Differential spectra of a class of power permutations with characteristic 5

被引:0
作者
Haode Yan
Chengju Li
机构
[1] Southwest Jiaotong University,School of Mathematics
[2] Guangxi Key Laboratory of Cryptography and Information Security,Shanghai Key Laboratory of Trustworthy Computing
[3] East China Normal University,undefined
[4] State Key Laboratory of Integrated Services and Networks,undefined
来源
Designs, Codes and Cryptography | 2021年 / 89卷
关键词
Power permutation; Differential uniformity; Differential spectrum; Elliptic curve; 11T06; 94A60; 11T71;
D O I
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中图分类号
学科分类号
摘要
Let n be a positive integer and 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} over F5n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_{5^n}$$\end{document}, where d=5n-32\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=\frac{5^n-3}{2}$$\end{document}. In this paper, we study the differential properties of the power permutation F(x). It is shown that F(x) is differentially 4-uniform when n is even, and differentially 5-uniform when n is odd. Based on some knowledge on elliptic curves over finite fields, the differential spectrum of F(x) is also determined.
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页码:1181 / 1191
页数:10
相关论文
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