椭圆曲线密码体制中快速标量乘算法实现

摘要

椭圆曲线密码(ECC)，是一种以椭圆曲线离散对数问题为出发点而制定出的各种公钥密码体制，在1985年由学者Koblitz和Miller两人分别独立提出。ECC的主要特征是采用有限域上的椭圆曲线有限点群而非是传统的基于离散对数问题密码体制中所采用的有限循环群。因为标量乘算法是ECC中最耗时同时也是最为重要的算法，因为其运算效率的高低将直接影响到ECC实现的效率。本篇论文即是研究椭圆曲线密码中的标量乘法，以期能够探寻出一种快速安全的标量乘算法。%The elliptic curve cryptosystem(ECC),which is based on elliptic curve discrete logarithm problem as the starting point and develop all kinds of public key cryptosystems,in 1985 put forward by scholars both Koblitz and Miller independently.The main characteristic of ECC is adopting the elliptic curve over finite field is limited point group rather than the traditional based on discrete logarithm problem of password system adopted by the finite cyclic group.Because scalar multiplication algorithm is the most time-consuming ECC is also the most important algorithms,because of its computational efficiency height will directly affect the efficiency of ECC implementation.This paper is to study the scalar multiplication in elliptic curve cryptosystem,in order to find out a fast scalar multiplication algorithm security.