def compute_point_xy(self):
in_str = self.input_seed + "point"
x_hash = utils.hash_sha512(in_str)
self.point_x = int(x_hash, 16) % self.prime_p
end = False
while not end:
ring = Integers(self.prime_p)
tmp = power_mod(self.point_x, 3, self.prime_p) + \
self.coeff_a * self.point_x + self.coeff_b
y = ring(tmp)
if not utils.is_quadratic_residue(y, self.prime_p):
x_hash = utils.hash_sha512(x_hash)
self.point_x = int(x_hash, 16) % self.prime_p
else:
sq_root = int(y.square_root())
if sq_root % 2 == 0:
self.point_y = sq_root
else:
self.point_y = self.prime_p - sq_root
end = True
def compute_point_xy(self):
in_str = self.input_seed + "point"
x_hash = utils.hash_sha512(in_str)
self.point_x = int(x_hash, 16) % self.prime_p
end = False
while not end:
ring = Integers(self.prime_p)
tmp = power_mod(self.point_x, 3, self.prime_p) + \
self.coeff_a * self.point_x + self.coeff_b
y = ring(tmp)
if not utils.is_quadratic_residue(y, self.prime_p):
x_hash = utils.hash_sha512(x_hash)
self.point_x = int(x_hash, 16) % self.prime_p
else:
sq_root = int(y.square_root())
if sq_root % 2 == 0:
self.point_y = sq_root
else:
self.point_y = self.prime_p - sq_root
end = True
def ro_function(self, x, exp, p):
is_qr = utils.is_quadratic_residue(x, p)
if is_qr:
sq_root = pow(x, exp, p)
if sq_root % 2 == 0:
return sq_root
else:
return (p - sq_root)
else:
sq_root = pow(p - x, exp, p)
if sq_root % 2 == 0:
return (p - sq_root)
else:
return sq_root
def ro_function(self, x, exp, p):
is_qr = utils.is_quadratic_residue(x, p)
if is_qr:
sq_root = pow(x, exp, p)
if sq_root % 2 == 0:
return sq_root
else:
return (p - sq_root)
else:
sq_root = pow(p - x, exp, p)
if sq_root % 2 == 0:
return (p - sq_root)
else:
return sq_root