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中国科学院大学学报 ›› 2009, Vol. 26 ›› Issue (5): 695-702.DOI: 10.7523/j.issn.2095-6134.2009.5.016

• 论文 • 上一篇    下一篇

局部环Z/pZ上的椭圆曲线密码系统

李明, 王鲲鹏   

  1. 中国科学院研究生院信息安全国家重点实验室,北京 100049
  • 收稿日期:2008-07-17 修回日期:2009-04-29 发布日期:2009-09-15
  • 通讯作者: 李明
  • 基金资助:

    中国高技术研究发展计划(863)项目(2006AA01Z427)和国家重点基础研究发展计划(973)项目(2007CB311201)资助 

Cryptosystem based on elliptic curve over local ring Z/pZ

LI Ming, WANG Kun-Peng   

  1. State Key Lab of Information Security,Graduate University of the Chinese Academy of Sciences,Beijing 100049,China
  • Received:2008-07-17 Revised:2009-04-29 Published:2009-09-15

摘要:

介绍了适用于环上椭圆曲线的加法公式,完善了局部环Z/pnZ上椭圆曲线密码学的基础理论,构造了环Z/pnZ上的基于角色的椭圆曲线密码系统.根据环Z/pnZ的结构特点,简化了其上椭圆曲线的加法完备系统,从而大大提高了环Z/pnZ上的椭圆曲线计算点加的效率;另外,给出了E(Z/pnZ)上密码群生成元的选取方法;证明Z/pnZ上的密码体系与有限域Fp的椭圆曲线密码体系有相同的安全程度;最后在环Z/pnZ上给出一个基于角色的椭圆曲线密码方案.

关键词: 椭圆曲线密码, Z/pnZ上的椭圆曲线, 完备系统, 基于角色的密码系统

Abstract:

We introduce the addition formula on E(R) where R denotes a ring,complete the theory of elliptic curve cryptography over local ring Z/pnZ,and propose a role-based cryptosystem on E(Z/pnZ).We analyze the structure of ring Z/pnZ.On the basis of the relation between Z/pnZ and Fp,we simplify the complete system of addition laws on E(Z/pnZ),which makes addition much more efficient than before.We present a method to select generators of the cryptographic groups.We prove that the security level of the ECC over local ring Z/pnZ is equal to that over finite field Fp.A role-based cryptosystem is proposed.

Key words: elliptic curve cryptography, elliptic curves over local ring Z/pnZ, complete system, role-based cryptosystem

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