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https://doi.org/10.21857/ygjwrcdkgy

On known constructions of APN and AB functions and their relation to each other

Marco Calderini ; Department of Informatics, University of Bergen, Bergen 5005, Norway
Lilya Budaghyan ; Department of Informatics, University of Bergen, Bergen 5005, Norway
Claude Carlet orcid id orcid.org/0000-0002-6118-7927 ; Department of Informatics, University of Bergen, Bergen 5005, Norway LAGA, University of Paris 8, Saint-Denis 93526, France


Puni tekst: engleski pdf 550 Kb

str. 79-105

preuzimanja: 400

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Sažetak

This work is dedicated to APN and AB functions which are optimal against differential and linear cryptanlysis when used as Sboxes in block ciphers. They also have numerous applications in other branches of mathematics and information theory such as coding theory, sequence design, combinatorics, algebra and projective geometry. In this paper we give an overview of known constructions of APN and AB functions, in particular, those leading to infinite classes of these functions. Among them, the bivariate construction method, the idea first introduced in 2011 by the third author of the present paper, turned out to be one of the most fruitful. It has been known since 2011 that one of the families derived from the bivariate construction contains the infinite families derived by Dillon’s hexanomial method. Whether the former family is larger than the ones it contains has stayed an open problem which we solve in this paper. Further we consider the general bivariate construction from 2013 by the third author and study its relation to the recently found infinite families of bivariate APN functions.

Ključne riječi

Boolean functions; almost perfect nonlinear (APN) functions, almost bent (AB) functions; cryptography

Hrčak ID:

261468

URI

https://hrcak.srce.hr/261468

Datum izdavanja:

25.8.2021.

Posjeta: 793 *