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 functionsCryptographic S-boxesAlmost 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
Creative Commons Attribution
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}
}
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