Lattice-based linearly homomorphic signature scheme over binary field  

作　　者：WANG FengHe HU YuPu WANG BaoCang 

机构地区：[1]Key Laboratory of Computer Networks and Information Security of Ministry of Education, Xidian University [2]Department of Mathematics and Physics, Shandong Jianzhu University

出　　处：《Science China(Information Sciences)》2013年第11期234-242,共9页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.60970119,61173151,61173152)

摘　　要：To design an efficient post-quantum linearly homomorphic signature scheme, using the pre-image sampling function, a lattice-based linearly homomorphic signature scheme over a binary field is proposed in this paper. Linear homomorphism is achieved through the homomorphism of the lattice-based hash function used in the proposed signature scheme. It is shown that the proposed scheme satisfies the privacy property. Based on the hardness of the short integer solution problem, the proposed scheme is unforgeahle against the type 1 and type 2 adversaries in the random oracle model. Moreover, compared with a presented linearly homomorphic signature scheme in 2011, the proposed scheme has some advantages with respect to the public key size, signature length and computational cost.To design an efficient post-quantum linearly homomorphic signature scheme, using the pre-image sampling function, a lattice-based linearly homomorphic signature scheme over a binary field is proposed in this paper. Linear homomorphism is achieved through the homomorphism of the lattice-based hash function used in the proposed signature scheme. It is shown that the proposed scheme satisfies the privacy property. Based on the hardness of the short integer solution problem, the proposed scheme is unforgeahle against the type 1 and type 2 adversaries in the random oracle model. Moreover, compared with a presented linearly homomorphic signature scheme in 2011, the proposed scheme has some advantages with respect to the public key size, signature length and computational cost.

关 键 词：linearly homomorphic signature LATTICE short integer solution problem pre-image sampling function 

分 类 号：TN918.1[电子电信—通信与信息系统]