收稿日期: 2008-07-17
修回日期: 2009-04-29
网络出版日期: 2009-09-15
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
Received date: 2008-07-17
Revised date: 2009-04-29
Online published: 2009-09-15
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
李明 , 王鲲鹏 . 局部环Z/pZ上的椭圆曲线密码系统[J]. 中国科学院大学学报, 2009 , 26(5) : 695 -702 . DOI: 10.7523/j.issn.2095-6134.2009.5.016
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.
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