Determining the Nonlinearity of a New Family of APN Functions

DOI10.1007/978-3-540-77224-8_11zbMath1195.94048arXiv0707.1223OpenAlexW1485694296MaRDI QIDQ5386079

Eimear Byrne, Gary McGuire, Nadya Markin, Carl Bracken

Publication date: 17 April 2008

Published in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1223

zbMATH Keywords

Walsh spectrumnonlinearityWalsh transformAPNAlmost perfect nonlinearalmost bentABdiscrete binary Fourier transform

Mathematics Subject Classification ID

Cryptography (94A60)

Related Items (15)

Quasi-perfect linear codes from planar and APN functions ⋮ On third-order nonlinearity of biquadratic monomial Boolean functions ⋮ Plateaudness of Kasami APN functions ⋮ Binomial differentially 4 uniform permutations with high nonlinearity ⋮ Constructions of cyclic codes and extended primitive cyclic codes with their applications ⋮ Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions ⋮ On the number of the rational zeros of linearized polynomials and the second-order nonlinearity of cubic Boolean functions ⋮ More constructions of APN and differentially 4-uniform functions by concatenation ⋮ A few more quadratic APN functions ⋮ Symmetric bilinear forms over finite fields with applications to coding theory ⋮ A non-cyclic triple-error-correcting BCH-like code and some minimum distance results ⋮ Some Results on the Known Classes of Quadratic APN Functions ⋮ О приближении дискретных функций линейными функциями ⋮ An Assmus--Mattson Theorem for Rank Metric Codes ⋮ Constructing functions with low differential uniformity

Cites Work

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• New families of quadratic almost perfect nonlinear trinomials and multinomials
• Codes, bent functions and permutations suitable for DES-like cryptosystems
• Another proof of Kasami's theorem
• A new APN function which is not equivalent to a power mapping
• Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
• Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences

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