改进的格上基于多身份全同态加密方案

Improved Multi-Identity Based Fully Homomorphic Encryption Scheme over Lattices

针对格上基于多身份的全同态加密方案（m IBFHE）中陷门函数低效的问题,提出一种改进的格上m IBFHE方案.首先利用MP12陷门函数结合对偶Regev算法构造出一种可转化的基于身份的加密（IBE）方案,并构造出一种支持标准模型下IBE方案转化的Mask系统;然后基于该系统利用特征向量思想将构造出的IBE方案转化为m IBFHE方案.对比分析结果表明,新方案较同类方案在陷门生成和原像采样阶段均有效率提升,且格的维数、密文和运算密文尺寸等明显缩短.在标准模型下,方案的安全性归约至格上容错学习问题的难解性,并包含严格的安全性证明.

Aiming at low efficiency of trapdoor function in multi-identity based fully homomorphic encryption（ m IBFHE） schemes,a new m IBFHE scheme was proposed. Firstly,the MP12 trapdoor function with Dual-Regev algorithm was combined to construct a transformable identity-based encryption（ IBE）scheme,and a Mask system which supports to transform IBE scheme presented to m IBFHE scheme under standard model. Then,based on presented Mask system and eigenvector idea,the IBE schemes was transformed to m IBFHE scheme. Comparing with the similar schemes,the efficiency of the scheme is improved in trapdoor generation and preimage sampling stage,and the lattice dimension,the size of ciphertext and evaluated ciphertext,etc. are obviously reduced. The security of the presented scheme strictly is reduced to the hardness of learning with errors problem in the standard model.