Eisenstein环上的圆锥曲线公钥密码系统  

Public Key Cryptosystem for Conic Curve over Eisenstein Ring

作　　者：潘瑞[1] 王丽君[1] 李端端[1] 李旭[1] 

机构地区：[1]辽宁科技大学计算机科学与工程学院,鞍山114051

出　　处：《计算机工程》2009年第22期155-158,共4页Computer Engineering

摘　　要：为了实现安全有效的曲线密码系统,引入Eisenstein环Z[ω]。论述剩余类环Z[ω]/(r)上圆锥曲线Cr(a,b)的基本性质,证明Cr(a,b)中分别用映射方式和坐标方式定义的2种加法运算的一致性,以(Cr(a,b),⊕)构成一个有限的Abel群。验证在Cn(a,b)上寻找基点的算法适用于Cr(a,b),给出ElGamal密码系统在Cr(a,b)上的数值模拟,结果表明改进后的圆锥曲线密码系统具有明文嵌入方便、运算速度快、易于实现的优点。In order to realize secure and effective curves cryptosystem over curves, this paper introduces Eisenstein ring Z[ω]. It discusses some basic properties of conic curve Cr（a,b） over the residue class ring Z[ω]/（r）. It is proved that the two kinds of addition algorithms respectively defined by mapping manner and coordinate manner are consistent with each other. A limited Abel group is composed by （Cr （a, b）, ＋）. It validates that the algorihtm which is used for finding a base point over C,, （a,b） is suitable for Cr （a,b）. Numerical simulation of ElGamal cryptosystem over C （a,b） is given, and the results show that the improved conic curve cryptosystem has several merits such as being easy to embed plaintext, high computing speed and easy to be implemented.

关 键 词：剩余类环 不可分数 圆锥曲线离散对数 公钥密码系统 数值模拟 

分 类 号：TP309.2[自动化与计算机技术—计算机系统结构]