| 局部环Z/pZ上的椭圆曲线密码系统 |
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| 引用本文： | 李明,王鲲鹏.局部环Z/pZ上的椭圆曲线密码系统[J].中国科学院研究生院学报,2009,26(5):695-702. |
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| 作者姓名： | 李明 王鲲鹏 |
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| 作者单位： | 中国科学院研究生院信息安全国家重点实验室,北京,100049 |
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| 基金项目： | 中国高技术研究发展计划(863)项目，国家重点基础研究发展计划(973)项目 |
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| 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.
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| 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 |
| 收稿时间： | 2008-07-17 |
| 修稿时间： | 2009-04-29 |
Cryptosystem based on elliptic curve over local ring Z/pnZ |
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| LI Ming,WANG Kun-Peng.Cryptosystem based on elliptic curve over local ring Z/pnZ[J].Journal of the Graduate School of the Chinese Academy of Sciences,2009,26(5):695-702. |
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| Authors: | LI Ming WANG Kun-Peng |
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| Institution: | State Key Lab of Information Security,Graduate University of the Chinese Academy of Sciences,Beijing 100049,China |
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| 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. |
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| Keywords: | elliptic curve cryptography elliptic curves over local ring Z/pnZ complete system role-based cryptosystem |
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