A Note on the Kasami Power Function

Doreen Hertel

Paper 2005/436

A Note on the Kasami Power Function

Doreen Hertel

Abstract

This work is motivated by the observation that the function $\F m$ to $\F m$ defined by $x^{d} + (x + 1)^{d} + a$ for some $a \in \F m$ can be used to construct difference sets. A desired condition is, that the function $φ_{d} (x) := x^{d} + (x + 1)^{d}$ is a $2^{s}$ -to-1 mapping. If $s = 1$ , then the function $x^{d}$ has to be APN. If $s > 1$ , then there is up to equivalence only one function known: The function is a -to-1 mapping if is the Gold parameter with . We show in this paper, that is also a -to-1 mapping if is the Kasami parameter with and odd. We hope, that this observation can be used to construct more difference sets.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. submitted to IEEE Transactions on Information Theory
Keywords: number theory finite field
Contact author(s): doreen hertel @ mathematik uni-magdeburg de
History: 2005-11-30: received
Short URL: https://ia.cr/2005/436
License: CC BY

BibTeX

@misc{cryptoeprint:2005/436,
      author = {Doreen Hertel},
      title = {A Note on the Kasami Power Function},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/436},
      year = {2005},
      url = {https://eprint.iacr.org/2005/436}
}