Please use this identifier to cite or link to this item: https://doi.org/10.1007/978-3-642-30615-0_3
Title: New families of differentially 4-uniform permutations over double-struck F 22k
Authors: Tan, Y. 
Qu, L.
Tan, C.H. 
Li, C.
Keywords: differentially 4-uniform mapping
Permutation polynomial
S-box
switching method
Issue Date: 2012
Citation: Tan, Y.,Qu, L.,Tan, C.H.,Li, C. (2012). New families of differentially 4-uniform permutations over double-struck F 22k. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 7280 LNCS : 25-39. ScholarBank@NUS Repository. https://doi.org/10.1007/978-3-642-30615-0_3
Abstract: Differentially 4-uniform permutations over double-struck F 22k, especially those with high nonlinearity and high algebraic degree, are cryptographically significant mappings as they are good choices for the substitution boxes (S-boxes) in many symmetric ciphers. For instance, the currently endorsed Advanced Encryption Standard (AES) uses the inverse function, which is a differentially 4-uniform permutation. However, up to now, there are only five known infinite families of such mappings which attain the known maximal nonlinearity. Most of these five families have small algebraic degrees and only one family can be defined over double-struck F 22k for any positive integer k. In this paper, we apply the powerful switching method on the five known families to construct differentially 4-uniform permutations. New infinite families of such permutations are discovered from the inverse function, and some sporadic examples are found from the others by using a computer. All newly found infinite families can be defined over fields double-struck F 22k for any k and their algebraic degrees are 2k - 1. Furthermore, we obtain a lower bound for the nonlinearity of one infinite family. © 2012 Springer-Verlag.
Source Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
URI: http://scholarbank.nus.edu.sg/handle/10635/117262
ISBN: 9783642306143
ISSN: 03029743
DOI: 10.1007/978-3-642-30615-0_3
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