Cryptology ePrint Archive: Report 2016/022

On derivatives of polynomials over finite fields through integration

Enes Pasalic and Amela Muratovic-Ribic and 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.

Category / Keywords: secret-key cryptography /