环Z_n上圆锥曲线和公钥密码协议  

The Conic Curves over Z_n and Public-Key Cryptosystem Protocol

作　　者：孙琦[1] 朱文余[1] 王标 

机构地区：[1]四川大学数学学院

出　　处：《四川大学学报（自然科学版）》2005年第3期471-478,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：现代通信国家重点实验室基金项目(51436010505SC0101)

摘　　要：通过对Zn上圆锥曲线Cn(a,b)定义加法运算,证明了Zn上的圆锥曲线Cn(a,b)在所定义的加法运算下构成一个有限交换群.特别地,给出了点之间运算的直接公式,并进一步对Zn上圆锥曲线Cn(a,b)的基本性质进行了深入的讨论,为各种密码协议在Cn(a,b)上模拟提供了可能性.作为一个例子,给出了基于环Zn上的圆锥曲线的一类数字签名方案,它是KMOV方案在Cn(a,b)上的模拟.This paper defines an operation on the rational points of conic curves C_n(a,b) over the residue class ring Z_n. This operation is called addtion forces C_n(a,b) into a finite abelian group. In specialty, the authors give an explicit formula of an operation on the points of conic carves, and make extensive discussion on the fundamental properties of conic curves over Z_n, which makes it possible to eatablish various kinds of cryptographic protocols over the conics. As an application, they propose a digital signature scheme over C_n(a,b), which may be regarded as an analogue of KMOV based on conics.

关 键 词：环Zn 圆锥曲线 数字签名方案 

分 类 号：O156.1[理学—数学]