New secondary constructions of differentially 4-uniform permutations over

DOI10.1080/00207160.2016.1227433zbMath1421.94067OpenAlexW2508861523MaRDI QIDQ4976347

Chik How Tan, Jie Peng, Qichun Wang

Publication date: 28 July 2017

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2016.1227433

zbMATH Keywords

nonlinearitydifferentially 4-uniform permutationalgebraic degreeS-boxcycle set

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Data encryption (aspects in computer science) (68P25)

Related Items (4)

More low differential uniformity permutations over \(\mathbb{F}_{2^{2 k}}\) with \(k\) odd ⋮ New links between nonlinearity and differential uniformity ⋮ Low differentially uniform permutations from the Dobbertin APN function over \(\mathbb{F}_{2^n} \) ⋮ Constructing differentially 4-uniform involutions over \(\mathbb{F}_{2^{2k}}\) by using Carlitz form

Cites Work

• Binomial differentially 4 uniform permutations with high nonlinearity
• Differentially 4-uniform bijections by permuting the inverse function
• A few more quadratic APN functions
• Differential cryptanalysis of DES-like cryptosystems
• Further results on differentially 4-uniform permutations over \(\mathbb{F}_{2^{2m}}\)
• New families of quadratic almost perfect nonlinear trinomials and multinomials
• A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree
• Constructing new APN functions from known ones
• Codes, bent functions and permutations suitable for DES-like cryptosystems
• Constructing differentially 4-uniform permutations over \(\mathrm{GF}(2^{2m})\) from quadratic APN permutations over \(\mathrm{GF}(2^{2m+1})\)
• A new almost perfect nonlinear function which is not quadratic
• Constructing new differentially 4-uniform permutations from the inverse function
• A new family of differentially 4-uniform permutations over \(\mathbb{F}_{2^{2k}}\) for odd \(k\)
• The weights of the orthogonals of the extended quadratic binary Goppa codes
• New classes of almost bent and almost perfect nonlinear polynomials
• Classes of Quadratic APN Trinomials and Hexanomials and Related Structures
• Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
• Constructing Differentially 4-Uniform Permutations Over <formula formulatype="inline"><tex Notation="TeX">${\BBF}_{2^{2k}}$</tex> </formula> via the Switching Method
• The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes
• Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)

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