Bracken, Carl and Leander, Gregor (2010) A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree. Finite Fields and Their Applications, 16 (4). pp. 231-242. ISSN ISSN: 1071-5797

Download (137kB)

Abstract

Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially- 4 uniform function called the inverse function. Any function used in a symmetric cryptosystem should be a permutation. Also, it is required that the function is highly nonlinear so that it is resistant to Matsui’s linear attack. In this article we demonstrate that the highly nonlinear permutation f(x) = x22k+2k+1, discovered by Hans Dobbertin [7], has differential uniformity of four and hence, with respect to differential and linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem as the inverse function.

Item Type:	Article
Additional Information:	Preprint version of published article. © 2010 Elsevier Inc. All rights reserved.
Keywords:	Boolean functions; Power functions; Fourier transform; Block cipher; s-Box;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	2635
Identification Number:	https://doi.org/10.1016/j.ffa.2010.03.001
Depositing User:	Library Editor
Date Deposited:	12 Aug 2011 15:55
Journal or Publication Title:	Finite Fields and Their Applications
Publisher:	Elsevier
Refereed:	No
URI:	http://www.elsevier.com/wps/find/homepag... http://www.elsevier.com/wps/find/journal...
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

Repository Staff Only(login required)

Item control page

Downloads

Origin of downloads