cramer shoup 加密代码

Cramer-Shoup加密算法是一种公钥加密算法，由Victor Shoup在1997年提出。它是基于一种离散对数问题构造的加密方案，可以提供安全的加密、解密和签名操作。

下面是一个简单的Python实现，使用了pycryptodome库来提供加密、解密和哈希函数：

from Crypto.Util.number import getPrime, bytes_to_long
from Crypto.Random.random import randint

class CramerShoup:
    def __init__(self, bits):
        p_size = bits // 2
        q_size = bits - p_size
        self.p = getPrime(p_size)
        self.q = getPrime(q_size)
        self.g1 = pow(randint(2, self.p - 1), (self.p - 1)//self.q, self.p)
        self.g2 = pow(randint(2, self.p - 1), (self.p - 1)//self.q, self.p)
        self.x1 = randint(2, self.q - 1)
        self.x2 = randint(2, self.q - 1)
        self.y1 = pow(self.g1, self.x1, self.p)
        self.y2 = pow(self.g1, self.x2, self.p)
        self.h = pow(self.g2, self.x1 * self.x2, self.p)

    def encrypt(self, msg):
        m = bytes_to_long(msg.encode())
        r = randint(2, self.q - 1)
        u1 = pow(self.g1, r, self.p)
        u2 = pow(self.g2, r, self.p)
        e = pow(self.h, r, self.p) * m % self.p
        c = (u1, u2, e)
        return c

    def decrypt(self, c):
        u1, u2, e = c
        v = pow(u1, self.x2, self.p)
        w = pow(u2 * pow(self.y2, e, self.p) % self.p, self.x1, self.p)
        m = e * pow(v, self.p - 2, self.p) % self.p * pow(w, self.p - 2, self.p) % self.p
        return m.to_bytes((m.bit_length() + 7) // 8, 'big').decode()

    def sign(self, msg):
        m = bytes_to_long(msg.encode())
        k = randint(2, self.q - 1)
        r = pow(self.g1, k, self.p)
        h = int.from_bytes(hash(msg.encode()), 'big') % self.q
        s = (k + self.x1 * h) % self.q
        t = (self.x2 * h + k * s) % self.q
        sigma = (r, s, t)
        return sigma

    def verify(self, msg, sigma):
        r, s, t = sigma
        h = int.from_bytes(hash(msg.encode()), 'big') % self.q
        u1 = pow(self.g1, t, self.p) * pow(self.y1, s, self.p) % self.p
        u2 = pow(self.g2, t, self.p) * pow(self.y2, s, self.p) % self.p
        v = pow(self.g1, h, self.p) * r % self.p
        if u1 == v:
            return True
        else:
            return False

使用示例：

# 初始化密钥对
cs = CramerShoup(256)

# 加密消息
msg = "Hello, World!"
c = cs.encrypt(msg)
print("Encrypted message:", c)

# 解密消息
m = cs.decrypt(c)
print("Decrypted message:", m)

# 签名消息
sigma = cs.sign(msg)
print("Signature:", sigma)

# 验证签名
if cs.verify(msg, sigma):
    print("Signature is valid")
else:
    print("Signature is not valid")

注意：这是一个简单的实现，没有进行任何优化和安全性分析。在实际应用中，请使用经过验证的加密库和算法。