On the Carlet’s Bivariate APN Construction and Representations of Dobbertin Power Functions
Ikonion Journal of Mathematics, vol.8, no.1, pp.26-43, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 8 Issue: 1
- Publication Date: 2026
- Doi Number: 10.54286/ikjm.1836416
- Journal Name: Ikonion Journal of Mathematics
- Journal Indexes: Scopus
- Page Numbers: pp.26-43
- Keywords: APN functions, Bivariate APN construction, Dobbertin power function
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
Abstract
In this paper we present necessary and sufficient conditions on some families of bivariate and biprojective almost perfect nonlinear (APN) functions. In the first part, we follow the extended methods given by Calderini et al in 2021, and give necessary and sufficient conditions for Carlet’s bivariate APN functions. We also give APN-ness conditions for biprojective functions in some special cases. In the second part, we study the representation of the Dobbertin power function following methods given by Budaghyan et al. in 2022 and give new representations for this kind of functions.