RSA加密算法的快速实现  

Fast Implementation of RSA Algorithm

作　　者：卢秀慧[1] 杨瑞峰[1] 贾建芳[1] 

机构地区：[1]中北大学信息与通信工程学院,山西太原030051

出　　处：《沈阳建筑大学学报（自然科学版）》2012年第6期1143-1147,共5页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(61004045);山西省科技攻关项目(20100321056-01)

摘　　要：目的研究一种快速模幂乘算法,以解决RSA加密算法中大整数模幂乘运算速度慢的问题.方法利用SMM(Symmetry of Modulo Multiplication)算法的乘同余对称特性改进滑动窗口模幂乘算法.根据窗口宽度将大整数划分为多个非零元素的集合,将大整数的模幂乘运算转换为一系列平方模运算和乘模运算的迭代,通过减小每一次迭代中操作数的基,提高乘法运算速度和求模运算效率.结果将采用改进算法实现的1 024 bit长密钥模幂乘算法与滑动窗口算法和BR算法相比,改进算法的计算速度是滑动窗口算法速度的1.1倍,是传统BR算法速度的2倍.结论经乘同余特性改进后的滑动窗口模幂乘算法,保障数据安全性的同时提高了加密效率.Aiming at the time-consuming large integer modular power multiplication of RSA algorithm,the sliding window coding algorithm is analyzed and improved by the symmetry of modulo multiplication algorithm.According to the window width,the large integer can be divided into a set of non-zero elements,which are used to transfer modular power multiplication to a series of modular squaring and modular multiplication.By simplifying the calculation of large operands in each iteration,the algorithm shortens the time it spends in multiplication and reduces the modular computation amounts.The algorithm has higher efficiency to implement the 1024 bit long key modular power multiplication.Compared to sliding window coding algorithm,its operation speed is about 1.1 times,and to conventional BR algorithm,about 2 times.Along with the high security,the algorithm has high performance.

关 键 词：公钥密码学 滑动窗口编码 模乘 数据安全 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]