The simplest method for constructing APN polynomials EA-inequivalent to power functions

Lilya Budaghyan

Abstract

The first APN polynomials EA-inequivalent to power functions have been constructed in [1,2] 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 function: 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 from [1,2] cannot be obtained by the introduced method. [1] L. Budaghyan, C. Carlet, A. Pott. New Classes of Almost Bent and Almost Perfect Nonlinear Functions. IEEE Trans. Inform. Theory, vol. 52, no. 3, pp. 1141-1152, March 2006. [2] L. Budaghyan, C. Carlet, A. Pott. New Constructions of Almost Bent and Almost Perfect Nonlinear Functions. Proceedings of the Workshop on Coding and Cryptography 2005, pp. 306-315, 2005.

Available format(s)
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Affine equivalenceAlmost bentAlmost perfect nonlinearCCZ-equivalenceDifferential uniformityNonlinearityS-boxVectorial Boolean function
Contact author(s)
lilya @ science unitn it
History
Short URL
https://ia.cr/2007/058

CC BY

BibTeX

@misc{cryptoeprint:2007/058,
author = {Lilya Budaghyan},
title = {The simplest method for constructing APN polynomials EA-inequivalent to power functions},
howpublished = {Cryptology ePrint Archive, Paper 2007/058},
year = {2007},
note = {\url{https://eprint.iacr.org/2007/058}},
url = {https://eprint.iacr.org/2007/058}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.