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Designs, Codes and Cryptography

Erschienen in:

12.02.2016

Antiderivative functions over \(\mathbb {F}_{2^n}\)

verfasst von: Valentin Suder

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1-2/2017

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Abstract

In this paper, we use a linear algebra point of view to describe the derivatives and higher order derivatives over \(\mathbb {F}_{2^n}\). On one hand, this new approach enables us to prove several properties of these functions, as well as the functions that have these derivatives. On the other hand, we provide a method to construct all of the higher order derivatives in given directions. We also demonstrate some properties of the higher order derivatives and their decomposition as a sum of functions with 0-linear structure. Moreover, we introduce a criterion and an algorithm to realize discrete antidifferentiation of vectorial Boolean functions. This leads us to define a new equivalence of functions, that we call differential equivalence, which links functions that share the same derivatives in directions given by some subspace. Finally, we discuss the importance of finding 2-to-1 functions.

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Titel: Antiderivative functions over
verfasst von: Valentin Suder
Publikationsdatum: 12.02.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1-2/2017
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-016-0186-7

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