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Generation of n-quasigroups by proper families of functions

  • Aleksey V. Galatenko EMAIL logo , Valentin A. Nosov , Anton E. Pankratiev and Kirill D. Tsaregorodtsev
Published/Copyright: September 6, 2025

Abstract

Finite quasigroups and n-quasigroups are a promising platform for cryptoalgorithm implementation. One of the key problems consists in memory-efficient generation of wide classes of n-quasigroups of a large order. We describe a possible solution based on proper families of functions, show that the number of n-quasigroups generated thereby is bounded from below in terms of the cardinality of the image of the corresponding proper family, study possible values that this cardinality can take, and give two examples of quadratic proper families of Boolean functions with a high image cardinality.


Originally published in Diskretnaya Matematika (2023) 35, №1, 35–53 (in Russian).


Funding statement: This research was supported by the Interdisciplinary Scientific and Educational School of Moscow University «Brain, Cognitive systems, Artificial intelligence».

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Received: 2022-11-28
Published Online: 2025-09-06
Published in Print: 2025-08-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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