Paper 2020/1515 Original: eprint.iacr.org/2020/1515 ↗
The classification of quadratic APN functions in 7 variables
Abstract
Almost perfect nonlinear functions possess the optimal resistance to the differential cryptanalysis and are widely studied. Most known APN functions are obtained as functions over finite fields $GF(2^n)$ and very little is known about combinatorial constructions of them in $\mathbb{F}_2^n$. In this work we propose two approaches for obtaining quadratic APN functions in $\mathbb{F}_2^n$. The first approach exploits a secondary construction idea, it considers how to obtain a quadratic APN function in $n+1$ variables from a given quadratic APN function in $n$ variables using special restrictions on new terms. The second approach is searching quadratic APN functions that have matrix form partially filled with standard basis vectors in a cyclic manner. This approach allowed us to find a new APN function in 7 variables. We proved that the updated list of quadratic APN functions in dimension 7 is complete up to CCZ-equivalence.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2021-11-26: last updated
- 2020-12-04: published
- Short URL
- https://ia.cr/2020/1515
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2020/1515,
author = {Konstantin Kalgin and Valeriya Idrisova},
title = {The classification of quadratic APN functions in 7 variables},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/1515},
year = {2020},
url = {https://eprint.iacr.org/2020/1515}
}