Abstract
In the paper, it is proved that almost all quasigroups are strongly polynomially complete, i.e., are not isotopic to quasigroups that are not polynomially complete.
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Acknowledgments
While working on the paper, the authors had the pleasant opportunity to discuss the material with V. A. Artamonov. The authors thank the referees for constructive comments, which contributed to a significant improvement in the presentation.
Funding
This work was financially supported by DRDO (India), the project “Quasigroup Based Cryptography: Security Analysis and Development of Crypto-Primitives and Algorithms (QGSEC)”, grant no. SAG/4600/TCID/Prog/QGSEC.
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Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 8-14 https://doi.org/10.4213/mzm13229.
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Galatenko, A.V., Galatenko, V.V. & Pankrat’ev, A.E. Strong Polynomial Completeness of Almost All Quasigroups. Math Notes 111, 7–12 (2022). https://doi.org/10.1134/S0001434622010023
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DOI: https://doi.org/10.1134/S0001434622010023