def test_jacobi_properties(self):
p = random_prime(5)
q = random_prime(5)
n = p * q
a = random.randint(p // 2, p - 1)
b = a + n
self.assertEqual(jacobi(a, n), jacobi(b, n))
def __init__(self, bit_size):
"""
Given the bit size of the RSA key, construct a RsaKeyGenerator, which will generated a
key at least as big as the specified key size.
"""
self.p = random_prime(bit_size)
self.q = random_prime(bit_size)
self.n = self.p * self.q
self.e = 0
self.d = 0
self.limit = (self.p - 1) * (self.q - 1)
self.public_key = self.gen_public_key()
self.private_key = self.gen_private_key()
def test_mod_inverse(self):
self.assertEqual(mod_inverse(3, 11), 4)
self.assertEqual(mod_inverse(10, 17), 12)
p = random_prime(3)
a = random.randint(1, p - 1)
a_inv = mod_inverse(a, p)
self.assertEqual(a * a_inv % p, 1)
def test_legendre_properties(self):
p = 7
a = 4
# 11 = 4 (mod 7)
b = 11
self.assertEqual(legendre(a, p), legendre(b, p))
p = random_prime(100)
a = random.randint(p // 2, p - 1)
# an easy was of asserting $a \equiv b \pmod{p}$
b = a + p
self.assertEqual(legendre(a, p), legendre(b, p))
p = random_prime(100)
a = random.randint(p // 2, p - 1)
b = random.randint(p // 2, p - 1)
self.assertEqual(legendre(a * b, p), legendre(a, p) * legendre(b, p))
def test_solovay_2(self):
# This test is slow for large primes
p = random_prime(16)
self.assertTrue(is_prime(p, 'solovay-strassen'))
ps = list(primes(20))
self.assertTrue(all(is_prime(p, 'solovay-strassen') for p in ps))
def test_miller_rabin_small_2(self):
n = 64
prime = random_prime(n)
self.assertTrue(is_prime(prime))
def test_miller_rabin_random_large(self):
n = 64
actual = random_prime(n)
self.assertEqual(actual.bit_length(), n)
self.assertTrue(is_prime(actual))
#!/usr/bin/python3
from math import sqrt
import sys
sys.path.append('../../')
from crypto.random import random_prime
def quadratic(a, b, c):
d = b**2 - 4 * a * c
return (-b + sqrt(d)) / (2 * a), (-b - sqrt(d)) / (2 * a)
p = random_prime(16)
q = random_prime(16)
n = p * q
phi = (p - 1) * (q - 1)
a = 1
b = -(n + 1 - phi)
c = n
print(p, q)
print(quadratic(a, b, c))