A direct proof of APN-ness of the Kasami functions

Claude Carlet; Kwang Ho Kim; Sihem Mesnager

Paper 2020/100

A direct proof of APN-ness of the Kasami functions

Claude Carlet, Kwang Ho Kim, and Sihem Mesnager

Abstract

Using recent results on solving the equation $X^{2^{k} + 1} + X + a = 0$ over a finite field $\GF 2^{n}$ , we address an open question raised by the first author in WAIFI 2014 concerning the APN-ness of the Kasami functions $x \mapsto x^{2^{2 k} - 2^{k} + 1}$ with $g c d (k, n) = 1$ , $x \in \GF 2^{n}$

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: APN function Equation Muller-Cohen-Matthews (MCM) polynomial Dickson polynomial Zeros of a polynomial Irreducible polynomial.
Contact author(s): smesnager @ univ-paris8 fr
History: 2020-02-04: received
Short URL: https://ia.cr/2020/100
License: CC BY

BibTeX

@misc{cryptoeprint:2020/100,
      author = {Claude Carlet and Kwang Ho Kim and Sihem Mesnager},
      title = {A direct proof of {APN}-ness of the Kasami functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/100},
      year = {2020},
      url = {https://eprint.iacr.org/2020/100}
}