def test_gf_irreducible():
assert gf_irreducible_p(gf_irreducible(1, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(2, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(3, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(4, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(5, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(6, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(7, 11, ZZ), 11, ZZ) == True
def gen(self):
irr_poly = Poly(alpha ** self.m + alpha + 1, alpha).set_domain(GF(self.q))
if gf_irreducible_p([int(c) for c in irr_poly.all_coeffs()], self.q, ZZ):
quotient_size = len(power_dict(self.n, irr_poly, self.q))
else:
quotient_size = 0
log.info("irr(q_size: {}): {}".format(quotient_size, irr_poly))
while quotient_size < self.n:
irr_poly = Poly([int(c.numerator) for c in gf_irreducible(self.m, self.q, ZZ)], alpha)
quotient_size = len(power_dict(self.n, irr_poly, self.q))
log.info("irr(q_size: {}): {}".format(quotient_size, irr_poly))
g_poly = None
for i in range(self.b, self.b + self.d - 1):
if g_poly is None:
g_poly = minimal_poly(i, self.n, self.q, irr_poly)
else:
g_poly = lcm(g_poly, minimal_poly(i, self.n, self.q, irr_poly))
g_poly = g_poly.trunc(self.q)
log.info("g(x)={}".format(g_poly))
return irr_poly, g_poly
def irreducible_poly(m, p, var):
return Poly([int(c.numerator) for c in gf_irreducible(m, p, ZZ)], var)
from participant import *
from fieldelement import *
import random
from sympy.polys.galoistools import gf_irreducible
from sympy.polys.domains import ZZ
if __name__ == "__main__":
""" Here we are trying to use a well known NIST curve. We get a generator P
of the curve (with cofactor = 1) which we know the order. We must still
generate a random Q linearly independent of P with the same order """
""" Generate the curve over a finite field"""
p = 2**256 - 2**224 + 2**192 + 2**96 - 1
k = 3
q = p**k
irreducible_poly = switchCoefs(gf_irreducible(k, p, ZZ))
a = FieldElement([
115792089210356248762697446949407573530086143415290314195533631308867097853948,
0, 0
], p, k, irreducible_poly)
b = FieldElement([
41058363725152142129326129780047268409114441015993725554835256314039467401291,
0, 0
], p, k, irreducible_poly)
ec = EllipticCurve(a, b)
""" Get 2 random independent points P and Q with the same order, by
extending the field to k=3 so that p^k = 3mod4 and we can easily obtain
square roots of elements of the field """
# Just to make sure our assumption is correct
if (q % 4) != 3:
raise ValueError("q is not 3 mod 4")
def getIrreducible(p, n):
return switchCoefs(gf_irreducible(n, p, ZZ))
