On the classification of APN functions up to dimension five

DOI10.1007/s10623-008-9194-6zbMath1184.94227OpenAlexW2020301329MaRDI QIDQ1009090

Marcus Brinkmann, Gregor Leander

Publication date: 31 March 2009

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

Full work available at URL: https://doi.org/10.1007/s10623-008-9194-6

Mathematics Subject Classification ID

Related Items (41)

Trims and extensions of quadratic APN functions ⋮ Invariants for EA- and CCZ-equivalence of APN and AB functions ⋮ A note on APN permutations in even dimension ⋮ Decomposition of permutations in a finite field ⋮ Characterization of almost perfect nonlinear functions in terms of subfunctions ⋮ On quadratic APN functions and dimensional dual hyperovals ⋮ On the symmetric properties of APN functions ⋮ An improved affine equivalence algorithm for random permutations ⋮ On the Sixth International Olympiad in Cryptography NSUCRYPTO ⋮ On relations between CCZ- and EA-equivalences ⋮ CCZ equivalence of power functions ⋮ Differential Attacks Against SPN: A Thorough Analysis ⋮ Threshold implementations of small S-boxes ⋮ Cryptanalytic time-memory-data trade-offs for FX-constructions and the affine equivalence problem ⋮ A new construction of differentially 4-uniform \((n,n-1)\)-functions ⋮ Triplicate functions ⋮ The classification of quadratic APN functions in 7 variables and combinatorial approaches to search for APN functions ⋮ On the equivalence between a new family of APN quadrinomials and the power APN functions ⋮ On equivalence between known families of quadratic APN functions ⋮ Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions ⋮ Unnamed Item ⋮ Almost perfect and planar functions ⋮ More constructions of APN and differentially 4-uniform functions by concatenation ⋮ Two notions of differential equivalence on Sboxes ⋮ Intersection of Hamming codes avoiding Hamming subcodes ⋮ On CCZ-equivalence, extended-affine equivalence, and function twisting ⋮ THE LINEAR SPECTRUM OF QUADRATIC APN FUNCTIONS ⋮ Classification of quadratic APN functions with coefficients in \(\mathbb{F}_2\) for dimensions up to 9 ⋮ On an algorithm generating 2-to-1 APN functions and its applications to ``The big APN problem ⋮ Some Results on the Known Classes of Quadratic APN Functions ⋮ Relative difference sets, graphs and inequivalence of functions between groups ⋮ Perfect nonlinear functions and cryptography ⋮ On the EA-classes of known APN functions in small dimensions ⋮ Construction of Lightweight S-Boxes Using Feistel and MISTY Structures ⋮ Bundles, presemifields and nonlinear functions ⋮ О приближении дискретных функций линейными функциями ⋮ Характеризация отображений через свойство неизометричности ⋮ A lower bound on the number of inequivalent APN functions ⋮ Unnamed Item ⋮ Quadratic almost bent functions -- their partial characterization and design in the spectral domain ⋮ On known constructions of APN and AB functions and their relation to each other

Uses Software

• OEIS

Cites Work

• Unnamed Item
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• Codes, bent functions and permutations suitable for DES-like cryptosystems
• New classes of almost bent and almost perfect nonlinear polynomials
• A new APN function which is not equivalent to a power mapping
• Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
• Estimating the Efficiency of Backtrack Programs
• Every one a Winner or how to Avoid Isomorphism Search when Cataloguing Combinatorial Configurations
• The On-Line Encyclopedia of Integer Sequences

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