基于剩余类环Z_n上圆锥曲线的公钥密码体制  

Public-key Cryptosystem Based on the Conic Curves over Z_n

作　　者：王标[1] 朱文余[1] 孙琦[1] 

机构地区：[1]四川大学数学学院

出　　处：《四川大学学报（工程科学版）》2005年第5期112-117,共6页Journal of Sichuan University (Engineering Science Edition)

基　　金：国家自然科学基金项目(10128103);现代通信国家重点实验室基金项目(51436010505sc0101)

摘　　要：为了实现更高效的曲线上的密码体制,讨论了当n为两个素数的乘积时剩余类环Zn上圆锥曲线Cn(a,b)的基本性质,证明Cn(a,b)中用映射方式和以坐标方式定义的两种运算是一致的,该运算使得Cn(a,b)的有理点构成Abel群。给出了在Cn(a,b)上寻找基点的简单方法,并给出RSA和ElGamal密码体制在Cn(a,b)上的模拟。这两类密码体制的安全性基于大数分解和有限Abel群(Cn(a,b),)上离散对数问题的困难性,具有明文嵌入方便、运算速度快、易于实现等优点。In order to get more efficient cryptosystem over curves , this paper discussed some basic properties of conic Cn （ a, b） over the residue class ring Zn, where n is the product of two primes . We proved that the rational points of Cn （ a, b） form an abelian group, whose operation may be given in two ways： one by reduction map and another by a formula with respect to the coordinates. And we also provided a simple method to find a base point. As applications, we gave analogues of RSA and EIGamal cryptosystem over Cn （ a, b ）. The two analogues are easy to implement and their seeurities are based on the difficulty of integer factorization and the discrete logarithm over Cn（ a, b ） respectively.

关 键 词：剩余类环 圆锥曲线离散对数 大数分解 公钥密码系统 数值模拟 标准二进制表示 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]