Paper 2018/769 Original: eprint.iacr.org/2018/769 ↗
Constructing APN functions through isotopic shifts
Abstract
Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, information theory as well as mathematics. Building new APN families is a challenge which has not been successfully addressed for more than seven years now. The most general known equivalence relation preserving APN property in characteristic 2 is CCZ-equivalence. Extended to general characteristic, it also preserves planarity. In the case of quadratic planar functions, it is a particular case of isotopic equivalence. We apply the idea of isotopic equivalence to transform APN functions in characteristic 2 into other functions, some of which can be APN. We deduce new quadratic APN functions and a new quadratic APN family.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2018-09-10: last updated
- 2018-08-27: published
- Short URL
- https://ia.cr/2018/769
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2018/769,
author = {Lilya Budaghyan and Marco Calderini and Claude Carlet and Robert S. Coulter and Irene Villa},
title = {Constructing APN functions through isotopic shifts},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/769},
year = {2018},
url = {https://eprint.iacr.org/2018/769}
}