Geodesic
Non-associative structures in homomorphic encryption
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 209-215.

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In this paper, we obtain a classification of quasigroup rings by the quantity of elements with null left annihilator for different quasigroups. This classification becomes possible due to a criterion of being an element with null left annihilator in a quasigroup ring. By virtue of this criterion, we make a calculation to find regularities using various fields and quasigroups with order $4$. This outcome helps us to obtain two results where any two quasigroup rings have the same number of elements with null left annihilator and the element of the quasigroup ring $\mathrm{GF}(p)Q$ with fixed quasigroup $Q$ has null left annihilator in the quasigroup ring $\mathrm{GF}(p^n)Q$. 
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V. Markov; A. V. Mikhalev; E. S. Kislitsyn. Non-associative structures in homomorphic encryption. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 209-215. http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a10/

[1] Belousov V. D., Osnovy teorii kvazigrupp i lup, Nauka, M., 1967

[2] Gribov A. V., Zolotykh P. A., Mikhalev A. V., “Postroenie algebraicheskoi kriptosistemy nad kvazigruppovym koltsom”, Matem. voprosy kriptografii, 4:4 (2010), 23–33 | MR

[3] Katyshev S. Yu., Markov V. T., Nechaev A. A., Ispolzovanie neassotsiativnykh gruppoidov dlya realizatsii protsedury otkrytogo raspredeleniya klyuchei, 2014

[4] Gentry C., A fully homomorphic encryption scheme, PhD thesis, Stanford Univ., 2009 | Zbl