(n,m)函数抗差分功耗攻击指标的研究综述  

Survey of results of(n,m)-functions against differential power attack

作　　者：周宇[1] 陈智雄[2] 卓泽朋[3] 杜小妮 ZHOU Yu;CHEN Zhixiong;ZHUO Zepeng;DU Xiaoni(Science and Technology on Communication Security Laboratory,Chengdu 610041,China;Fujian Provincial Key Laboratory of Applied Mathematics,Putian University,Putian 351100,China;School of Mathematical Science,Huaibei Normal University,Huaibei 235000,China;College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]保密通信重点实验室,四川成都610041 [2]莆田学院福建省应用数学重点实验室,福建莆田351100 [3]淮北师范大学数学科学学院,安徽淮北235000 [4]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西安电子科技大学学报》2021年第1期50-60,86,共12页Journal of Xidian University

基　　金：国家重点研发计划(2017YFB0802000);国家自然科学基金(61772292,61772022);四川省科技计划(2020JDJQ0076);福建省自然科学基金(2018J01425)。

摘　　要：(n,m)函数是对称密码算法的最基本部件,其密码学性质的优劣一定程度上决定着对称密码算法的安全性。因此,如何设计和分析满足多种密码学性质的(n,m)函数是对称密码部件研究中重要的基础问题。随着对称密码算法的侧信道分析研究的深入,在(n,m)函数抵抗差分功耗攻击方面出现了一些指标:信噪比、透明阶和混淆系数,这些指标也逐渐成为衡量(n,m)函数密码性能好坏的重要参考之一,目前已被应用在S盒的设计和评估中。从理论角度综述了(n,m)函数的信噪比、透明阶和混淆系数方面研究成果,主要包括:(n,m)函数和布尔函数的信噪比与传统密码学指标的关系;(n,m)函数和布尔函数的透明阶与传统密码学性质的关系,布尔函数与其分解函数的透明阶的关系以及小变元平衡函数透明阶的分布;(n,m)函数的混淆系数刻画;一些公开算法中S盒的三种指标综合分析。最后,给出了这三个指标的研究展望。(n,m)functions(or S-boxes)are the most basic components in symmetric cryptography,and its cryptographic properties determine some security of symmetric cryptography.Therefore,how to design and analyze(n,m)functions which satisfy various cryptographic properties is an important problem in the research on symmetric cryptography.With the development of the research on the side channel of symmetric cipher algorithms,there are some indicators in the aspect of(n,m)functions resisting differential power attack:the signal-to-noise ratio,transparency order and confusion coefficient.These indicators have gradually become the main indicators to measure the cryptographic properties of(n,m)functions cryptography,and have been applied to the design and analysis of block cipher S-boxes.In this paper,the research results of the signal-to-noise ratio(SNR),transparency order(TO)and confusion coefficient(CC)of(n,m)functions are summarized,including:(1)some relationships between the signal-to-noise ratio of(n,m)functions and the traditional cryptographic indicators;(2)some relationships between the transparency order of(n,m)functions and the traditional cryptographic property;some relationships between the transparency order of a Boolean function and its decomposition functions;few distributions of the transparency order of small variable balance functions;(3)the confusion coefficient of(n,m)function(s);(4)a comprehensive analysis of three indicators of a S-box in some public algorithms.Finally,the research prospect of these three indicators is given.

关 键 词：(n m)函数 布尔函数 抗差分功耗分析 透明阶 信噪比 混淆系数 

分 类 号：TN918.1[电子电信—通信与信息系统]