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https://github.com/darkrenaissance/darkfi.git
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153 lines
3.9 KiB
Python
153 lines
3.9 KiB
Python
from bls_py import bls12381
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from bls_py import pairing
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from bls_py import ec
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from bls_py.fields import Fq, Fq2, Fq6, Fq12, bls12381_q as Q
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import random
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import numpy as np
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# Section 3.6 from "Why and How zk-SNARK Works"
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def rand_scalar():
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return random.randrange(1, bls12381.q)
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#x = rand_scalar()
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#y = ec.y_for_x(x)
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g1 = ec.generator_Fq(bls12381)
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g2 = ec.generator_Fq2(bls12381)
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null = ec.AffinePoint(Fq(Q, 0), Fq(Q, 1), True, bls12381)
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assert g1 + null == g1
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null2 = ec.AffinePoint(Fq2.zero(Q), Fq2.zero(Q), True, bls12381)
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assert null2 + g2 == g2
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#################################
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# Verifier (trusted setup)
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#################################
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# samples a random value (a secret)
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s = rand_scalar()
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# calculate the shift
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a = rand_scalar()
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# calculates encryptions of s for all powers i in 0 to d
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# E(s^i) = g^s^i
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d = 10
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encrypted_powers = [
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g1 * (s**i) for i in range(d)
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]
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encrypted_powers_g2 = [
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g2 * (s**i) for i in range(d)
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]
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encrypted_shifted_powers = [
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g1 * (a * s**i) for i in range(d)
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]
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# evaluates unencrypted target polynomial with s: t(s)
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target = (s - 1) * (s - 2)
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# CRS = common reference string = trusted setup parameters
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target_crs = g1 * target
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alpha_crs = g2 * a
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# Proving key = (encrypted_powers, encrypted_shifted_powers)
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# Verify key = (target_crs, alpha_crs)
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# encrypted values of s provided to the prover
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# Actual values of s are toxic waste and discarded
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#################################
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# Prover
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#################################
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# delta shift
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delta = rand_scalar()
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# E(p(s)) = p(s)G
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# = c_d s^d G + ... + c_1 s^1 G + c_0 s^0 G
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# = s^3 G - 3 s^2 G + 2 s G
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# E(h(s)) = sG
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# t(s) = s^2 - 3s + 2
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# E(h(s)) t(s) = s^3 G - 3 s^2 G + 2 s G
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# Lets test these manually:
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e_s = encrypted_powers
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e_p_s = e_s[3] - 3 * e_s[2] + 2 * e_s[1]
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e_h_s = e_s[1]
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t_s = s**2 - 3*s + 2
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# exponentiate with delta
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e_p_s *= delta
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e_h_s *= delta
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assert t_s == target
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assert e_p_s == e_h_s * t_s
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e_as = encrypted_shifted_powers
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e_p_as = e_as[3] - 3 * e_as[2] + 2 * e_as[1]
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# exponentiate with delta
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e_p_as *= delta
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assert e_p_s * a == e_p_as
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#############################
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# x^3 - 3x^2 + 2x
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main_poly = np.poly1d([1, -3, 2, 0])
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# (x - 1)(x - 2)
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target_poly = np.poly1d([1, -1]) * np.poly1d([1, -2])
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# Calculates polynomial h(x) = p(x) / t(x)
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cofactor, remainder = main_poly / target_poly
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assert remainder == np.poly1d([0])
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# Using encrypted powers and coefficients, evaluates
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# E(p(s)) and E(h(s))
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def evaluate(poly, encrypted_powers, identity):
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coeffs = list(poly.coef)[::-1]
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result = identity
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for power, coeff in zip(encrypted_powers, coeffs):
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#print(coeff, power)
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coeff = int(coeff)
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# I have to do this for some strange reason
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# Because if coeff is negative and I do += power * coeff
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# then it gives me a different result than what I expect
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if coeff < 0:
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result -= power * (-coeff)
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else:
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result += power * coeff
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# Add delta to the result
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# Free extra obfuscation to the polynomial
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return result * delta
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encrypted_poly = evaluate(main_poly, encrypted_powers, null)
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assert encrypted_poly == e_p_s
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encrypted_cofactor = evaluate(cofactor, encrypted_powers_g2, null2)
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# Alpha shifted powers
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encrypted_shift_poly = evaluate(main_poly, encrypted_shifted_powers, null)
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# resulting g^p and g^h are provided to the verifier
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# proof = (encrypted_poly, encrypted_cofactor, encrypted_shift_poly)
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#################################
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# Verifier
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#################################
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# Last check that p = t(s) h
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# Check polynomial cofactors:
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#assert encrypted_poly == encrypted_cofactor * target
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# e(g^p, g) == e(g^t, g^h)
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res1 = pairing.ate_pairing(encrypted_poly, g2)
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res2 = pairing.ate_pairing(target_crs, encrypted_cofactor)
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assert res1 == res2
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# Verify (g^p)^a == g^p'
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# Check polynomial restriction:
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res1 = pairing.ate_pairing(encrypted_shift_poly, g2)
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res2 = pairing.ate_pairing(encrypted_poly, alpha_crs)
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assert res1 == res2
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#assert encrypted_poly * a == encrypted_shift_poly
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