信息安全研究 ›› 2016, Vol. 2 ›› Issue (3): 220-224.

• 学术论文 • 上一篇    下一篇

一种基于LWE的同态加密方案

张峰娟   

  1. 西安电子科技大学通信工程学院
  • 收稿日期:2016-03-15 出版日期:2016-03-15 发布日期:2016-03-16
  • 通讯作者: 张峰娟
  • 作者简介:硕士,主要研究方向为密码学、信息安全、同态加密.

A Fully Homomorphic Encryption Scheme Based LWE

  • Received:2016-03-15 Online:2016-03-15 Published:2016-03-16

摘要: 目前同态加密体制主要建立在2个主要的问题之上:Regev的错误学习问题(LWE)和HowgraveGraham的近似最大公因子问题(AGCD).首先把LWE问题规约到AGCD问题上,然后基于AGCD问题,提出一种加法同态加密体制.与之前的体制相比较,其安全性不依赖于所谓的稀疏子集合求和问题(SSSP)的假定困难性,而是仅仅依赖于LWE问题的困难性.最后,给出了正确性分析和安全性证明.

关键词: 全同态加密, LWE, AGCD, 规约

Abstract: Two main problems serve as foundations of current homomorphic encryption schemes: Regevs learning with errors problem (LWE) and HowgraveGrahams approximate greatest common divisor problem (AGCD). Firstly, we introduce a reduction from LWE to AGCD. Secondly, we propose a new AGCDbased additive homomorphic encryption scheme, which outperforms previous proposals: its security does not rely on the presumed hardness of the socalled sparse subset sum problem (SSSP), but on the hardness of LWE. Lastly, correctness analysis and security proof are given.

Key words: full homomorphic encryption, LWE, AGCD, reduction