On the minimal value set size of APN functions

Ingo Czerwinski

Paper 2020/705

On the minimal value set size of APN functions

Ingo Czerwinski

Abstract

We give a lower bound for the size of the value set of almost perfect nonlinear (APN) functions in explicit form and proof it with methods of linear programming. It coincides with the bound given in [CHP17]. For even it is and sharp as the simple example shows. The sharp lower bound for odd has to lie between and . Sharp bounds for the cases and are explicitly given.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Boolean functions Cryptographic S-boxes Almost perfect nonlinear (APN)Value set size
Contact author(s): ingo @ czerwinski eu
History: 2021-05-05: revised; 2020-06-14: received; See all versions
Short URL: https://ia.cr/2020/705
License: CC BY

BibTeX

@misc{cryptoeprint:2020/705,
      author = {Ingo Czerwinski},
      title = {On the minimal value set size of {APN} functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/705},
      year = {2020},
      url = {https://eprint.iacr.org/2020/705}
}