Cryptology ePrint Archive: Report 2020/1515

The classification of quadratic APN functions in 7 variables

Konstantin Kalgin and Valeriya Idrisova

Abstract: Almost perfect nonlinear functions possess the optimal resistance to the differential cryptanalysis and are widely studied. Most known APN functions are obtained as functions over finite fields $GF(2^n)$ and very little is known about combinatorial constructions of them in $\mathbb{F}_2^n$. In this work we propose two approaches for obtaining quadratic APN functions in $\mathbb{F}_2^n$. The first approach exploits a secondary construction idea, it considers how to obtain a quadratic APN function in $n+1$ variables from a given quadratic APN function in $n$ variables using special restrictions on new terms. The second approach is searching quadratic APN functions that have matrix form partially filled with standard basis vectors in a cyclic manner. This approach allowed us to find a new APN function in 7 variables. We proved that the updated list of quadratic APN functions in dimension 7 is complete up to CCZ-equivalence.

Category / Keywords: foundations / APN functions, Boolean functions

Date: received 2 Dec 2020, last revised 25 Dec 2020

Contact author: vvitkup at yandex ru

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Version: 20201225:181002 (All versions of this report)

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