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