97 lines
2.1 KiB
Python
97 lines
2.1 KiB
Python
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from random import choice
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def gcd(a: int, b: int) -> int:
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if b == 0:
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return a
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return gcd(b, a % b)
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def gcd_extended(a: int, b: int) -> tuple[int, int, int]:
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if b == 0:
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return a, 1, 0
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gcd, x, y = gcd_extended(b, a % b)
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return gcd, y, x - (a // b) * y
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def mod_inverse(n: int, x: int) -> int:
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inv_x = gcd_extended(n, x)[2]
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if inv_x <= 0:
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inv_x += n
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return inv_x
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def mod_extended(x: int, y: int, n: int) -> int:
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if y == 0:
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return 1
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z = mod_extended(x, y // 2, n)
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if y % 2 == 0:
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return (z * z) % n
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return (x * z * z) % n
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def generate_keys(p: int, q: int) -> tuple[tuple[int, int], tuple[int, int]]:
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n = p * q
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phi = (p - 1) * (q - 1)
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e = 3
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for ferm_number in [5, 17, 257, 65537]:
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if ferm_number < phi:
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e = ferm_number
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d = mod_inverse(phi, e)
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return (e, n), (d, n)
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def encrypt(message: str, key: tuple[int, int]):
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e, n = key
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encrypted_message = [mod_extended(ord(char), e, n) for char in message]
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return encrypted_message
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def decrypt(encrypted_message: str, key: tuple[int, int]):
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d, n = key
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decrypted_message = [chr(mod_extended(char, d, n))
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for char in encrypted_message]
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return "".join(decrypted_message)
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def get_primes(n: int):
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sieve = [True] * n
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primes = []
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for p in range(2, n):
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if sieve[p]:
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primes.append(p)
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for i in range(p * p, n, p):
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sieve[i] = False
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return primes
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def main() -> None:
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primes = get_primes(100000)
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p = choice(primes)
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q = choice(primes)
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while p == q:
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q = choice(primes)
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message = "Lorem ipsum dolor sit amet, consectetur adipiscing elit."
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public, private = generate_keys(p, q)
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encrypted_message = encrypt(message, public)
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decrypted_message = decrypt(encrypted_message, private)
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print("Public key: ", public)
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print("Private key:", private)
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print("Original message: ", message)
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print("Encrypted message:", "".join(map(str, encrypted_message)))
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print("Decrypted message:", decrypted_message)
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if __name__ == "__main__":
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main()
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