多属性环境下基于容错学习的全同态加密方案

摘要

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.%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.