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Title:
The classification of quadratic APN functions in 7 variables
Authors: Konstantin Kalgin, 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.
ePrint: https://eprint.iacr.org/2020/1515
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