A new family of differentially 4-uniform permutations over for odd k

被引：0

作者：

Peng Jie ^{[1
,2
]}

Tan Chik How ^{[3
]}

Wang QiChun ^{[3
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[2] Shanghai Key Lab Intelligent Informat Proc, Shanghai 200433, Peoples R China

[3] Natl Univ Singapore, Temasek Labs, Singapore 117411, Singapore

来源：

SCIENCE CHINA-MATHEMATICS | 2016年 / 59卷 / 06期

基金：

中国国家自然科学基金;

关键词：

differential uniformity; permutation; algebraic degree; nonlinearity; coset; APN; TRINOMIALS;

D O I：

10.1007/s11425-016-5122-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the differential uniformity of a class of permutations over with n even. These permutations are different from the inverse function as the values x (-1) are modified to be (gamma x)(-) on some cosets of a fixed subgroup aOE (c)gamma > of . We obtain some sufficient conditions for this kind of permutations to be differentially 4-uniform, which enable us to construct a new family of differentially 4-uniform permutations that contains many new Carlet-Charpin-Zinoviev equivalent (CCZ-equivalent) classes as checked by Magma for small numbers n. Moreover, all of the newly constructed functions are proved to possess optimal algebraic degree and relatively high nonlinearity.

引用

页码：1221 / 1234

页数：14

共 31 条

[21] New explicit constructions of differentially 4-uniform permutations via special partitions of F22k
Peng, Jie
Tan, Chik How
FINITE FIELDS AND THEIR APPLICATIONS, 2016, 40 : 73 - 89
[22] A new family of differentially 4-uniform permutations over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_{2^{2k} }$$\end{document} for odd k
Jie Peng
Chik How Tan
QiChun Wang
Science China Mathematics, 2016, 59 (6) : 1221 - 1234
[23] Constructing differentially 4-uniform involutions over F22k by using Carlitz form
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FINITE FIELDS AND THEIR APPLICATIONS, 2022, 78
[24] A new class of differential 4-uniform permutations from exponential permutation
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[25] A new class of differential 4-uniform permutations from exponential permutation
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[26] Differentially 4-uniform bijections by permuting the inverse function
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[27] Differentially 4-uniform bijections by permuting the inverse function
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Designs, Codes and Cryptography, 2015, 77 : 117 - 141
[28] More constructions of APN and differentially 4-uniform functions by concatenation
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SCIENCE CHINA-MATHEMATICS, 2013, 56 (07) : 1373 - 1384
[29] A note on the differential spectrum of a differentially 4-uniform power function
Xiong, Maosheng
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FINITE FIELDS AND THEIR APPLICATIONS, 2017, 48 : 117 - 125
[30] Low differentially uniform permutations from the Dobbertin APN function over F2n
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DISCRETE MATHEMATICS, 2021, 344 (12)

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