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

Fast Arithmetic Design Based on Algabriac Geometry of Elleptic Curve Cryptosystem over Finite Prime Field

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。

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.