Journal of Computer Applications ›› 2018, Vol. 38 ›› Issue (5): 1377-1382.DOI: 10.11772/j.issn.1001-9081.2017102568

Previous Articles     Next Articles

Fully homomorphic encryption scheme based on learning with errors under multi-attribute environment

BAI Ping1, ZHANG Wei1,2   

  1. 1. College of Cryptographic Engineering, Engineering College of Armed Police Force, Xi'an Shaanxi 710086, China;
    2. Key Laboratory of Network and Information Security, Engineering College of Armed Police Force, Xi'an Shaanxi 710086, China
  • Received:2017-10-30 Revised:2017-12-06 Online:2018-05-10 Published:2018-05-24
  • Contact: 白平
  • Supported by:
    This work is partially supported by the National Cryptography Development Fund of China (MMJJ20170112), the Natural Science Foundation of Shaanxi Province (2016JQ6037).


白平1, 张薇1,2   

  1. 1. 武警工程大学 密码工程学院, 西安 710086;
    2. 武警工程大学 信息安全保密重点实验室, 西安 710086
  • 通讯作者: 白平
  • 作者简介:白平(1990-),男,内蒙古乌兰察布人,硕士研究生,主要研究方向:密码学;张薇(1976-),女,陕西西安人,教授,博士,主要研究方向:密码学、信息安全。
  • 基金资助:

Abstract: Learning With Errors (LWE)-based fully homomorphic encryption scheme was presented by Gentry, Sahai and Waters (GENTRY C, SALAHAI A, WATERS B. Homomorphic encryption from learning with errors:conceptually-simpler, asymptotically-faster, attribute-based[C]//Proceedings of the 33rd Annual Cryptology Conference. Berlin:Springer, 2013:75-92), namely GSW scheme, can only work under single-attribute settings. Aiming at this problem and introducing the concept of fully system, a fully homomorphic encryption scheme under multi-attribute settings was constructed. In the proposed scheme, whether a user was legitimate was determined through a conditional equation. Then, a new ciphertext matrix that meeting the requirements of GSW13 was constructed by using ciphertext expansion algorithm. Finally fuzzy system technology was used to complete the construction. INDistinguishability-X-Chosen Plain Attack (IND-X-CPA) security was proved under the standard model. The advantage of the proposed scheme lies in that it can be used in multi-attribute environment. The disadvantage is that the computational complexity is increased.

Key words: fully homomorphic encryption, fuzzy system, privacy protection, attribute-based encryption, learning with errors problem

摘要: 针对Gentry、Sahai和Waters提出的基于容错学习(LWE)问题全同态加密方案(GENTRY C,SALAHAI A,WATERS B.Homomorphic encryption from learning with errors:conceptually-simpler,asymptotically-faster,attribute-based[C]//Proceedings of the 33rd Annual Cryptology Conference.Berlin:Springer,2013:75-92)中只能在单个属性环境下工作的问题,通过借鉴"模糊系统"技术,构造了多属性环境下基于LWE的全同态加密方案。首先根据条件等式判断是否为合法用户,然后利用密文扩展算法构造新的密文矩阵,最后采用"模糊系统"技术进行方案构造。在标准的基于X不可区分的选择明文攻击(IND-X-CPA)安全游戏中证明了安全性。所提方案优点是可以将满足一定属性的基于属性加密(ABE)方案转换成多属性环境下的全同态加密方案,缺陷是运算复杂度有所增加。

关键词: 全同态加密, 模糊系统, 隐私保护, 属性加密, 容错学习问题

CLC Number: