Power functions with low uniformity on odd characteristic finite fields

DOI10.1007/s11425-010-3149-xzbMath1246.12007OpenAlexW2066045160MaRDI QIDQ625803

Zhengbang Zha, Xue-Li Wang

Publication date: 25 February 2011

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-010-3149-x

zbMATH Keywords

finite fieldalmost perfect nonlinear functiondifferential uniform function

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Shift register sequences and sequences over finite alphabets in information and communication theory (94A55) Finite fields (field-theoretic aspects) (12E20)

Related Items (16)

Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method ⋮ On \((-1)\)-differential uniformity of ternary APN power functions ⋮ Optimal \(p\)-ary cyclic codes with minimum distance four from monomials ⋮ On the minimum distance of negacyclic codes with two zeros ⋮ Survey on recent trends towards generalized differential and boomerang uniformities ⋮ Further results on differentially 4-uniform permutations over \(\mathbb{F}_{2^{2m}}\) ⋮ A new large class of functions not APN infinitely often ⋮ Low \(c\)-differential uniformity of the swapped inverse function in odd characteristic ⋮ Differential spectrum of a class of APN power functions ⋮ CONSTRUCTING NEW APN FUNCTIONS FROM KNOWN PN FUNCTIONS ⋮ The differential spectrum of a class of power functions over finite fields ⋮ Some classes of power functions with low \(c\)-differential uniformity over finite fields ⋮ The multivariate method strikes again: new power functions with low differential uniformity in odd characteristic ⋮ New constructions of APN polynomial functions in odd characteristic ⋮ A fast multi-obstacle muscle wrapping method using natural geodesic variations ⋮ Several classes of polynomials with low differential uniformity over finite fields of odd characteristic

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• New classes of almost bent and almost perfect nonlinear polynomials
• A new APN function which is not equivalent to a power mapping
• New families of almost perfect nonlinear power mappings
• Almost perfect nonlinear power functions on GF(2/sup n/): the Welch case

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