Some classes of power functions with low c-differential uniformity over finite fields

Functions with low c-differential uniformity have optimal resistance to some types of differential cryptanalysis. In this paper, we investigate the c-differential uniformity of power functions over finite fields of odd characteristic. Based on some known almost perfect nonlinear functions, we present several classes of power functions f(x)=xd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(x)=x^d$$\end{document} with cΔf≤3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{c}\varDelta _f\le 3$$\end{document}. Especially, two new classes of perfect c-nonlinear power functions are proposed.