On derivatives of polynomials over finite fields through integration

Enes Pasalic; Amela Muratovic-Ribic; Samir Hodzic; Sugata Gangopadhyay

Paper 2016/022

On derivatives of polynomials over finite fields through integration

Enes Pasalic, Amela Muratovic-Ribic, Samir Hodzic, and Sugata Gangopadhyay

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.
Contact author(s): enes pasalic6 @ gmail com
History: 2016-01-10: received
Short URL: https://ia.cr/2016/022
License: CC BY

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}
}