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.
作者
关杰
黄俊君
GUAN Jie;HUANG Junjun(PLA SSF Information Engineering University,Zhengzhou 450001,China)
出处
《电子与信息学报》
EI
CSCD
北大核心
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)。
