Constructing differentially 4-uniform permutations over GF(22m) from quadratic APN permutations over GF(22m+1)

In this paper, by means of the idea proposed by Carlet (ACISP 1-15, 2011 ), differentially 4-uniform permutations with the best known nonlinearity over are constructed using quadratic APN permutations over . Special constructions are given using the Gold functions. The algebraic degree of the constr...

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Veröffentlicht in:	Designs, codes, and cryptography codes, and cryptography, 2014-08, Vol.72 (2), p.249-264
Hauptverfasser:	Li, Yongqiang, Wang, Mingsheng
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Applied sciences Circuits Coding and Information Theory Combinatorics. Ordered structures Computer Science Cryptography Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Exact sciences and technology Field theory and polynomials Information and Communication Information, signal and communications theory Mathematics Order, lattices, ordered algebraic structures Sciences and techniques of general use Signal and communications theory Telecommunications and information theory
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Zusammenfassung:	In this paper, by means of the idea proposed by Carlet (ACISP 1-15, 2011 ), differentially 4-uniform permutations with the best known nonlinearity over are constructed using quadratic APN permutations over . Special constructions are given using the Gold functions. The algebraic degree of the constructions and their compositional inverses is also investigated. One construction and its compositional inverse both have algebraic degree m + 1 over .
ISSN:	0925-1022 1573-7586
DOI:	10.1007/s10623-012-9760-9