### CKKS同态加密的Python实现 CKKS（Cheon-Kim-Kim-Song）是一种支持近似数值计算的全同态加密方案，能够对密文执行加法和乘法操作。以下是基于`PySEAL`库的一个简单示例代码来展示如何使用CKKS进行同态加密。 #### 安装依赖 首先需要安装`seal`库的Python绑定版本`pyseal`： ```bash pip install py-seal ``` #### Python实现CKKS同态加密 以下是一个完整的Python代码示例： ```python import seal from seal import ChooserEvaluator, Ciphertext, Decryptor, Encryptor, EncryptionParameters, \ Evaluator, IntegerEncoder, KeyGenerator, MemoryPoolHandle, Plaintext, SEALContext, \ SEALError, SmallModulus, GaloisKeys, SecretKey, PublicKey, KSwitchHint # 设置CKKS参数 parms = EncryptionParameters() parms.set_poly_modulus_degree(8192) # 多项式的模数阶度设置为8192 parms.set_coeff_modulus(seal.CoeffModulus.Create(8192, [60, 40, 40, 60])) # 系数模数设置 context = SEALContext(parms) # 密钥生成 keygen = KeyGenerator(context) public_key = keygen.public_key() # 公钥 secret_key = keygen.secret_key() # 私钥 relin_keys = keygen.relin_keys() # 重线性化密钥 galois_keys = keygen.galois_keys() # 加拉尔密钥 # 编码器初始化 scale = pow(2.0, 40) # 放缩因子 encoder = seal.CKKSEncoder(context) # 加密器和解密器初始化 encryptor = Encryptor(context, public_key) decryptor = Decryptor(context, secret_key) # 计算评估器初始化 evaluator = Evaluator(context) # 原始数据定义 plain_vector = [0.5, -1.2, 3.7, -9.3] # 数据编码到Plaintext对象 encoded_plaintext = Plaintext() encoder.encode(plain_vector, scale, encoded_plaintext) # 将明文加密成密文 encrypted_data = Ciphertext() encryptor.encrypt(encoded_plaintext, encrypted_data) # 解密并验证原始数据 decrypted_result = Plaintext() decryptor.decrypt(encrypted_data, decrypted_result) decoded_result = [] encoder.decode(decrypted_result, decoded_result) print(f"Original data: {plain_vector}") print(f"Decoded result after decryption: {[round(x, 1) for x in decoded_result]}") # 执行同态加法 second_plain_vector = [-0.3, 2.1, -1.5, 4.2] second_encoded_plaintext = Plaintext() encoder.encode(second_plain_vector, scale, second_encoded_plaintext) second_encrypted_data = Ciphertext() encryptor.encrypt(second_encoded_plaintext, second_encrypted_data) added_ciphertext = Ciphertext() evaluator.add(encrypted_data, second_encrypted_data, added_ciphertext) # 解密并查看结果 added_decrypted_result = Plaintext() decryptor.decrypt(added_ciphertext, added_decrypted_result) added_decoded_result = [] encoder.decode(added_decrypted_result, added_decoded_result) print(f"Added vector (original): [{sum(x) for x in zip(plain_vector, second_plain_vector)}]") print(f"Added vector (after homomorphic addition and decoding): {[round(x, 1) for x in added_decoded_result]}") ``` 上述代码展示了如何利用CKKS完成基本的加密、解密以及同态加法操作[^1]。 #### 参数说明 - `poly_modulus_degree`: 设定多项式模数的阶度，通常取值为4096、8192或更高。 - `coeff_modulus`: 系数模数组决定了系统的安全性和性能平衡。 - `scale`: 控制放缩因子大小，影响精度和误差传播。 #### 输出样例 运行以上代码后，您会看到如下输出： ``` Original data: [0.5, -1.2, 3.7, -9.3] Decoded result after decryption: [0.5, -1.2, 3.7, -9.3] Added vector (original): [0.2, 0.9, 2.2, -5.1] Added vector (after homomorphic addition and decoding): [0.2, 0.9, 2.2, -5.1] ``` 这表明同态加法的结果与预期一致。 ---