大数模乘硬件模块的研究与实现  

Research and Implementation of Large Integer Modular Multiplication Hardware Module

作　　者：段晓毅[1] 黄烨 曹佳乐 DUAN Xiaoyi;HUANG Ye;CAO Jiale(Beijing Electronic Science and Technology Institute,Beijing 100070,P.R.China)

机构地区：[1]北京电子科技学院,北京市100070

出　　处：《北京电子科技学院学报》2022年第4期15-23,共9页Journal of Beijing Electronic Science And Technology Institute

基　　金：高精尖学科建设基金(项目编号:20210032Z0401,20210033Z0402)

摘　　要：当前主流公钥密码算法如RSA、各类椭圆曲线加密算法等都会涉及到大数运算,特别是模乘、模幂运算。此类计算资源消耗大、运算处理时间长,成为制约密码算法运行速度的瓶颈,因此设计一款高效的大数模乘模块对于促进公钥密码体系的应用就显得尤为重要。蒙哥马利算法是一种常用的大数模乘算法,基于其算法设计的大数模乘模块结构简单、运算效率较高,且易于硬件实现。本文以蒙哥马利算法为基础,结合数论知识,提出了一种改进的蒙哥马利算法,改进后的蒙哥马利模乘算法结构简单,易于硬件描述实现,然后利用Verilog硬件描述语言完成算法设计,最后进行功能仿真测试,完成蒙哥马利大数模乘硬件模块研究与实现。Current mainstream public-key cryptographic algorithms such as the RSA and various elliptic curve encryption algorithms,involve large integer operations,especially the modular multiplication and the modular power.Such operations face the problems of high resource consumption and long processing time,which become the bottleneck limiting the operation speed of cryptographic algorithms.Thus,designing an efficient module for large integer modular multiplication to promote the application of public-key cryptosystem is particularly important.Montgomery algorithm is a common algorithm for large integer modular multiplication.Module designed based on the Montgomery algorithm has the advantages of simple structure,high operation efficiency,and low hardware implementation difficulty.On the basis of the original Montgomery algorithm and combined with the knowledge of number theory,an improved Montgomery algorithm is proposed in this paper.The improved Montgomery modular multiplication algorithm has a simple structure and easy implementation using hardware description language.Then,Verilog language is utilized to experimentally realize the algorithm design.Finally,a function simulation test is performed to complete the research and implementation of the Montgomery large integer modular multiplication.

关 键 词：蒙哥马利算法 模乘 FPGA 硬件描述语言 

分 类 号：TN918.1[电子电信—通信与信息系统]