def mod_sqrt(a, modulus):
root1 = None
root2 = None
if legendre_symbol(a, modulus) != 1:
root1 = None
root2 = None
elif modulus % 2 == 0: # Non-prime modulus's are not supported
print("Not a prime")
root1 = None
root2 = None
elif modulus % 8 == 1 or modulus % 8 == 5:
s = 0
m = None
n = modulus - 1
while n % 2 == 0:
n = n / 2
s += 1
m = n
e = s
z = random.randint(1, modulus - 1)
while legendre_symbol(z,
modulus) != -1: # z is a non-quadratic residue
z = random.randint(1, modulus - 1)
c = fast_power(z, m, modulus)
x = fast_power(a, (m + 1) / 2, modulus)
t = fast_power(a, m, modulus)
while t != 1:
i = 1
for i in range(1, e):
if fast_power(t, 2**i, modulus) == 1:
break
b = fast_power(c, 2**(e - i - 1), modulus)
x = (b * x) % modulus
t = (t * b * b) % modulus
c = (b * b) % modulus
e = i
root1 = x
root2 = modulus - x
elif modulus % 8 == 3 or modulus % 8 == 7:
x = fast_power(a, (modulus + 1) / 4, modulus)
root1 = x
root2 = (-x) % modulus
return (root1, root2)
def test_legendre_symbol_7(self):
p = 269
a = 0
expected = 0
self.assertEqual(legendre_symbol(a, p), expected)
def test_legendre_symbol_6(self):
p = 269
a = 248
expected = 1
self.assertEqual(legendre_symbol(a, p), expected)
def test_legendre_symbol_4(self):
p = 97
a = 72
expected = 1
self.assertEqual(legendre_symbol(a, p), expected)
def test_legendre_symbol_3(self):
p = 97
a = 5
expected = -1
self.assertEqual(legendre_symbol(a, p), expected)
def test_legendre_symbol_2(self):
p = 83
a = 7
expected = 1
self.assertEqual(legendre_symbol(a, p), expected)
def test_legendre_symbol_1(self):
print("\n\nRunning test for src module: legendre_symbol")
p = 83
a = 80
expected = -1
self.assertEqual(legendre_symbol(a, p), expected)
