python实现RSA加密算法

以下是Python实现RSA加密算法的示例代码：

import random
import math

def is_prime(num):
    """
    判断一个数是否为素数
    """
    if num <= 1:
        return False
    for i in range(2, int(math.sqrt(num)) + 1):
        if num % i == 0:
            return False
    return True

def gcd(a, b):
    """
    求两个数的最大公约数
    """
    if b == 0:
        return a
    else:
        return gcd(b, a % b)

def generate_key(p, q):
    """
    生成RSA公钥和私钥
    """
    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 = inverse(e, phi)
    return ((e, n), (d, n))

def inverse(a, m):
    """
    求a在模m意义下的逆元
    """
    x, y, r = 0, 1, m
    u, v, s = 1, 0, a
    while s != 0:
        q = r // s
        r, s = s, r - q * s
        x, u = u, x - q * u
        y, v = v, y - q * v
    return x % m

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

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

# 生成RSA公钥和私钥
p = 61
q = 53
public_key, private_key = generate_key(p, q)
print("公钥：", public_key)
print("私钥：", private_key)

# 加密数据
plaintext = "Hello, world!"
ciphertext = encrypt(public_key, plaintext)
print("加密后的数据：", ciphertext)

# 解密数据
plaintext = decrypt(private_key, ciphertext)
print("解密后的数据：", plaintext)