69 lines
2.0 KiB
Python
69 lines
2.0 KiB
Python
|
# Constantine
|
||
|
|
# Copyright (c) 2018-2019 Status Research & Development GmbH
|
||
|
|
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
|
||
|
|
# Licensed and distributed under either of
|
||
|
|
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
|
||
|
|
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
|
||
|
|
# at your option. This file may not be copied, modified, or distributed except according to those terms.
|
||
|
|
|
||
|
|
# ############################################################
|
||
|
|
#
|
||
|
|
# BN254 test generator
|
||
|
|
#
|
||
|
|
# ############################################################
|
||
|
|
|
||
|
|
# Parameters
|
||
|
|
u = Integer('0x44E992B44A6909F1')
|
||
|
|
p = 36*u^4 + 36*u^3 + 24*u^2 + 6*u + 1
|
||
|
|
r = 36*u^4 + 36*u^3 + 18*u^2 + 6*u + 1
|
||
|
|
cofactor = 1
|
||
|
|
|
||
|
|
# Finite fields
|
||
|
|
F = GF(p)
|
||
|
|
K2.<u> = PolynomialRing(F)
|
||
|
|
# F2.<beta> = F.extension(u^2+9)
|
||
|
|
# K6.<v> = PolynomialRing(F2)
|
||
|
|
# F6.<eta> = F2.extension(v^3-beta)
|
||
|
|
# K12.<w> = PolynomialRing(F6)
|
||
|
|
# K12.<gamma> = F6.extension(w^2-eta)
|
||
|
|
|
||
|
|
# Curves
|
||
|
|
b = 3
|
||
|
|
G1 = EllipticCurve(F, [0, b])
|
||
|
|
# G2 = EllipticCurve(F2, [0, b/beta])
|
||
|
|
|
||
|
|
# Test generator
|
||
|
|
set_random_seed(1337)
|
||
|
|
|
||
|
|
for i in range(10):
|
||
|
|
print('---------------------------------------')
|
||
|
|
P = G1.random_point()
|
||
|
|
(Px, Py, Pz) = P
|
||
|
|
print('Px: ' + Integer(Px).hex())
|
||
|
|
print('Py: ' + Integer(Py).hex())
|
||
|
|
print('Pz: ' + Integer(Pz).hex())
|
||
|
|
exponent = randrange(r) # Pick an integer below curve order
|
||
|
|
print('scalar: ' + Integer(exponent).hex())
|
||
|
|
|
||
|
|
Q = exponent * P
|
||
|
|
(Qx, Qy, Qz) = Q
|
||
|
|
print('Qx: ' + Integer(Qx).hex())
|
||
|
|
print('Qy: ' + Integer(Qy).hex())
|
||
|
|
print('Qz: ' + Integer(Qz).hex())
|
||
|
|
|
||
|
|
# CurveOrder sanity check
|
||
|
|
#
|
||
|
|
# P = G1.random_point()
|
||
|
|
# (Px, Py, Pz) = P
|
||
|
|
# print('Px: ' + Integer(Px).hex())
|
||
|
|
# print('Py: ' + Integer(Py).hex())
|
||
|
|
# print('Pz: ' + Integer(Pz).hex())
|
||
|
|
#
|
||
|
|
# print('order: ' + Integer(r).hex())
|
||
|
|
#
|
||
|
|
# Q = (r * cofactor) * P
|
||
|
|
# (Qx, Qy, Qz) = Q
|
||
|
|
# print('Qx: ' + Integer(Qx).hex())
|
||
|
|
# print('Qy: ' + Integer(Qy).hex())
|
||
|
|
# print('Qz: ' + Integer(Qz).hex())
|