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。该文描述了代数几何与ECC的数学基础及椭圆曲线离散对数问题困难性,讨论了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,设计了一种二进制扩域上ECC快速算法,使得ECC在电子商务中实际安全应用成为可能。
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. It also discusses the elliptic curve discrete logarithm problem (ECDLP) and the security applications of ECC on E-commerce . A fast arithmetic of ECC based on binary field is designed by the map of between affine coordinates and protective coordinates. This make it possible that ECC's practical applications in the electronic commerce.
出处
《计算机工程》
CAS
CSCD
北大核心
2003年第19期35-37,共3页
Computer Engineering
基金
国家自然科学基金资助项目(69771005)
国家"863"计划项目(301-3-2)
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
PKI
Finite field
Elliptic curve
Point multiplication
Discrete logarithm
Algebraic geometry
Electronic commerce
