Round these two respects , how to structure security elliptic curve cryptography and the implementations of ecc is first discussed in this paper . then we have analysed especially the scalar multiplication on the elliptic curves , and present a new algorithm to quickly implement the fixed point scalar multiplication according to the idea of interleaving exponentiation algorithm and power division . this algorithm is much faster than fixed - base windowing method ; and a little faster than fixed - base comb method 围绕这两个方面的问题,本文首先讨论了如何构造安全的椭圆曲线密码体制和椭圆曲线密码体制的应用;然后重点分析了椭圆曲线上数乘运算的快速实现,并结合interleavingexponentiation算法和幂分割的思想,提出一种计算固定点数乘的快速算法,该算法的计算速度明显快于fixed - basewindowing算法,稍快于fixed - basecomb算法。
One special feature of this paper is that it provides fast implementation means for the all kinds of modular exponentiation algorithms , which facilitate the implementation of the rsa public key algorithms . the paper improved the sliding window algorithm by largely reducing the space complexity . meanwhile this paper represents an efficient combined algorithm to improve the processing of encryption and decryption 大数模幂乘运算是实现rsa等公钥密码的基本运算,其运行效率决定了rsa公钥密码的性能,文章主要研究了各种模幂算法的快速实现方法,提出运用组合算法的思想来减少算法运行时间;并对滑动窗口取幂算法进行了部分改进,用线性表来存储预计算数据,从而减少了算法的复杂度,进一步提高了rsa加/解密的效率,并在试验测试中得到较为满意的结果。
This article provides a brief description of rsa public key cryptography , an analysis and compare of all kinds of present existed modular exponentiation in rsa public key cryptography , a colligation of the fastest accelerating software algorithm - vlnw sliding window methods and hardware mapping fast montgomery modular multiplication algorithm that can improve the implementary efficiency of rsa public key cryptography for achieving the novel algorithm - mnexp algorithm 本文简单介绍了rsa公钥密码体制,分析比较rsa公钥密码中已有的模幂运算方法,将得到的最快软件加速算法vlnw滑动窗口法和硬件映射最快的montgomery模乘算法综合,得到改进后的mnexp算法能有效提高rsa公钥密码的实现效率。椭圆曲线密码系统被认为可以替代rsa算法的一种公钥密码体制。