A new family of differentially 4-uniform permutations over F_(2^(2k))for odd k  

作　　者：PENG Jie TAN ChikHow WANG QiChun 

机构地区：[1]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China [2]Shanghai Key Laboratory of Intelligent Information Processing,Shanghai 200433,China [3]Temasek Laboratories,National University of Singapore,Singapore 117411,Singapore

出　　处：《Science China Mathematics》2016年第6期1221-1234,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61202463 and 61202471);Shanghai Key Laboratory of Intelligent Information Processing(Grant No.IIPL-2014-005)

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 x^(-1) are modified to be(γx)^(-1) on some cosets of a fixed subgroup γ of F_(2n)~*. 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.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 x^（-1） are modified to be（γx）^（-1） on some cosets of a fixed subgroup γ of F_（2n）~＊. 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.

关 键 词：differential uniformity PERMUTATION algebraic degree nonlinearity COSET 

分 类 号：TN918.1[电子电信—通信与信息系统]