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Cryptography and Communications

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26.09.2018

On the differential equivalence of APN functions

verfasst von: Anastasiya Gorodilova

Erschienen in: Cryptography and Communications | Ausgabe 4/2019

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Abstract

Carlet et al. (Des. Codes Cryptogr. 15, 125–156, 1998) defined the associated Boolean function γ_F(a,b) in 2n variables for a given vectorial Boolean function F from \(\mathbb {F}_{2}^{n}\) to itself. It takes value 1 if a≠0 and equation F(x) + F(x + a) = b has solutions. This article defines the differentially equivalent functions as vectorial functions having equal associated Boolean functions. It is an open problem of great interest to describe the differential equivalence class for a given Almost Perfect Nonlinear (APN) function. We determined that each quadratic APN function G in n variables, n ≤ 6, that is differentially equivalent to a given quadratic APN function F, can be represented as G = F + A, where A is affine. For the APN Gold function F, we completely described all affine functions A such that F and F + A are differentially equivalent. This result implies that the class of APN Gold functions up to EA-equivalence contains the first infinite family of functions, whose differential equivalence class is non-trivial.

Vorheriger Artikel A lower bound on the size of the largest metrically regular subset of the Boolean cube

Nächster Artikel Construction of a Near-Optimal Quasi-Complementary Sequence Set from Almost Difference Set

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Titel: On the differential equivalence of APN functions
verfasst von: Anastasiya Gorodilova
Publikationsdatum: 26.09.2018
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 4/2019
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-018-0329-y

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