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Permutation polynomials x~(2k+1+3)+ax2k+2+bx over F_(22k) and their differential uniformity

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Science China(Information Sciences) 2020年第10期63卷 255-257页

作者： Jie PENG Lijing ZHENG Chunsheng WU Haibin KAN Mathematics and Science College Shanghai Normal University School of Mathematics and Physics University of South China Department of Mathematics Lianyungang Normal University Shanghai Key Laboratory of Intelligent Information Processing School of Computer ScienceFudan University Fudan-Zhongan Joint Laboratory of Blockchain and Information Security Shanghai Blockchain Engineering Research Center Shanghai Institute for Advanced Communication and Data Science Shanghai Institute of Intelligent Electronics & Systems

Dear editor,A polynomial f（x）∈Fq[x] is called a permutation polynomial （PP） over the finite field Fq if the associated mapping f:c （?） f（c） from Fq to itself is bijective.A PP f is called a complete permutation polynomial if f（x）+x is a *** over finite fields of even characteristic have wide applications,including cryptography,coding theory,and communication *** many block ciphers with substitution-permutation network structure,the substitution box is usually a PP over F_(22k)for some positive integer *** resist the differential attacks,the differential uniformity of this

关键词： Finite fields Permutation polynomial Binomial Trinomial differential uniformity

Permutation polynomials with low differential uniformity over finite fields of odd characteristic

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Science China Mathematics 2013年第7期56卷 1429-1440页

作者： JIA WenJie ZENG XiangYong LI ChunLei HELLESETH Tor HU Lei Faculty of Mathematics and Computer Science Hubei University State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences Department of Informatics University of Bergen

In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that t... 详细信息

关键词： permutation perfect nonlinear function almost perfect nonlinear function differential uniformity

Some Functions with Low differential uniformity

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Wuhan University Journal of Natural Sciences 2010年第6期15卷 479-487页

作者： SUN Guanghong WU Chuankun College of Sciences Hohai University Nanjing 210098Jiangsu China State Key Laboratory of Information Security Institute ofSoftware Chinese Academy of Sciences Beijing 100190 China

We study the functions with low differential uniformity,and concentrates mainly on the properties of perfect nonlinear（PN） functions,including the properties of the derivative of the components of those *** sufficient and necessary conditions have been explored to judge when a function is a PN *** conditions may be useful in constructing new PN *** also construct some functions with differential 4-uniformity that have rarely been studied in the *** of the constructed functions with differential 4-uniformity have high nonlinearity as ***,a class of functions with differential 4-uniformity which are not extended affine equivalent to any power functions are constructed.

关键词： differential uniformity perfect nonlinear function Carlet-Charpin-Zinoviev equivalence derivative function spectrum

On the differential uniformity and Nonlinearity of a Class of Permutation Quadrinomials Over F_(2 2 m)

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Communications in Mathematical Research 2022年第2期38卷 223-245页

作者： Mengyu Hu Nian Li Xiangyong Zeng Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and StatisticsHubei UniversityWuhanChina

Permutation polynomials with low differential uniformity and high nonlinearity are preferred in cryptographic systems. In 2018, Tu, Zeng and Helleseth constructed a new class of permutation quadrinomials over the finite field F_(2 2m) for an odd integer m. In this paper, we aim to investigate the differential uniformity and nonlinearity of this class of permutation polynomials so as to find 4-uniform permutation polynomials with high nonlinearity.

关键词： differential uniformity finite field nonlinearity permutation polynomial

On the differential uniformities of functions over finite fields

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Science China Mathematics 2013年第7期56卷 1477-1484页

作者： QU LongJiang LI Chao DAI QingPing KONG ZhiYin Department of Mathematics and System Science Science College National University of Defense Technology Science and Technology on Information Assurance Laboratory

In this paper, the possible value of the differential uniformity of a function over finite fields is discussed. It is proved that, the differential uniformity of a function over Fq can be any even integer between 2 and q when q is even; and it can be any integer between 1 and q except q-1 when q is odd. Moreover, for any possible differential uniformity t, an explicit construction of a differentially t-uniform function is given.

关键词： differential uniformity functions finite field explicit construction

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

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Science China Mathematics 2016年第6期59卷 1221-1234页

作者： PENG Jie TAN ChikHow WANG QiChun School of Mathematics and Statistics Central China Normal UniversityWuhan 430079China Shanghai Key Laboratory of Intelligent Information Processing Shanghai 200433China Temasek Laboratories National University of SingaporeSingapore 117411Singapore

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