多密钥全同态加密的研究现状与发展趋势

Research and development trend of multi⁃key encryption schemes

全同态加密是隐私保护的一种技术,可以使数据在密文状态下进行运算且运算结果解密之后与在明文状态下的运算结果一致。多密钥全同态加密允许在不同密钥下加密的密文之间进行同态操作。加密方案中存在密钥交换、密文扩展等影响运算效率的多项式函数,而且投入实际应用的方案需具备良好的计算效率。以同态加密的3个发展阶段为分水岭,分别梳理每一阶段的多密钥全同态加密的基本构造流程并分析学者们对其进行的核心优化方法。最后简要讨论多密钥全同态加密方案面临的问题并展望未来可能的优化方向。

The full homomorphic encryption is a privacy protection technology that ensures that the data can be operated in the ciphertext state and the results are consistent with those of the operation in the plaintext state.The multi⁃key fully homomorphic encryption(MFHE)allows the homomorphic operation between ciphertexts encrypted under different keys.An encryption scheme contains polynomial functions,such as key exchange and ciphertext extension,which affects the computing efficiency and imposes challenges on its applications.In this paper,based on its three development stages,the multi⁃key homomorphic encryption is profoundly investigated;and the basic construction process and the core optimization methods of each stage are well analyzed.Finally,challenges and future directions of the multi⁃key fully homomorphic encryption are discussed.