses $D * p$ (for $0 < p < 1$)'', though to resolve catastrophic crashes more quickly a formula which increases the leak rate in the event of a long streak of non-finalized blocks may be optimal. - -This drained ether can be burned or returned to the validator after $\omega$ days. Whether leaked assets should be burned or returned as well as the exact formula for the inactivity leak is outside the scope of this paper as these are questions of economic incentives, not Byzantine-fault-tolerance. - -The inactivity leak introduces the possibility of two conflicting checkpoints being finalized without any validator getting slashed (as in Figure \ref{fig:bigcrash}), with validators only losing money on only one of the two checkpoints. Assume the validators are split into two subsets, with subset $\mathbf{V}_A$ voting on chain $A$ and subset $\mathbf{V}_B$ voting on chain $B$. On chain $A$, $\mathbf{V}_B$'s deposits will leak, and vice versa, leading to each subset having a supermajority on its respective chain, allowing two conflicting checkpoints to be finalized without any validators being explicitly slashed (but each subset will lose a large portion of their deposit on one of the two chains due to leaks). If this situation happens, then each validator should simply favor whatever finalized checkpoint it saw first. - -The exact algorithm for recovering from these various attacks remains an open problem. For now, we assume validators can detect obviously malfeasant behavior (e.g., not including evidence) and manually create a ``minority soft fork''. This minority fork can be viewed as a blockchain in its own right that competes with the majority chain in the market, and if the majority chain truly is operated by colluding malicious attackers then we can assume that the market will favor the minority fork. - -\begin{figure}[htb] -\centering -\includegraphics[width=3in]{bigcrash.pdf} -\caption{\textbf{Inactivity leak}. The checkpoint on the left can be finalized immediately. The checkpoint on the right can be finalized after some time, once offline validator deposits sufficiently deplete.} -\label{fig:bigcrash} -\end{figure} - - -\section{Conclusions} -We presented Casper, a novel proof of stake system derived from the Byzantine fault tolerance literature. Casper includes: two slashing conditions, a correct-by-construction fork choice rule inspired by \cite{sompolinsky2013accelerating}, and dynamic validator sets. Finally we introduced extensions to Casper (not reverting finalized checkpoints and the inactivity leak) to defend against two common attacks. - -Casper remains imperfect. For example, a wholly compromised block proposal mechanism will prevent Casper from finalizing new blocks. Casper is a PoS-based strict security improvement to almost any PoW chain. The problems that Casper does not wholly solve, particularly related to 51\% attacks, can still be corrected using user-activated soft forks. Future developments will undoubtedly improve Casper's security and reduce the need for user-activated soft forks. - - - - - -\textbf{Future Work.} The current Casper system builds upon a proof of work block proposal mechanism. We wish to convert the block proposal mechanism to proof of stake. We wish to prove accountable safety and plausible liveness even when the weights of the validator set change with rewards and penalties. Another problem for future work is a formal specification of a fork-choice rule taking into account the common attacks on proof of stake. Future workpapers will explain and analyze the financial incentives within Casper and their consequences. A particular economic problem related to such automated strategies to block attackers is proving upper bounds on the ratio between the degree of disagreement between different clients and the cost incurred by the attacker. - - - -\textbf{Acknowledgements.} We thank Jon Choi, Karl Floersch, Ozymandias Haynes, and Vlad Zamfir for frequent discussions. - -\bibliographystyle{naturemag} -\bibliography{ethereum} -%\section{References} -%\bibliographystyle{plain} -%\bibliography{ethereum} -%\thebibliography - -%\input{appendix.tex} -%\clearpage - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\end{document} - \ No newline at end of file diff --git a/papers/casper-basics/eth_header.tex b/papers/casper-basics/eth_header.tex deleted file mode 100644 index eb7910a..0000000 --- a/papers/casper-basics/eth_header.tex +++ /dev/null @@ -1,144 +0,0 @@ -% make in the latest NIPS format (as of this writing, 2017) - -\usepackage[nonatbib,final]{nips_2017} -%\usepackage[nonatbib,final]{nips_2017} - -\usepackage{color} -\usepackage{graphicx} -\DeclareGraphicsExtensions{.pdf,.eps,.png,.jpg} % search for .pdf, then .eps, then .pngs, then .jpg - -% look in these subdirectories for graphics referenced by \includegraphics -% each entry must end with a / -\graphicspath{{figs/}{figures/}{images/}{./}} - -\newcommand*{\red}[1]{ \color{red} #1} - -%\usepackage{tabularx} -\usepackage{url} -\usepackage{amsmath} - -% this is for environments \subfigure and \subtable -\usepackage{subcaption} - -% These packages are FORBIDDEN -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\usepackage{lmodern} % messes up \textsc -%\usepackage{cite} % messes up NIPS -%\usepackage{fullpage} % messes up NIPS -%\usepackage{natbib} % messes up NIPS -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\usepackage{array} % replacement for eqnarray. 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Then in text you only type \figref{myfig} and LaTeX -% will do the rest. -\newcommand{\tblref}[1]{Table~\ref{#1}} -%\renewcommand*{\figref}[1]{Fig.~\ref{#1}} -\renewcommand{\eqref}[1]{eq.~(\ref{#1})} -\newcommand{\Subref}[1]{(\subref{#1})} - - -\newcommand{\figref}[1]{Figure~\ref{#1}} -\newcommand{\Figref}[1]{Figure~\ref{#1}} -\newtheorem{theorem}{Theorem} -\newtheorem{lemma}[theorem]{Lemma} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% for \sout{} for strikeout -% \usepackage[normalem]{ulem} - - -% for better manipulation of tables -\usepackage{makecell} -\renewcommand\theadfont{\bfseries} - - -%----------------------------------------------------------------------------- -% Misc symbols that I like -%----------------------------------------------------------------------------- -\newcommand*{\opname}[1]{\operatorname{#1}} - - -\renewcommand*{\to}{\rightarrow} - - -%%%% - - diff --git a/papers/casper-basics/ethereum.bib b/papers/casper-basics/ethereum.bib deleted file mode 100644 index ef524a3..0000000 --- a/papers/casper-basics/ethereum.bib +++ /dev/null @@ -1,617 +0,0 @@ -@article{algorand, - author = {Jing Chen and Silvio Micali}, - title = {{ALGORAND:} The Efficient and Democratic Ledger}, - journal = {CoRR}, - volume = {abs/1607.01341}, - year = {2016}, - url = {http://arxiv.org/abs/1607.01341}, - timestamp = {Wed, 07 Jun 2017 14:41:27 +0200}, - biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/Micali16}, - bibsource = {dblp computer science bibliography, http://dblp.org} -} - -@inproceedings{shi2017, - author = {Rafael Pass and Elaine Shi}, - title = {FruitChains: A Fair Blockchain}, - booktitle = {Proceedings of the ACM Symposium on Principles of Distributed Computing}, - series = {PODC 2017}, - year = {2017}, - isbn = {978-1-4503-4992-5}, - location = {Washington, DC, USA}, - pages = {315--324}, - numpages = {10}, - url = {http://doi.acm.org/10.1145/3087801.3087809}, - doi = {10.1145/3087801.3087809}, - acmid = {3087809}, - publisher = {ACM}, - address = {New York, NY, USA}, - keywords = {blockchains, distributed consensus, fairness, nash equilibrium}, -} - -@MISC{dfinity, - TITLE = {Introducing Dfinity Crypto Techniques}, - URL = {https://dfinity.org/pdf-viewer/pdfs/viewer.html?file=../library/intro-dfinity-crypto.pdf}, - YEAR = {2017}, - Month = {05} -} - - - - -@MISC{nakamoto, - TITLE = {Bitcoin: A Peer-to-Peer Electronic Cash Systems}, - author = {Satoshi Nakamoto}, - URL = {https://bitcoin.org/bitcoin.pdf}, - YEAR = {2008}, - Month = {11} -} - - - -@INPROCEEDINGS{castro1999practical, - AUTHOR = {Miguel Castro and Barbara Liskov and et. al}, - BOOKTITLE = {Proceedings of the Third Symposium on Operating Systems Design and Implementation}, - EDITOR = {Paul J. 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