R-ORTHOGONALITY OF LATIN SQUARES USING BIVARIATE PERMUTATION POLYNOMIALS

G. R. Vadiraja Bhatta; B. R. Shankar; Prasanna Poojary

doi:10.17777/pjms2022.25.2.159

R-ORTHOGONALITY OF LATIN SQUARES USING BIVARIATE PERMUTATION POLYNOMIALS

G. R. Vadiraja Bhatta
, B. R. Shankar
, Prasanna Poojary^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Cryptographic 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.

Original language	English
Pages (from-to)	159-171
Number of pages	13
Journal	Proceedings of the Jangjeon Mathematical Society
Volume	25
Issue number	2
DOIs	https://doi.org/10.17777/pjms2022.25.2.159
Publication status	Published - 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.17777/pjms2022.25.2.159

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abstract = "Cryptographic 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.",

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AB - Cryptographic 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.

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R-ORTHOGONALITY OF LATIN SQUARES USING BIVARIATE PERMUTATION POLYNOMIALS

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