利用中国剩余定理改进大数模平方计算研究  

Speeding Modular Squaring Algorithms of Larger-Number Using CRT

作　　者：施月玲[1] 夏涛[1] 丁宏[1] 

机构地区：[1]杭州电子科技大学计算机学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2007年第1期42-45,共4页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：浙江省自然科学基金重点项目(ZD0101)

摘　　要：一般大数模幂运算可以分解成若干次模平方和模乘运算,所以加快模平方运算的速度就可以提高大数模幂计算的效率,从而解决公钥密码体系加解密速度比较慢的问题。该文介绍了一种利用中国剩余定理来改进模平方算法的方法,同时在该算法基础上利用广义中国剩余定理和剩余系的转换来进一步提高模平方的效率。并对不同算法适用环境进行了比较。Modular exponentiation can be decomposed into several modular squaring and modular multiplication. So we can accelerate the computation of modular exponentiation by optimizing modular squaring of larger number, and we can resolve question of slowly calculating of the public- key cryptography systems. An algorithm of optimizing modular squaring using Chinese remainder theorem is introduced. At the same time another algorithm of optimizing modular squaring based on generalized Chinese remainder theorem is introduced. The several algorithms are compared in the different surroundings.

关 键 词：大数模平方 中国剩余定理 剩余数集 模乘 

分 类 号：TP339[自动化与计算机技术—计算机系统结构]