def test_jacobian_multi():
ret = JacobianGroupBTC(
(
FiniteFieldBTC(5),
FiniteFieldBTC(8),
FiniteFieldBTC(1)
)
) @ EllipticCurveCyclicSubgroupBTC(2)
ans = jacobian_multiply((5, 8, 1), 2)
assert (
ret.value[0].value,
ret.value[1].value,
ret.value[2].value
) == ans
ans = jacobian_multiply((5, 8, 1), 3)
ret = JacobianGroupBTC(
EllipticCurveGroupBTC(
(
FiniteFieldBTC(5),
FiniteFieldBTC(8),
)
)
) @ EllipticCurveCyclicSubgroupBTC(3)
assert (
ret.value[0].value,
ret.value[1].value,
ret.value[2].value
) == ans
ret = EllipticCurveGroupBTC(ret)
assert (
ret.value[0].value,
ret.value[1].value,
) == from_jacobian(ans)
def ecrecover_substitute(z, v, r, s):
P, A, B, N, Gx, Gy = b.P, b.A, b.B, b.N, b.Gx, b.Gy
x = r
beta = pow(x * x * x + A * x + B, (P + 1) // 4, P)
y = beta if v % 2 ^ beta % 2 else (P - beta)
Gz = b.jacobian_multiply((Gx, Gy, 1), (N - z) % N)
XY = b.jacobian_multiply((x, y, 1), s)
Qr = b.jacobian_add(Gz, XY)
Q = b.jacobian_multiply(Qr, pow(r, N - 2, N))
Q = b.from_jacobian(Q)
return signed(Q)
def ecrecover_substitute(z, v, r, s):
P, A, B, N, Gx, Gy = b.P, b.A, b.B, b.N, b.Gx, b.Gy
x = r
beta = pow(x*x*x+A*x+B, (P + 1) / 4, P)
y = beta if v % 2 ^ beta % 2 else (P - beta)
Gz = b.jacobian_multiply((Gx, Gy, 1), (N - z) % N)
XY = b.jacobian_multiply((x, y, 1), s)
Qr = b.jacobian_add(Gz, XY)
Q = b.jacobian_multiply(Qr, pow(r, N - 2, N))
Q = b.from_jacobian(Q)
return signed(Q)
import bitcoin as b
import random
import sys
import math
from ethereum.tools import tester as t
from ethereum import utils
import substitutes
import time
vals = [random.randrange(2**256) for i in range(12)]
test_points = [b.jacobian_multiply((b.Gx, b.Gy, 1), r) for r in vals]
G = [b.Gx, b.Gy, 1]
Z = [0, 0, 1]
def neg_point(p):
return [p[0], b.P - p[1], p[2]]
s = t.Chain()
s.head_state.gas_limit = 10**9
tests = sys.argv[1:]
if '--log' in tests:
t.set_logging_level(int((tests + [1])[tests.index('--log') + 1]))
if '--modexp' in tests or not len(tests):
c = s.contract('jacobian_arith.se', language='serpent')
def jacobian_mul_substitute(A, B, C, N):
output = b.jacobian_multiply((A, B, C), N)
return signed(output)
def jacobian_mul_substitute(A, B, C, N):
output = b.jacobian_multiply((A, B, C), N)
return signed(output)