Paper 2021/405
Revisiting some results on APN and algebraic immune functions
Claude Carlet
Abstract
We push a little further the study of two characterizations of almost perfect nonlinear (APN) functions introduced in our recent monograph. We state open problems about them, and we revisit in their perspective a well-known result from Dobbertin on APN exponents. This leads us to new results about APN power functions and more general APN polynomials with coefficients in a subfield F_{2^k} , which ease the research of such functions and of differentially uniform functions, and simplifies the related proofs by avoiding tedious calculations. In a second part, we give slightly simpler proofs than in the same monograph, of two known results on Boolean functions, one of which deserves to be better known but needed clarification, and the other needed correction.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Boolean functionAlmost perfect nonlinearcorrelation immune
- Contact author(s)
- claude carlet @ gmail com
- History
- 2021-12-18: last of 4 revisions
- 2021-03-27: received
- See all versions
- Short URL
- https://ia.cr/2021/405
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/405,
author = {Claude Carlet},
title = {Revisiting some results on {APN} and algebraic immune functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/405},
year = {2021},
url = {https://eprint.iacr.org/2021/405}
}
