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Cryptography and Communications
Published in: Cryptography and Communications 6/2019

17-05-2019

Several new classes of self-dual bent functions derived from involutions

Authors: Gaojun Luo, Xiwang Cao, Sihem Mesnager

Published in: Cryptography and Communications | Issue 6/2019

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Abstract

Bent functions are a kind of Boolean functions which have the maximum Hamming distance to linear and affine functions, they have some interesting applications in combinatorics, coding theory, cryptography and sequences. However, generally speaking, how to find new bent functions is a hard work and is a hot research project during the past decades. A subclass of bent functions that has received attention since Dillon’s seminal thesis (1974) is the subclass of those Boolean functions that are equal to their dual (or Fourier transform in Dillon’s terminology): the so-called self dual bent functions. In this paper, we propose a construction of involutions from linear translators, and provide two methods for constructing new involutions by utilizing some given involutions. With the involutions presented in this paper, several new classes of self-dual bent functions are produced.
previous article Multiple characters transforms and generalized Boolean functions
next article Frobenius linear translators giving rise to new infinite classes of permutations and bent functions

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Metadata
Title
Several new classes of self-dual bent functions derived from involutions
Authors
Gaojun Luo
Xiwang Cao
Sihem Mesnager
Publication date
17-05-2019
Publisher
Springer US
Published in
Cryptography and Communications / Issue 6/2019
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-019-00371-9

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