基于群环上的公钥密码体制  

A public-key cryptosystem based on the group rings

作　　者：郭瑞[1] 李志慧[1] 毛卫霞[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2009年第4期6-10,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60873119);陕西省自然科学基础研究计划资助项目(2007A06)

摘　　要：给出了基于群环上的离散对数问题的公钥密码体制.利用有限域上一般线性群中矩阵的阶等于其Jordan标准形的阶这一结论,结合有限域上线性代数的有关理论,给出了基于一般线性群上的一类交换群环中可逆元的存在性以及构造方法,并说明在这一群环上存在离散对数问题,利用这一群环的良好的密码性质构造出基于群环上的公钥加密体制.对该密码体制的安全性以及对加密解密计算代价和密码体制的实现方法进行了讨论,并用实例证明了该密码体制的可行性.The public-key cryptosystem based on discrete logarithm over group rings is proposed.Using the fact that the order of a matrix in the general linear group on a finite field is equal to that of its Jordan s normal form and the linear algebra theory over finite field,the existence and construction of invertible elements in a kind of commutative group rings based on a general linear group are given,and it is shown that the problem of discrete logarithm problem exists in these group rings.Using these good cryptography properties in these group rings, a public-key cryptosystem based on them is given. At last, the security level of this cryptosystem, the cost of computation and the method of implementation are discussed. Also, the feasibility of this cryptography is proved by an example.

关 键 词：群环 自同构 离散对数问题 一般线性群 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]