公钥密码体制的同态性分析

同态加密算法是基于秘密同态的概念,是秘密同态的一个子集。同态加密技术可以对加密数据直接进行运算,并且运算结果也自动加密。正是基于此,使得同态加密技术在安全多方计算、数据库加密、电子投票等领域具有广泛的应用。同态特性主要包括加法特性、乘法特性、混合乘法特性。文章对目前广泛应用的三大公钥密码体制的同态特性进行了分析,并对满足加法同态的Pallier密码体制进行了研究。为后续研究全同态加密算法提供理论基础和方法指导。

The Homomorphism Analysis of Public Key Cryptosystem

Homomorphic encryption algorithm is based on the concept of homomorphism,which is a subset of the homomorphism.Homomorphic encryption technology can do the operation to ciphertext directly,the operation results can be encrypted automatically,and the technology has a very broad application in secure multi-party computation,data encryption,electronic voting and other fields.A Homomorphic property includes additively homomorphism,multiplicatively homomorphism,and mixed multiplicatively homomorphism.We study the homomorphic property of the three public key cryptosystem widely used now,and analyze Pallier cryptosystem that meets additively homomorphism,which can provide theoretical basis and guidance to the follow-up study of fully homomorphic encryption algorithm.