×

zbMATH — the first resource for mathematics

The simplest method for constructing APN polynomials EA-inequivalent to power functions. (English) Zbl 1177.94133
Carlet, Claude (ed.) et al., Arithmetic of finite fields. First international workshop, WAIFI 2007, Madrid, Spain, June 21–22, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73073-6/pbk). Lecture Notes in Computer Science 4547, 177-188 (2007).
Summary: In 2005 Budaghyan, Carlet and Pott constructed the first APN polynomials EA-inequivalent to power functions by applying CCZ-equivalence to the Gold APN functions. It is a natural question whether it is possible to construct APN polynomials EA-inequivalent to power functions by using only EA-equivalence and inverse transformation on a power APN mapping: this would be the simplest method to construct APN polynomials EA-inequivalent to power functions. In the present paper we prove that the answer to this question is positive. By this method we construct a class of APN polynomials EA-inequivalent to power functions. On the other hand it is shown that the APN polynomials constructed by Budaghyan, Carlet and Pott cannot be obtained by the introduced method.
For the entire collection see [Zbl 1121.11002].

MSC:
94A60 Cryptography
PDF BibTeX XML Cite
Full Text: DOI