A new family of differentially 4-uniform permutations over F(22k) for odd k

被引：3

作者：

PENG Jie ^{[1
,2
]}

TAN ChikHow ^{[3
]}

WANG QiChun ^{[3
]}

机构：

[1] School of Mathematics and Statistics, Central China Normal University

[2] Temasek Laboratories, National University of Singapore

[3] Shanghai Key Laboratory of Intelligent Information Processing

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;

D O I：

暂无

中图分类号：

TN918.1 [理论];

学科分类号：

070104 ;

摘要：

We study the differential uniformity of a class of permutations over F2 n with n even. These permutations are different from the inverse function as the values xare modified to be(γx)on some cosets of a fixed subgroup γ of F~*. 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 11 条

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