Partially APN functions with APN-like polynomial representations

被引：0
作者：
Lilya Budaghyan
Nikolay Kaleyski
Constanza Riera
Pantelimon Stănică
机构：
[1] University of Bergen,Department of Informatics
[2] Western Norway University of Applied Sciences,Department of Computer Science, Electrical Engineering and Mathematical Sciences
[3] Naval Postgraduate School,Department of Applied Mathematics
来源：
Designs, Codes and Cryptography | 2020年 / 88卷
关键词：
Boolean function; Almost perfect nonlinear (APN); Partial APN (pAPN); CCZ-equivalence; 94A60; 94C10; 06B30;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper we investigate several families of monomial functions with APN-like exponents that are not APN, but are partially 0-APN for infinitely many extensions of the binary field F2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_2$$\end{document}. We also investigate the differential uniformity of some binomial partial APN functions. Furthermore, the partial APN-ness for some classes of multinomial functions is investigated. We show also that the size of the pAPN spectrum is preserved under CCZ-equivalence.
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页码：1159 / 1177
页数：18
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