Year: 2025
Type: article
Abstract: Letqbe an odd prime power with$q\equiv 3\ ({\mathrm {mod}}\,4)$. In this paper, we study the differential and boomerang properties of the function$F_{2,u}(x)=x^{2}\big (1+u\eta (x)\big)$over$\mathbb {F}_{q}$, where$u\in \mathbb {F}_{q}^{*}$and$\eta $is the quadratic character of$\mathbb {F}_{q}$. We determine the differential uniformity of$F_{2,u}$for any$u\in \mathbb {F}_{q}^{*}$, as well as the differential spectra and boomerang uniformity of the locally-APN functions$F_{2,\pm 1}$, thereby disproving a conjecture proposed in Budaghyan and Pal (2024), which states that there exist infinitely many values ofqandusuch that$F_{2,u}$is an APN function.
Authors: Sihem Mesnager, Huawei Wu
Institution: Université Paris 8
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408358906