def generate_private_key(phiN):
e = randrange(phiN//2 + 1, phiN-1)
g, _, _ = num.extended_gcd(e, phiN)
while g != 1:
e = randrange(phiN//2 + 1, phiN-1)
g, _, _ = num.extended_gcd(e, phiN)
return e
def generate(digits=10):
"""
Creates an RSA encryption system object
Parameters
----------
digits : The number of digits N should have
Returns
-------
RSA: The RSA system containing:
* The public key (N,e)
* The private key (N,d)
"""
# generate p,q
N = -1
while N < 10**digits or N > 10**(digits + 1):
p = number_theory_functions.generate_prime(digits // 2 + 1)
q = number_theory_functions.generate_prime(digits // 2)
if p is None or q is None:
continue
N = p * q
phi = (p - 1) * (q - 1)
gcd = -1
e = 1
while gcd != 1:
e = randrange(1, phi)
gcd, a, b = number_theory_functions.extended_gcd(e, phi)
d = number_theory_functions.modular_inverse(e, phi)
return RSA((N, e), (N, d))
def encrypt(self, m):
"""
Encrypts the plaintext m using the RSA system
Parameters
----------
m : The plaintext to encrypt
Returns
-------
c : The encrypted ciphertext
"""
if m is None:
return None
gcd, a, b = number_theory_functions.extended_gcd(
self.private_key[0], m)
if gcd != 1:
return None
return number_theory_functions.modular_exponent(
m, self.public_key[1], self.private_key[0])
def test_extended_gcd(self):
values = [(119952, 34425, 153), (428848, 123075, 547), (-39, 3, 3)]
for (a, b, d) in values:
(gcd, x, y) = number_theory_functions.extended_gcd(a, b)
self.assertEqual(d, gcd)
self.assertEqual(gcd, a * x + b * y)
self.assertIsNone(
number_theory_functions.modular_inverse(119952, 34425))
class TestRSA(unittest.TestCase):
def test_encrypt_decrypt(self):
rsa = RSA.generate(10)
plaintexts = [123456789, 17, 9999, 102930]
for M in plaintexts:
C = rsa.encrypt(M)
MM = rsa.decrypt(C)
self.assertEqual(M, MM)
if __name__ == '__main__':
a = 5279
b = -797
r = lambda x: 1 * x
d, x, y = map(r, number_theory_functions.extended_gcd(a, b))
print(f"{d} = {x}a + {y}b ")
print(
f"Iron man will give {x} million bills and loki will give back {y} coins"
)
N = 12215009
e = 3499
d = 5425399
rsa = RSA((N, e), (N, d))
m = 42
print(rsa.decrypt(rsa.encrypt(m)))
unittest.main()