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

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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).

多属性环境下基于容错学习的全同态加密方案

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:
    国家密码发展基金资助项目(MMJJ20170112);陕西省自然科学基金资助项目(2016JQ6037)。

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

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