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Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Results on Characterizations of Plateaued Functions in Arbitrary Characteristic

Authors : Sihem Mesnager, Ferruh Özbudak, Ahmet Sınak

Published in: Cryptography and Information Security in the Balkans

Publisher: Springer International Publishing

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Abstract

Bent and plateaued functions play a significant role in cryptography since they can have various desirable cryptographic properties. In this work, we first provide the characterizations of plateaued functions in terms of the moments of their Walsh transforms. Next, we generalize the characterizations of Boolean bent and plateaued functions in terms of their second-order derivatives to arbitrary characteristic. Moreover, we present a new characterization of plateaued functions in terms of fourth power moments of their Walsh transforms. Furthermore, we give a new proof of the characterization of vectorial bent functions. Finally, we present the characterizations of vectorial s-plateaued functions in terms of moments of their Walsh transforms and the zeros of their second-order derivatives.

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previous chapter Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes
next chapter Cryptographically Strong S-Boxes Generated by Modified Immune Algorithm
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Metadata
Title
Results on Characterizations of Plateaued Functions in Arbitrary Characteristic
Authors
Sihem Mesnager
Ferruh Özbudak
Ahmet Sınak
Copyright Year
2016
Book
Cryptography and Information Security in the Balkans

Print ISBN: 978-3-319-29171-0

Electronic ISBN: 978-3-319-29172-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-29172-7_2

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