Bhatta, G.R.Shankar, B.R.Poojary, P.2026-02-042022Proceedings of the Jangjeon Mathematical Society, 2022, 25, 2, pp. 159-17115987264https://doi.org/10.17777/pjms2022.25.2.159https://idr.nitk.ac.in/handle/123456789/22787Cryptographic applications of Latin squares require to study them in various aspects. In this paper, the formation and observation of Latin squares using bivariate permutation polynomials over some finite rings are established with respect to their properties like self orthogonalization, r-orthogonalization, and r-mirror orthogonalization. We also identified why some particular cases fail to form self orthogonal Latin squares, and we illustrate it by giving examples. © 2022 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.CryptographyPermutation polynomialr-orthogonalityRingSelf-orthogonality