Keccak类S盒的线性性质研究  

Research on Linear Properties of Keccak-like S-box

作　　者：关杰[1] 黄俊君 GUAN Jie;HUANG Junjun(PLA SSF Information Engineering University,Zhengzhou 450001,China)

机构地区：[1]战略支援部队信息工程大学,郑州450001

出　　处：《电子与信息学报》2020年第7期1790-1795,共6页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61572516,61272041,61272488)。

摘　　要：该文将Keccak的S盒一般化为n元Keccak类S盒,研究了Keccak类S盒的线性性质。证明了这类S盒的相关优势的取值都为0或2-k,其中k∈Z且0≤k≤[2-1n],并且对于此范围内的任意k,都存在输入输出掩码使得相关优势取到2-k;证明了当输出掩码确定时,其非平凡相关优势都相等;给出了非平凡相关优势为最大值2-1时的充要条件与计数,解决了这类S盒的Walsh谱分布规律问题。In this paper,the S-box of Keccak is generalized into n-variable Keccak-like S-box,and the linear properties of n-variable Keccak-like S-box is studied.It is proved that all the values of correlation advantages of this kind of S-box are 0 or 2-k,where k∈Z and 0≤k≤[2-1n],and for any k in this range,there is an input mask and an output mask that make the correlation advantage be 2-k.Furthermore,it is proved that when the output mask is fixed,the values of the nontrivial correlation advantages of the S-box are determined.Then,the necessary and sufficient condition are given when the count for the nontrivial correlation advantage is the maximum value 2-1.Finally,the value distribution of the Walsh spectrum of Keccak-like S-box is presented.

关 键 词：哈希函数 Keccak S盒 线性性质 

分 类 号：TN918.1[电子电信—通信与信息系统]