elgamal公钥加密算法代码

ElGamal公钥加密算法是一种基于离散对数问题的公钥加密算法。它的安全性依赖于计算离散对数的困难性。以下是一个简单的ElGamal公钥加密算法的Python实现： ```python import random def mod_inverse(a, m): def extended_gcd(aa, bb): if aa == 0: return (bb, 0, 1) else: g, y, x = extended_gcd(bb % aa, aa) return (g, x - (bb // aa) * y, y) g, x, _ = extended_gcd(a, m) if g != 1: raise Exception('Modular inverse does not exist') else: return x % m def generate_key(q): alpha = random.randint(2, q-2) d = random.randint(1, q-2) beta = pow(alpha, d, q) return ((alpha, q, beta), d) def encrypt(public_key, plaintext): alpha, q, beta = public_key k = random.randint(1, q-2) s = pow(beta, k, q) c1 = pow(alpha, k, q) c2 = (s * plaintext) % q return (c1, c2) def decrypt(public_key, private_key, ciphertext): alpha, q, beta = public_key c1, c2 = ciphertext s = pow(c1, private_key, q) s_inverse = mod_inverse(s, q) plaintext = (c2 * s_inverse) % q return plaintext # Example usage q = 2579 public_key, private_key = generate_key(q) plaintext = 1234 ciphertext = encrypt(public_key, plaintext) decrypted_text = decrypt(public_key, private_key, ciphertext) print(f"Public Key: {public_key}") print(f"Private Key: {private_key}") print(f"Plaintext: {plaintext}") print(f"Ciphertext: {ciphertext}") print(f"Decrypted Text: {decrypted_text}") ``` 这个代码示例展示了ElGamal公钥加密算法的基本实现，包括密钥生成、加密和解密过程。