Relating differential distribution tables to other properties of substitution boxes
type: Item
instance of: scholarly article
title: Relating differential distribution tables to other properties of substitution boxes
zbMATH Open document ID: 0969.94014
DOI: 10.1023/A:1008359713877
author: Xian-Mo Zhang
author: Yuliang Zheng
author: Hideki Imai
published in: Designs, Codes and Cryptography
publication date: 2000-06-04T00:00:00Z
review text: Relationships among various characteristics of an \(n \times m\) S-box \((n > m)\) are investigated. First, in addition to the well-known differential distribution table two other tables, namely auto-correlation distribution table and correlation immunity distribution table associated with an S-box are introduced. The precise relationship among the three tables is established and later on used to show a number of results on various properties of S-boxes. Particularly, it is shown that the regularity of an S-box can be characterized by its difference distribution table. Then, a new tight lower bound on the differential uniformity of an S-box is given. Finally two upper bounds on the nonlinearity of S-boxes, one for a general, not necessarily regular, S-box and the other for the regular case are proved.
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 1420170
zbMATH Keywords: S-boxes
zbMATH Keywords: differential attack
zbMATH Keywords: linear attack
zbMATH Keywords: nonlinearity
zbMATH Keywords: differential distribution table
zbMATH Keywords: regularity
reviewed by: Jozef Vyskoč
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1420170