def public_keygen(self,
E=None,
P=None,
private_key=None,
output_type="x only"):
if E is not None:
self.E = E
if P is not None:
if isinstance(P, int):
y2 = (fast_power(P, 3, self.E.modulus) +
(P * self.E.A) + self.E.B) % self.E.modulus
y = mod_sqrt(y2, self.E.modulus)[0]
self.P = (P, mod_sqrt(y, self.E.modulus)[0])
self.P = P
if private_key is not None:
self.private_key = private_key
if None in [self.E, self.P, self.private_key]:
return None
self.QA = self.E.multiply(self.P, self.private_key)
if output_type == self.style[0]:
return self.QA
elif output_type == self.style[1]:
return self.QA[0]
else:
print("invalid type")
return None
def encrypt(self, plain_text, QB, E=None, P=None, output_type="x only"):
if E is not None:
self.E = E
if P is not None:
if isinstance(P, int):
y2 = (fast_power(P, 3, self.E.modulus) +
(P * self.E.A) + self.E.B) % self.E.modulus
y = mod_sqrt(y2, self.E.modulus)[0]
self.P = (P, mod_sqrt(y, self.E.modulus)[0])
self.P = P
if QB is not None:
if isinstance(QB, int):
y2 = (fast_power(QB, 3, self.E.modulus) +
(QB * self.E.A) + self.E.B) % self.E.modulus
y = mod_sqrt(y2, self.E.modulus)[0]
QB = (QB, mod_sqrt(y, self.E.modulus)[0])
M = self.E.msg_to_point(plain_text)
k = random.randint(1, self.E.modulus)
C1 = self.E.multiply(k, P)
C2 = self.E.add(M, E.multiply(k, QB))
if output_type == self.style[0]:
return (C1, C2)
elif output_type == self.style[1]:
return (C1[0], C2[0])
else:
print("Invalid type")
return None
def __init__(self, E, P):
self.E = E
self.style = ["whole point", "x only"]
if isinstance(P, int):
y2 = (fast_power(P, 3, self.E.modulus) +
(P * self.E.A) + self.E.B) % self.E.modulus
y = mod_sqrt(y2, self.E.modulus)[0]
self.P = (P, mod_sqrt(y, self.E.modulus)[0])
self.P = P
def test_mod_sqrt_5(self):
# Test where there is no sqrt
m = 3623
a = 88
expected_x = (None, None)
x = mod_sqrt(a, m)
self.assertEqual(expected_x, x)
def test_mod_sqrt_3(self):
#test with prime 3 mod 8, where there is a sqrt for a
m = 563
orig_x = 109
a = (orig_x * orig_x) % m
x = mod_sqrt(a, m)
self.assertIn(orig_x, x)
def test_mod_sqrt_4(self):
#test with prime 7 mod 8, where there is a sqrt for a
m = 719
orig_x = 230
a = (orig_x * orig_x) % m
x = mod_sqrt(a, m)
self.assertIn(orig_x, x)
def is_point_on_curve(self, P):
y2 = self.calculate_y2(P[0])
y = mod_sqrt(y2, self.modulus)
if y is not (None, None):
if y[0] == P[1] or y[1] == P[1]:
return True
return False
def calculate_point(self, x):
y2 = self.calculate_y2(x)
y = mod_sqrt(y2)
if y is (None, None):
return None
else:
return [(x, y[0]), (x, y[1])]
def decrypt(self, c1, c2, QA=None):
if QA is not None:
self.QA = QA
if isinstance(c1, int):
y2 = (fast_power(c1, 3, self.E.modulus) +
(c1 * self.E.A) + self.E.B) % self.E.modulus
y = mod_sqrt(y2, self.E.modulus)[0]
c1 = (c1, y)
if isinstance(c2, int):
y2 = (fast_power(c2, 3, self.E.modulus) +
(c2 * self.E.A) + self.E.B) % self.E.modulus
y = mod_sqrt(y2, self.E.modulus)[0]
c2 = (c2, y)
param2 = self.E.multiply(self.private_key, c1)
param2[1] = -param2[1]
return self.E.point_to_msg(self.E.add(c2, param2))
def test_mod_sqrt_1(self):
print("\n\nRunning test for src module: mod_sqrt")
# test with prime 1 mod 8, where there is a sqrt for a
m = 977
orig_x = 745
a = (orig_x * orig_x) % m
x = mod_sqrt(a, m)
self.assertIn(orig_x, x)
def test_mod_sqrt_2(self):
# Bulk test with all the primes under 1000
orig_x = None
primes = small_primes_generator(1000)
del primes[0]
for m in primes:
for i in range(1, m):
orig_x = i
a = (orig_x * orig_x) % m
x = mod_sqrt(a, m)
self.assertIn(orig_x, x)
def symmetric_keygen(self, QB, private_key=None, output_type="x only"):
if private_key is not None:
self.private_key = private_key
if QB is not None:
self.QB = QB
if None in [self.E, self.private_key]:
return None
if isinstance(self.QB, int):
y2 = (fast_power(self.QB, 3, self.E.modulus) +
(self.QB * self.E.A) + self.E.B) % self.E.modulus
y = mod_sqrt(y2, self.E.modulus)[0]
self.QB = (self.QB, y)
print("QB:")
print(QB)
sym_point = self.E.multiply(self.QB, self.private_key)
sym_key = sym_point[0]
if output_type == self.style[0]:
return sym_point
elif output_type == self.style[1]:
return sym_key
else:
print("invalid output type")
return None