一种高效的同态加密方案及其应用  

Efficient Homomorphic Encryption and Its Application

作　　者：杨浩淼[1] 金保隆 陈诚 吴新沿 

机构地区：[1]电子科技大学计算机科学与工程学院&网络空间安全中心,成都611731

出　　处：《密码学报》2017年第6期611-619,共9页Journal of Cryptologic Research

基　　金：国家重点研发计划资助(2017YFB0802000);国家自然科学基金项目(U1633114)

摘　　要：随着云计算与大数据技术的发展,人们越来越关心数据的隐私保护.如何在隐私保护的前提下完成云计算或大数据分析成为一个热门的研究课题.同态加密方案允许在密文态下进行计算,从而可以在不泻露数据内容的情况下完成计算,理论上可以满足隐私保护计算的需求.自从Gentry的工作后,学者们提出了许多全同态密码方案,但由于这些密码方案进行同态计算的效率很低而难以实际应用.Zhou提出的VHE(vector homomorphic encryption)加密方案可以比较高效地进行整数向量的同态计算,该方案是Brakerski的PVW方案的整数扩展,但比PVW方案有更强的计算能力.但该方案存在一些安全问题,导致其在实际应用中面临诸多安全威胁.本文介绍了一种VHE的改进方案,该改进方案比原VHE方案效率更高,并且其安全强度更高.本文对该改进方案做出了初步的安全分析,试图给出其安全性描述.为了验证加密方案的同态计算效率,本文还基于改进后的方案构建了简单的邮件搜索应用,相较于原本的VHE方案,运算效率明显提高,加密数据时的内存需求也大大减小,使得该方案有了被应用在一般配置的计算机上的可能.With the development of cloud computing and data mining, user's data privacy becomes more and more valuable. Privacy preserved computation turns out to be a good subject. Homomorphic encryption schemes allow the calculation of ciphertext without secret key. The calculations can be completed without any privacy leaking in theory. Many homomorphic encryption schemes have been proposed based on Gentry's work, and most of them cannot be used practically because of their low performance. Zhou proposed a somewhat homomorphic encryption scheme named VHE, which was an integral extension of PVW proposed by Brakerski. As a result, VHE has higher ability than PVW.However its applications are limited because there are some security problems with VHE. This paper introduces an enhanced version of VHE, which possesses a higher performance and better security.Some security analysis on it is given trying to clarify its security limits. A simple demo is also given to test its performance in homomorphic calculation. It shows to have a much higher performance than the original VHE scheme, and require much less memory when perform encryptions. This makes it possible to build applications based on VHE for low performance machines.

关 键 词：VHE 同态加密 LWE问题 整数向量加 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]