一整套RSA文件加密算法源代码

以下是Python实现的一整套RSA文件加密算法源代码：

import os
import random
import math

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

def gcd(a, b):
    """计算a和b的最大公约数"""
    while b != 0:
        a, b = b, a % b
    return a

def extended_gcd(a, b):
    """计算a和b的最大公约数以及贝祖等式中的x和y"""
    if b == 0:
        return (a, 1, 0)
    else:
        d, x, y = extended_gcd(b, a % b)
        return (d, y, x - (a // b) * y)

def generate_keypair(p, q):
    """生成公钥和私钥"""
    n = p * q
    phi = (p - 1) * (q - 1)
    e = random.randint(1, phi-1)
    while gcd(e, phi) != 1:
        e = random.randint(1, phi-1)
    d = extended_gcd(e, phi)[1]
    if d < 0:
        d += phi
    return ((e, n), (d, n))

def encrypt_file(filename, public_key):
    """使用公钥加密文件"""
    e, n = public_key
    with open(filename, 'rb') as f:
        plaintext = f.read()
    ciphertext = [pow(byte, e, n) for byte in plaintext]
    with open(filename + '.enc', 'wb') as f:
        for byte in ciphertext:
            f.write(byte.to_bytes((byte.bit_length()+7)//8, 'big'))

def decrypt_file(filename, private_key):
    """使用私钥解密文件"""
    d, n = private_key
    with open(filename, 'rb') as f:
        ciphertext = []
        while True:
            byte = f.read(1)
            if not byte:
                break
            ciphertext.append(int.from_bytes(byte, 'big'))
    plaintext = [pow(byte, d, n) for byte in ciphertext]
    with open(os.path.splitext(filename)[0], 'wb') as f:
        for byte in plaintext:
            f.write(byte.to_bytes((byte.bit_length()+7)//8, 'big'))

if __name__ == '__main__':
    p = 61
    q = 53
    if not (is_prime(p) and is_prime(q)):
        raise ValueError('p和q必须是素数！')
    public_key, private_key = generate_keypair(p, q)
    filename = 'test.txt'
    with open(filename, 'w') as f:
        f.write('Hello, World!')
    encrypt_file(filename, public_key)
    decrypt_file(filename + '.enc', private_key)
    with open(filename, 'r') as f:
        original_text = f.read()
    with open(os.path.splitext(filename)[0], 'r') as f:
        decrypted_text = f.read()
    print('公钥：', public_key)
    print('私钥：', private_key)
    print('原始文本：', original_text)
    print('解密后的文本：', decrypted_text)

在这个示例中，我们使用61和53两个素数生成RSA加密算法的公钥和私钥，并使用公钥加密一个文本文件，然后使用私钥解密该文件。注意，为了简化示例，我们使用了ASCII码来表示字符，但在实际应用中，我们应该使用更安全的加密方式来保护敏感信息。