github/darkfi
1
1
Fork 0
mirror of https://github.com/darkrenaissance/darkfi.git synced 2026-01-10 23:27:56 -05:00
Code Issues Packages Projects Releases Wiki Activity

Merge branch 'master' of github.com:darkrenaissance/darkfi

Browse Source
This commit is contained in:
ghassmo
2021-08-28 16:00:31 +03:00
parent dcd44c2a71 2f1ab4a53f
commit da9d285cac
1 changed files with 199 additions and 36 deletions
Download Patch File Download Diff File Expand all files Collapse all files

235
scripts/halo/halo2.sage
View File

@@ -8,8 +8,10 @@ P.<X> = K[]
# In other words, this is a t root of unity.
generator = K(5)
# There is a large 2^32 order subgroup in this curve because it is 2-adic
#t = (K(q) - 1) / 2^32
t = (K(q) - 1) / 2^32
assert int(t) % 2 != 0
delta = generator^(2^32)
assert delta^t == 1
def get_omega():
generator = K(5)
@@ -40,7 +42,6 @@ assert omega^n == 1
A = []
F = []
var_one = K(1)
var_zero = K(0)
var_x = K(4)
var_y = K(6)
@@ -55,58 +56,59 @@ var_z = var_sxy + var_1s_xy
# 1 instance column
# Row 1
A_1_1, A_2_1, A_3_1, A_4_1 = var_one, 0, 0, 0
# z = public z
A_1_1, A_2_1, A_3_1, A_4_1 = var_z, 0, 0, 0
F_1_1, F_2_1, F_3_1, F_4_1 = 1, 0, 0, 0
I_1 = 0
I_1 = var_z
# Row 2
# ~0 == 0
A_1_2, A_2_2, A_3_2, A_4_2 = var_zero, 0, 0, 0
F_1_2, F_2_2, F_3_2, F_4_2 = 0, 1, 0, 0
I_2 = 0
# Row 3
# Boolean check
# (1 - s)(s + 0) == 0
A_1_3, A_2_3, A_3_3, A_4_3 = var_s, var_s, var_zero, var_zero
F_1_3, F_2_3, F_3_3, F_4_3 = 0, 0, 1, 0
I_3 = 0
# Row 4
# s x y == sxy
A_1_4, A_2_4, A_3_4, A_4_4 = var_s, var_x, var_y, var_sxy
F_1_4, F_2_4, F_3_4, F_4_4 = 0, 0, 0, 1
I_4 = 0
# Row 5
# (1 - s)(x + y) = (1-s)(x+y)
A_1_5, A_2_5, A_3_5, A_4_5 = var_s, var_x, var_y, var_1s_xy
F_1_5, F_2_5, F_3_5, F_4_5 = 0, 0, 1, 0
I_5 = 0
# Row 6
# (1 - 0)(sxy + (1-s)(x+y)) = z
A_1_6, A_2_6, A_3_6, A_4_6 = var_zero, var_sxy, var_1s_xy, var_z
F_1_6, F_2_6, F_3_6, F_4_6 = 0, 0, 1, 0
I_6 = 0
# Row 7
# z = public z
A_1_7, A_2_7, A_3_7, A_4_7 = var_z, 0, 0, 0
F_1_7, F_2_7, F_3_7, F_4_7 = 0, 1, 0, 0
I_7 = var_z
A1 = [A_1_1, A_1_2, A_1_3, A_1_4, A_1_5, A_1_6, A_1_7]
A2 = [A_2_1, A_2_2, A_2_3, A_2_4, A_2_5, A_2_6, A_2_7]
A3 = [A_3_1, A_3_2, A_3_3, A_3_4, A_3_5, A_3_6, A_3_7]
A4 = [A_4_1, A_4_2, A_4_3, A_4_4, A_4_5, A_4_6, A_4_7]
F1 = [F_1_1, F_1_2, F_1_3, F_1_4, F_1_5, F_1_6, F_1_7]
F2 = [F_2_1, F_2_2, F_2_3, F_2_4, F_2_5, F_2_6, F_2_7]
F3 = [F_3_1, F_3_2, F_3_3, F_3_4, F_3_5, F_3_6, F_3_7]
F4 = [F_4_1, F_4_2, F_4_3, F_4_4, F_4_5, F_4_6, F_4_7]
I = [I_1, I_2, I_3, I_4, I_5, I_6, I_7]
A1 = [A_1_1, A_1_2, A_1_3, A_1_4, A_1_5, A_1_6]
A2 = [A_2_1, A_2_2, A_2_3, A_2_4, A_2_5, A_2_6]
A3 = [A_3_1, A_3_2, A_3_3, A_3_4, A_3_5, A_3_6]
A4 = [A_4_1, A_4_2, A_4_3, A_4_4, A_4_5, A_4_6]
F1 = [F_1_1, F_1_2, F_1_3, F_1_4, F_1_5, F_1_6]
F2 = [F_2_1, F_2_2, F_2_3, F_2_4, F_2_5, F_2_6]
F3 = [F_3_1, F_3_2, F_3_3, F_3_4, F_3_5, F_3_6]
F4 = [F_4_1, F_4_2, F_4_3, F_4_4, F_4_5, F_4_6]
I = [I_1, I_2, I_3, I_4, I_5, I_6]
# There should be 5 unused blinding rows.
# see src/plonk/circuit.rs: fn blinding_factors(&self) -> usize;
# We have 9 so we are perfectly fine.
# Add 9 empty rows
assert n - len(A1) == 9
for i in range(9):
assert n - len(A1) == 10
for i in range(10):
A1.append(K.random_element())
A2.append(K.random_element())
A3.append(K.random_element())
@@ -122,8 +124,8 @@ assert (len(A1) == len(A2) == len(A3) == len(A4) == len(F1) == len(F2)
for A_1_i, A_2_i, A_3_i, A_4_i, F_1_i, F_2_i, F_3_i, F_4_i, I_i in zip(
A1, A2, A3, A4, F1, F2, F3, F4, I):
assert (F_1_i * (A_1_i - 1)
+ F_2_i * (A_1_i - I_i)
assert (F_1_i * (A_1_i - I_i)
+ F_2_i * A_1_i
+ F_3_i * ((1 - A_1_i) * (A_2_i + A_3_i) - A_4_i)
+ F_4_i * (A_1_i * A_2_i * A_3_i - A_4_i)) == 0
@@ -151,23 +153,149 @@ for i, (A_1_i, A_2_i, A_3_i, A_4_i, F_1_i, F_2_i, F_3_i, F_4_i, I_i) in \
assert f_4_X(omega^i) == F_4_i
# beta, gamma
beta = K.random_element()
gamma = K.random_element()
# 0 1 2 3 4 5 6 ... 15
# A1: 1, 0, s, s, s, 0, z
# 16 17 18 19 20 21 22 ... 31
# A2: -, -, s, x, x, sxy, -
# 32 33 34 35 36 37 38 ... 47
# A3: -, -, 0, y, y, (1-s)(x+y), -
# 48 49 50 51 52 53 54 ... 63
# A4: -, -, 0, sxy, (1-s)(x + y), z, -
# 64 65 66 67 68 69 70 ... 79
# A5: -, -, -, -, -, -, z
permuted_indices_A1 = []
# 0 1 2 3 4 5 ... 15
# A1: z, 0, s, s, s, 0,
#
# 16 17 18 19 20 21 ... 31
# A2: -, -, s, x, x, sxy,
#
# 32 33 34 35 36 37 ... 47
# A3: -, -, 0, y, y, (1-s)(x+y),
#
# 48 49 50 51 52 53 ... 63
# A4: -, -, 0, sxy, (1-s)(x + y), z,
#
# 64 65 66 67 68 69 ... 79
# A5: z, -, -, -, -, -,
# z = (0 53 64)
# 0 = (1 5 34 50)
# s = (2 3 4 18)
# x = (19 20)
# sxy = (21 51)
# y = (35 36)
# (1-s)(x+y) = (37 52)
permuted_indices = list(range(n * 5))
assert len(permuted_indices) == 80
# Apply the actual permutation cycles
# z
permuted_indices[0] = 53
permuted_indices[53] = 64
permuted_indices[64] = 0
# ~0
permuted_indices[1] = 5
permuted_indices[5] = 34
permuted_indices[34] = 50
permuted_indices[50] = 1
# s
permuted_indices[2] = 3
permuted_indices[3] = 4
permuted_indices[4] = 18
permuted_indices[18] = 2
# x
permuted_indices[19] = 20
permuted_indices[20] = 19
# sxy
permuted_indices[21] = 51
permuted_indices[51] = 21
# y
permuted_indices[35] = 36
permuted_indices[36] = 35
# (1-s)(x+y)
permuted_indices[37] = 52
permuted_indices[52] = 37
witness = A1 + A2 + A3 + A4 + I
for i, val in enumerate(witness):
assert val == witness[permuted_indices[i]]
# How to join lists together?
indices = ([omega^i for i in range(n)]
+ [delta * omega^i for i in range(n)]
+ [delta^2 * omega^i for i in range(n)]
+ [delta^3 * omega^i for i in range(n)]
+ [delta^4 * omega^i for i in range(n)])
assert len(indices) == 80
# Permuted indices
sigma_star = [indices[i] for i in permuted_indices]
s = [sigma_star[:n], sigma_star[n:2 * n], sigma_star[2 * n:3 * n],
sigma_star[3 * n:4 * n], sigma_star[4 * n:]]
assert s[0] + s[1] + s[2] + s[3] + s[4] == sigma_star
v = [A1, A2, A3, A4, I]
# We split the columns into sets of size m.
# Here we will use m = 1 for illustration purposes
# We have 6 usable rows
# n = 16 rows total
# row u (q_last) will be the 7th row
# So we have 9 unusable rows
q_blind = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
q_last = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
# Turn both of these into polynomial form
q_blind = P.lagrange_polynomial((omega^i, q_i) for i, q_i in enumerate(q_blind))
assert q_blind(omega^5) == 0
assert q_blind(omega^6) == 0
assert q_blind(omega^7) == 1
assert q_blind(omega^11) == 1
q_last = P.lagrange_polynomial((omega^i, q_i) for i, q_i in enumerate(q_last))
assert q_last(omega^5) == 0
assert q_last(omega^6) == 1
assert q_last(omega^7) == 0
assert q_last(omega^11) == 0
m = 5
assert n == 16
# 6 usable rows
u = 6
# There are 5 columns
# We will split the columns partitions into 5 partitions to make things easy
# So b = 5, and each partition contains only a single column
# We still iterate over the column to make it more obvious
m = 1
permutation_points = [(1, 1)]
last_y_value = 1
ZP = []
# a is the current column partition we are aggregating
for a in range(5):
# j iterates over the rows
for j in range(u):
current = last_y_value
# i iterates over the columns in our partition
for i in range(a * m, (a + 1)):
current *= v[i][j] + beta * delta^i * omega^j + gamma
current /= v[i][j] + beta * s[i][j] + gamma
last_y_value = current
permutation_points.append((omega^(j + 1), current))
ZP_a = P.lagrange_polynomial(permutation_points)
ZP.append(ZP_a)
permutation_points = [(1, last_y_value)]
# l_0(X) (1 - ZP,0(X)) = 0
# => ZP,0(1) = 1
assert ZP[0](1) == 1
# Checks for l_0(X) (ZP,a(X) - ZP,a-1(omega^u X)) = 1
# => ZP,a(Z) = ZP,a-1(omega^u X)
# This copies the end value from one partition to the next one
assert ZP[1](omega^0) == ZP[0](omega^u)
assert ZP[2](omega^0) == ZP[1](omega^u)
assert ZP[3](omega^0) == ZP[2](omega^u)
assert ZP[4](omega^0) == ZP[3](omega^u)
# Allow the last value to be either 0 or 1 for full ZK
assert ZP[4](omega^u) in (0, 1)
y = K.random_element()
gate_0 = f_1_X * (a_1_X - 1)
gate_1 = f_2_X * (a_1_X - a_5_X)
gate_0 = f_1_X * (a_1_X - a_5_X)
gate_1 = f_2_X * a_1_X
gate_2 = f_3_X * ((1 - a_1_X) * (a_2_X + a_3_X) - a_4_X)
gate_3 = f_4_X * (a_1_X * a_2_X * a_3_X - a_4_X)
@@ -175,4 +303,39 @@ h = gate_0 + y * gate_1 + y^2 * gate_2 + y^3 * gate_3
t = X^n - 1
for i in range(n):
assert h(omega^i) == 0
# Normally we do:
#h /= t
# But for some reason sage is producing fractional coefficients
h, rem = h.quo_rem(X^n - 1)
assert rem == 0
# We send commitments to the terms of h(X)
# h_0(x), ..., h_{d - 1}(x)
# Commitments:
# H = [H_0, ..., H_{d - 1}]
x = K.random_element()
# Send evaluations at x of everything we committed to so far
# A_0(x), ..., A_{m - 1}(x)
# ZP,0(x), ..., ZP,b-1(x)
# H_0(x), ..., H_{d-1}(x)
a_evals = [a_1_X(x), a_2_X(x), a_3_X(x), a_4_X(x), a_5_X(x)]
h_evals = []
# Iterate starting from lowest powers first
h_test = 0
for i, h_i in enumerate(h):
h_evals.append(h_i * x^i)
h_test += h_i * X^i
assert h_test == h
assert sum(h_evals) == h(x)
assert sum(h_evals) * t(x) == (
f_1_X(x) * (a_evals[0] - a_evals[4])
+ y * f_2_X(x) * a_evals[0]
+ y^2 * f_3_X(x) * ((1 - a_evals[0]) * (a_evals[1] + a_evals[2])
- a_evals[3])
+ y^3 * f_4_X(x) * (a_evals[0] * a_evals[1] * a_evals[2] - a_evals[3]))