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
收藏
页码：1221 / 1234
页数：14
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