使用python实现RSA加密解密算法

RSA加密解密算法是一种非对称加密算法，需要使用公钥和私钥进行加密和解密。下面是使用Python实现RSA加密解密算法的示例代码：

import random
from math import gcd

def generate_key(p, q):
    n = p * q
    phi = (p - 1) * (q - 1)
    e = random.randrange(1, phi)
    g = gcd(e, phi)
    while g != 1:
        e = random.randrange(1, phi)
        g = gcd(e, phi)
    d = mod_inverse(e, phi)
    return ((e, n), (d, n))

def mod_inverse(a, m):
    g, x, y = extended_gcd(a, m)
    if g != 1:
        raise Exception('No modular inverse')
    return x % m

def extended_gcd(a, b):
    if a == 0:
        return (b, 0, 1)
    else:
        g, y, x = extended_gcd(b % a, a)
        return (g, x - (b // a) * y, y)

def encrypt(pk, plaintext):
    key, n = pk
    cipher = [pow(ord(char), key, n) for char in plaintext]
    return cipher

def decrypt(pk, ciphertext):
    key, n = pk
    plain = [chr(pow(char, key, n)) for char in ciphertext]
    return ''.join(plain)

p = 61
q = 53
public_key, private_key = generate_key(p, q)

message = 'Hello, world!'
print('Original message:', message)

ciphertext = encrypt(public_key, message)
print('Encrypted message:', ciphertext)

plaintext = decrypt(private_key, ciphertext)
print('Decrypted message:', plaintext)

在上面的实现中，我们首先定义了一些函数来生成RSA密钥、模反元素以及扩展欧几里得算法。然后，我们使用生成的公钥和私钥对原始消息进行加密和解密。