有限域GF(P)上椭圆曲线密码体制的点乘快速算法研究.doc

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1、有限域GF(P)上椭圆曲线密码体制的点乘快速算法研究有限域GFP上椭圆曲线密码体制的点乘快速算法研究摘要椭圆曲线密码体制是一种建立在椭圆离散对数之上的公钥密码体制具有许多的优点被认为是下一代最通用的公钥密码系统但由于计算复杂其实现速度受到了很大制约点乘算法是实现椭圆曲线密码体制的基本运算同时也是最耗时的运算它的运算效率直接决定着ECC椭圆曲线密码体制的性能kP的运算即点乘k运算主要涉及两方面即整数的表示和椭圆曲线上点加倍点的实现要想加快点k乘算法的运行速度从点加和倍点方面着手是困难的因此本文从大整数的表示方式这一角度研究如何加快点乘算法的运行速度本文

2、的第一章主要介绍了与椭圆曲线密码体制相关的数学背景知识和椭圆曲线的优势等基本知识第二章则重点介k绍了如何利用射影坐标实现点加和倍点运算以及整数的二进制表示法在本文第三章中综合不同文献中提出的各种改进方案重点介绍了如何改进m进制算法和NAF算法来达到加快点乘运算的目的然后在理论上分析了这两种改进方案的优势最后根据本文介绍的算法思想编程实现了较快的实现kP运算的C程序关键词椭圆曲线密码体制点乘算法m进制算法NAF算法I有限域GFP上椭圆曲线密码体制的点乘快速算法研究AbstractEllipticcurvecryptosystemECCisbasedon

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7、ogramsandinthisthirdchapterfocusesonhowtoimprovethealgorithmandtheNAFbandalgorithmtoachievespeeduptheoperationbythepurposeFinallyaccordingtothispaperthealgorithmthinkingofprogrammingarelativelyrapidrealizationofkPcomputingCprogramKeywordsEllipticcurvecryptosystemalgorithmofpoin

8、tmultiplicationK-raymethodnon-adjacentformNAFII有限域GFP上