def inverse(self):
if self.degree() == 0:
new_value = self.value[0].inverse()
new = deepcopy(self)
new.value = [new_value]
return new
a, b, c = extended_euclid(self, self.field.q)
return c.inverse() * a
def pollard_rho(g, h, f):
x, y = g.identity(), h.identity()
a, b, c, d = 0, 0, 0, 0
for i in range(g.order()):
x, a, b = f(x, a, b, g, h)
y, c, d = f(y, c, d, g, h)
y, c, d = f(y, c, d, g, h)
if x == y:
# found a collision
u = (a-c) % g.order()
v = (d-b) % g.order()
# know that g^u=h^v
inv, gcd = nt.extended_euclid(v, g.order())[::2]
log_mod_gcd = ((u*inv) % g.order())//gcd
reduced = g.p//gcd
for j in range(gcd):
if pow(g, log_mod_gcd+j*reduced) == h:
return log_mod_gcd+j*reduced