Several classes of 0-APN power functions over ${\mathbb{F}}_{2^n}$

Abstract

Recently, the investigation of Partially APN functions has attracted a lot of attention. In this paper, with the help of resultant elimination and MAGMA, we propose several new infinite classes of 0-APN power functions over ${\mathbb{F}}_{2^n}$. By the main result in [4], these $0$-APN power functions are CCZ-inequivalent to the known ones. Moreover, these infinite classes of 0-APN power functions can explain some exponents for $1\le n\le 11$ which are not yet ``explained" in the tables of Budaghyan et al. [3].