公钥密码体制的同态性分析

摘要

Homomorphic encryption algorithm is based on the concept of homomorphism, which is a subset ot the homomorphism. Homomorphic encryption technology can do the operation to ciphertext directly, the op- eration 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 in- cludes additively homomorphism, muhiplicatively homomorphism, and mixed multiplicatively homomor- phism. We study the homomorphic property of the three public key cryptosystem widely used now, and ana- lyze Pallier cryptosystem that meets additively homomorphism, which can provide theoretical basis and guid- ance to the follow - up study of fully homomorphic encryption algorithm.%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。