基于小整数解问题上的格签名方案及其应用

Lattice signature and its application based on small integer solution problem

在随机预言模型下,基于小整数解(SIS)困难问题,提出了一种格签名方案,说明了格签名方案的参数选取规则。文中选取不同参数生成的签名密钥长度进行对比;然后论证该签名的安全性和有效性;最后,为了解决认证方案中对多方认证的公平性、同时性和可靠性问题,将签名方案与保密通信中的密钥分发和托管结合起来,基于数学上矩阵分解理论的奇异值分解(SVD)算法,提出一种新的授权与认证方案。

A lattice signature scheme was proposed and some parameter choosing rules were illustrated concerning Small Integer Solution （SIS） problem and random oracle model of lattice. Then the results of the length of the keys that were generated under different parameter circumstances were compared. Afterwards the security and efficiency with the signature scheme were verified. At last, for the purpose of fairness, and reliability in multipartite authentication, the signature scheme was combined with key distribution and escrow, a new authentication scheme with the Singular Value Decomposition （SVD） algorithm based on mathematical matrix decomposition theory was proposed.