Paper 2016/022 Original: eprint.iacr.org/2016/022 ↗
On derivatives of polynomials over finite fields through integration
Abstract
In this note, using rather elementary technique and the derived formula that relates the coefficients of a polynomial over a finite field and its derivative, we deduce many interesting results related to derivatives of Boolean functions and derivatives of mappings over finite fields. For instance, we easily identify several infinite classes of polynomials which cannot possess linear structures. The same technique can be applied for deducing a nontrivial upper bound on the degree of so-called planar mappings.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2016-01-10: last updated
- 2016-01-10: published
- Short URL
- https://ia.cr/2016/022
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2016/022,
author = {Enes Pasalic and Amela Muratovic-Ribic and Samir Hodzic and Sugata Gangopadhyay},
title = {On derivatives of polynomials over finite fields through integration},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/022},
year = {2016},
url = {https://eprint.iacr.org/2016/022}
}