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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     author = {V. Markov and A. V. Mikhalev and E. S. Kislitsyn},
     title = {Non-associative structures in homomorphic encryption},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {209--215},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a10/}
}
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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/