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计算机工程 ›› 2009, Vol. 35 ›› Issue (22): 155-158. doi: 10.3969/j.issn.1000-3428.2009.22.053

• 安全技术 • 上一篇    下一篇

Eisenstein环上的圆锥曲线公钥密码系统

潘 瑞,王丽君,李端端,李 旭   

  1. (辽宁科技大学计算机科学与工程学院,鞍山 114051)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2009-11-20 发布日期:2009-11-20

Public Key Cryptosystem for Conic Curve over Eisenstein Ring

PAN Rui, WANG Li-jun, LI Duan-duan, LI Xu   

  1. (College of Computer Science and Engineering, University of Science and Technology Liaoning, Anshan 114051)
  • Received:1900-01-01 Revised:1900-01-01 Online:2009-11-20 Published:2009-11-20

摘要:

为了实现安全有效的曲线密码系统,引入Eisenstein环 。论述剩余类环 上圆锥曲线 的基本性质,证明 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 构成一个有限的Abel群。验证在 上寻找基点的算法适用于 ,给出ElGamal密码系统在 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。

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

Abstract: In order to realize secure and effective curves cryptosystem over curves, this paper introduces Eisenstein ring . It discusses some basic properties of conic curve over the residue class ring . 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 . It validates that the algorihtm which is used for finding a base point over is suitable for . Numerical simulation of ElGamal cryptosystem over 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.

Key words: residue class ring, impartibility number, conic curve discrete logarithm, public key cryptosystem, numerical simulation

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