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。
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
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. 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.
中图分类号:
卢忱,魏美社,卞正中. 基于二进制扩域的椭圆曲线密码快速算法[J]. , 2003, 29(19): 45-47.
LU Chen, WEI Meishe, BIAN Zhengzhong. Fast Arithmetic of Elliptic Curve Cryptosystem Based on Binary Field[J]. , 2003, 29(19): 45-47.