椭圆曲线标量乘高效方案设计  

Energy-efficient scheme of elliptic curve cryptography scalar multiplication

作　　者：吴昆 胡现刚 张学超 汪晓睿 Wu Kun;Hu Xian′gang;Zhang Xuechao;Wang Xiaorui(Unit 91977 of People′s Liberation Army of China,Beijing 100071,China;Naval Staff Department of the Southern Theater Command,Zhanjiang 524000,China;Political and Legal Affairs Commission of the Central Military Commission,Beijing 100000,China)

机构地区：[1]91977部队,北京100071 [2]南部战区海军参谋部,广东湛江524000 [3]中央军委政法委,北京100000

出　　处：《网络安全与数据治理》2024年第8期28-34,共7页CYBER SECURITY AND DATA GOVERNANCE

摘　　要：对于一些资源受限的应用场景而言,椭圆曲线密码算法的计算量还是比较大,这严重影响了网络的生命周期,需要对算法进行轻量化改进以减少资源消耗。标量乘运算是影响椭圆曲线密码算法执行效率的关键,针对无线传感器节点的内存和处理特点,首先对其底层的域运算进行改进,提出了二进制域上的3-Karatsuba联合区块乘法算法、快速模约减算法、模平方及模逆算法,减少了域运算过程的基本运算和内存读写次数,最后基于Montgomery算法设计了GF(2~m)上的标量乘快速实现方案。在8 bit AVR微处理器上实验表明,完成一次GF(2~(163))域上的ECC点乘运算共需要5 160 991个时钟周期,时间消耗大约为0.70 s,改进后的方案在运算效率方面有一定优化。Due to the limited resources of the wireless sensor network,the elliptic curve cryptographic algorithm requires a large amount of computation,which seriously affects the life cycle of the network.It is necessary to make lightweight improvements to the algorithm to reduce resource consumption.Scalar multiplication is the key to the execution efficiency of elliptic curve cryptographic algorithms.By analyzing the storage and processing characteristics of wireless sensor nodes,we improve the underlying domain operations firstly,and propose the 3-Karatsuba block-combined multiplication algorithm,fast modular reduction algorithm,modular square and modular inverse algorithm on binary domain,which can reduce the times of basic operations and memory read and write.Finally,we design a fast implementation scheme of scalar multiplication on GF(2 m)based on the Montgomery algorithm.The results of experiments on 8 bit AVR microprocessor demonstrate that,completing an ECC point multiplication operation on the GF(2163)domain requires a total of 5160991 clock cycles,with a time consumption of approximately 0.70 seconds,our contribution can improve ECC scalar multiplication significantly.

关 键 词：椭圆曲线密码 标量乘 二进制域运算 模运算 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]