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.
出处
《计算机工程》
CAS
CSCD
北大核心
2009年第22期155-158,共4页
Computer Engineering
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
residue class ring
impartibility number
conic curve discrete logarithm
public key cryptosystem
numerical simulation
