Work

New GAPN functions with the lowest possible algebraic degree

Year: 2026

Type: article

Abstract: Most of the known (Almost) Perfect Nonlinear functions over an arbitrary finite field F p n have the lowest possible algebraic degree (2) and can be represented by Dembowski-Ostrom (DO) polynomials. We define Generalized DO (GDO) polynomials as homogeneous polynomials of algebraic degree p over finite fields with characteristic p . We illustrate the similarities between DO and GDO polynomials when studied through generalized derivatives. We also discuss the differential uniformity and Walsh coefficients of GDO functions. Our main contribution is to use this framework in order to propose several new classes of Generalized Almost Perfect Nonlinear (GAPN) functions of algebraic degree p , the lowest possible over the finite field F p n .

Source: Finite Fields and Their Applications

DOI: 10.1016/j.ffa.2026.102885

Authors: Noureddine El-Asri, Valentin Suder

Institution: Université de Rouen Normandie

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,720

Funder: Agence Nationale de la Recherche