将下面代码修改成正确格式并加上注释 import random import math def is_prime(number): if number < 2: return False for i in range(2, int(number ** 0.5) + 1): if number % i == 0: return False return Truedef generate_key(length): while True: p = random.randint(2 ** (length//2 - 1), 2 ** (length//2)) if is_prime(p): break while True: q = random.randint(2 ** (length//2 - 1), 2 ** (length//2)) if is_prime(q) and q != p: break n = p * q phi_n = (p - 1) * (q - 1) while True: e = random.randint(2, phi_n - 1) if math.gcd(e, phi_n) == 1: break d = pow(e, -1, phi_n) public_key = (n, e) private_key = (n, d) return public_key, private_keydef encrypt(message, public_key): n, e = public_key m = int.from_bytes(message.encode(), 'big') c = pow(m, e, n) return c.to_bytes((c.bit_length() + 7) // 8, 'big') def decrypt(ciphertext, private_key): n, d = private_key c = int.from_bytes(ciphertext, 'big') m = pow(c, d, n) return m.to_bytes((m.bit_length() + 7) // 8, 'big') def main(): message = "Hello, this is a test message!" print("Original message:", message) public_key, private_key = generate_key(512) print("Public key:", public_key) print("Private key:", private_key) encrypted_message = encrypt(message, public_key) print("Encrypted message:", encrypted_message) decrypted_message = decrypt(encrypted_message, private_key) print("Decrypted message:", decrypted_message.decode()) if __name__ == "__main__": main()

下面是修改后的代码，加上了注释，更易于理解：

import random
import math

def is_prime(number):
    """
    判断一个数字是否为质数
    """
    if number < 2:
        return False
    for i in range(2, int(number ** 0.5) + 1):
        if number % i == 0:
            return False
    return True

def generate_key(length):
    """
    生成公私密钥对
    """
    while True:
        p = random.randint(2 ** (length//2 - 1), 2 ** (length//2))
        if is_prime(p):
            break
    while True:
        q = random.randint(2 ** (length//2 - 1), 2 ** (length//2))
        if is_prime(q) and q != p:
            break
    n = p * q
    phi_n = (p - 1) * (q - 1)
    while True:
        e = random.randint(2, phi_n - 1)
        if math.gcd(e, phi_n) == 1:
            break
    d = pow(e, -1, phi_n)
    public_key = (n, e)
    private_key = (n, d)
    return public_key, private_key

def encrypt(message, public_key):
    """
    使用公钥加密消息
    """
    n, e = public_key
    m = int.from_bytes(message.encode(), 'big')
    c = pow(m, e, n)
    return c.to_bytes((c.bit_length() + 7) // 8, 'big')

def decrypt(ciphertext, private_key):
    """
    使用私钥解密消息
    """
    n, d = private_key
    c = int.from_bytes(ciphertext, 'big')
    m = pow(c, d, n)
    return m.to_bytes((m.bit_length() + 7) // 8, 'big')

def main():
    """
    主函数，调用其他函数实现RSA加密解密
    """
    message = "Hello, this is a test message!"
    print("Original message:", message)

    public_key, private_key = generate_key(512)
    print("Public key:", public_key)
    print("Private key:", private_key)

    encrypted_message = encrypt(message, public_key)
    print("Encrypted message:", encrypted_message)

    decrypted_message = decrypt(encrypted_message, private_key)
    print("Decrypted message:", decrypted_message.decode())

if __name__ == "__main__":
    main()