多属性环境下基于容错学习的全同态加密方案

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-basedC]//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。

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

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-basedC]//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.