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有限素整数域椭圆曲线密码体制基于代数几何快速算法设计
引用本文:卢忱,严立军,卞正中.有限素整数域椭圆曲线密码体制基于代数几何快速算法设计[J].计算机工程与应用,2002,38(16):63-65,225.
作者姓名:卢忱  严立军  卞正中
作者单位:1. 西安交通大学,西安,710049
2. 第四军医大学,西安,710086
基金项目:国家自然科学基金资助项目(编号:69771005),国家863高技术研究发展计划课题(编号:301-3-2)
摘    要:椭圆曲线公钥密码体制(ECC)具有最高的位安全强度,将是对现有公钥密码体制的替代。文章描述了代数几何与ECC的数学基础,讨论了椭圆曲线离散对数困难性问题及ECC在电子商务中的安全应用。利用仿射坐标与射影坐标的映射关系,设计了一种有限素整数域上ECC快速算法,使得ECC在电子商务中实际安全应用成为可能。

关 键 词:PKI  有限域  椭圆曲线  点积  离散对数  代数几何  电子商务
文章编号:1002-8331-(2002)16-0063-03

Fast Arithmetic Design Based on Algabriac Geometry of Elleptic Curve Cryptosystem over Finite Prime Field
Lu Chen,Yan Lijun,Bian Zhengzhong.Fast Arithmetic Design Based on Algabriac Geometry of Elleptic Curve Cryptosystem over Finite Prime Field[J].Computer Engineering and Applications,2002,38(16):63-65,225.
Authors:Lu Chen  Yan Lijun  Bian Zhengzhong
Affiliation:Lu Chen 1 Yan Lijun 2 Bian Zhengzhong 11
Abstract:The Elliptic Curve Cryptosystem(ECC)provides the highest strength-per-bit of any cryptosystem known today.This paper describes the mathematics base of algebraic geometry and ECC.This paper also discusses the Elliptic curve discrete logarithm problem(ECDLP)and the security applications of ECC on E_commerce.A fast arithmetic of ECC based over finite prime field is designed by the map of between affine coordinates and projective coordinates.This make it possible that ECC's practical applications in the Electronic commerce.
Keywords:PKI  Finite Field  Elliptic curve  Point  Multiplication  Discrete logrithm  algebraic geometry  Electronic Commerce
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