Involutory differentially 4-uniform permutations from known constructions

DOI10.1007/s10623-018-0482-5zbMath1403.94058OpenAlexW2800690885MaRDI QIDQ1755990

Xiutao Feng, Shihui Fu

Publication date: 11 January 2019

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-018-0482-5

zbMATH Keywords

nonlinearitypermutationinvolutiondifferentially 4-uniform permutationalgebraic degree

Mathematics Subject Classification ID

Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items

On the boomerang uniformity of permutations of low Carlitz rank, New differentially 4-uniform permutations from modifications of the inverse function, More low differential uniformity permutations over \(\mathbb{F}_{2^{2 k}}\) with \(k\) odd, On CCZ-equivalence between the Bracken-Tan-Tan function and power functions, A new construction for involutions over finite fields, On inverses of permutation polynomials of the form \(x(x^s-a)^{(q^m-1)/s}\) over \(\mathbb{F}_{q^n}\), Unnamed Item, Two shorter proofs on the inverse and differential spectrum of Bracken-Leander exponent, Two-to-one mappings and involutions without fixed points over \(\mathbb{F}_{2^n}\), Constructing differentially 4-uniform involutions over \(\mathbb{F}_{2^{2k}}\) by using Carlitz form

Uses Software

• PRINCE
• Midori

Cites Work

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• New explicit constructions of differentially 4-uniform permutations via special partitions of \(\mathbb{F}_{2^{2 k}}\)
• Binomial differentially 4 uniform permutations with high nonlinearity
• Differentially 4-uniform bijections by permuting the inverse function
• New differentially 4-uniform permutations by modifying the inverse function on subfields
• Permutation polynomials EA-equivalent to the inverse function over \(\mathrm{GF}(2^n)\)
• Differential cryptanalysis of DES-like cryptosystems
• Further results on differentially 4-uniform permutations over \(\mathbb{F}_{2^{2m}}\)
• A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree
• One-to-one highly nonlinear power functions on \(\mathrm{GF}(2^n)\)
• 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 \(\mathrm{GF}(2^{2m+1})\)
• On EA-equivalence of certain permutations to power mappings
• 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 \(k\)
• Midori: A Block Cipher for Low Energy
• Cryptanalysis of a Theorem: Decomposing the Only Known Solution to the Big APN Problem
• On the Behaviors of Affine Equivalent Sboxes Regarding Differential and Linear Attacks
• On Known and New Differentially Uniform Functions
• New Construction of Differentially 4-Uniform Bijections
• A Generalisation of Dillon's APN Permutation With the Best Known Differential and Nonlinear Properties for All Fields of Size $2^{4k+2}$
• Higher Order Derivatives and Differential Cryptanalysis
• PRINCE – A Low-Latency Block Cipher for Pervasive Computing Applications
• 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.)
• Fast Software Encryption
• More constructions of differentially 4-uniform permutations on \(\mathbb {F}_{2^{2k}}\)