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darkfi/script/research/groth16/4.6.2-multi-variable-operand-polynomial.py
2021-09-16 12:07:51 +02:00

112 lines
2.3 KiB
Python

from bls_py import bls12381
from bls_py import pairing
from bls_py import ec
from bls_py.fields import Fq, Fq2, Fq6, Fq12, bls12381_q as Q
from finite_fields.modp import IntegersModP
from finite_fields.polynomial import polynomialsOver
import random
n = bls12381.n
g1 = ec.generator_Fq(bls12381)
g2 = ec.generator_Fq2(bls12381)
mod_field = IntegersModP(n)
poly = polynomialsOver(mod_field).factory
def lagrange(points):
result = poly([0])
for i, (x_i, y_i) in enumerate(points):
p = poly([y_i])
for j, (x_j, y_j) in enumerate(points):
if i == j:
continue
p *= poly([-x_j, 1]) / (x_i - x_j)
#print(poly)
#print(poly(1), poly(2), poly(3))
result += p
return result
l_a_points = [
(1, 1), (2, 1), (3, 0)
]
l_a = lagrange(l_a_points)
#print(l_a)
l_d_points = [
(1, 0), (2, 0), (3, 1)
]
l_d = lagrange(l_d_points)
#print(l_d)
# a x b = r_1
# a x c = r_2
# d x c = r_3
# a = 3
# d = 2
L = 3*l_a + 2*l_d
#print(L)
def poly_call(poly, x):
result = mod_field(0)
for degree, coeff in enumerate(poly):
result += coeff * (x**degree)
return result.n
assert poly_call(L, 1) == 3
assert poly_call(L, 2) == 3
assert poly_call(L, 3) == 2
def rand_scalar():
return random.randrange(1, bls12381.q)
#################################
# Verifier (trusted setup)
#################################
# samples a random value (a secret)
toxic_scalar = rand_scalar()
# calculate the shift
alpha_shift = rand_scalar()
l_a_s = poly_call(l_a, toxic_scalar)
l_d_s = poly_call(l_d, toxic_scalar)
enc_a_s = g1 * l_a_s
enc_a_s_alpha = enc_a_s * alpha_shift
enc_d_s = g1 * l_d_s
enc_d_s_alpha = enc_d_s * alpha_shift
# Proving key is enc_* values above
# Actual values of s are toxic waste and discarded
verify_key = g2 * alpha_shift
#################################
# Prover
#################################
a = 3
d = 2
assigned_a = enc_a_s * a
assigned_d = enc_d_s * d
assigned_a_shift = enc_a_s_alpha * a
assigned_d_shift = enc_d_s_alpha * d
operand = assigned_a + assigned_d
operand_shift = assigned_a_shift + assigned_d_shift
# proof = operand, operand_shift
#################################
# Verifier
#################################
e = pairing.ate_pairing
assert e(operand_shift, g2) == e(operand, verify_key)