Paper 2007/058
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.
Metadata
- Available format(s)
-
PDF
PS
- 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
- 2007-02-20: received
- Short URL
- https://ia.cr/2007/058
- License
-
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},
url = {https://eprint.iacr.org/2007/058}
}
