본문 바로가기
KERD
논문KCI 등재

R-ORTHOGONALITY OF LATIN SQUARES USING BIVARIATE PERMUTATION POLYNOMIALS

VADIRAJA BHATTA G. R.|SHANKAR B. R.|PRASANNA POOJARY
장전수학회 (Jangjeon Mathematical Society)|2022.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제25권 제2호|pp. 159-172|DOI 10.17777/pjms.2022.25.2.004

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

CryptographyPermutation polynomialRingSelf-orthogonalityr-orthogonality
주제분류수학

초록

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.

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.

참고문헌 (19)

  1. I. Janiszczak, "Isometry invariant permutation codes and mutually orthogonal Latin squares", Journal of Combinatorial Designs, 27(9), pp.541~551 (2019)
  2. G. Otokar, "Isotopy of Latin squares in cryptography", Tatra Mountains Mathematical Publications, 45(1), pp.27~36 (2010)
  3. R. L. Rivest, "Permutation polynomials modulo 2w", Finite Fields Appl., 7(2), pp.287~292 (2001)
  4. B. G. R. Vadiraja, "Permutation Polynomials modulo n, n = 2w and Latin Squares", Mathematical Combinatorics, 2, pp.58~65 (2009)
  5. J. H. Lint, "A course in combinatorics" (2001), Cambridge university press
  6. B. G. R. Vadiraja, "Nearrings, Near fields and Related Topics", pp.270~281 (2017), World Scientific
  7. B. G. R. Vadiraja, "Sequences of numbers via permutation polynomials over some finite rings", Proyecciones (Antofagasta), 39(5), pp.1295~1313
  8. B. G. R. Vadiraja, "Variations of diagonal cyclicity of Latin squares formed by permutation polynomials", Italian Journal of Pure and Applied Mathematics, 46, pp.438~452 (2021)
  9. B. G. R. Vadiraja, "Variations of Orthogonality of Latin Squares", Mathematical Combinatorics, 3, pp.55~61 (2015)
  10. R. Lidl, "Finite fields", pp.20~ (1997), Cambridge university press
  11. O. Krafft, "Diagonal-complete Latin squares", Eur. J. Combin., 24, pp.229~237 (2003)
  12. Y. Zhang, "Strongly symmetric self-orthogonal diagonal Latin squares and Yang Hui type magic squares", Discrete Math., 328, pp.79~87 (2014)
  13. E. Vatutin, "On some features of symmetric diagonal latin squares", CEUR Workshop Proceedings, 1940, pp.74~79 (2017)
  14. Z. Lie, "A few more r-orthogonal Latin squares", Discrete Mathematics, 238, pp.183~191 (2001)
  15. C. L. Colbourn, "Combinatorics advances", pp.49~75 (1995), Springer
  16. J. D´enes, "Latin squares: New developments in the theory and applications", pp.46~ (1991)
  17. The role of latin square in cipher systems: Matrix approach to model encryption modes of operation, "J. Kong", UCLA Computer Science Department, ~, pp.UCLA Computer Science Department Technical Report CSTR030038 (2008)
  18. J. Seberry, "Some constructions of mutually orthogonal latin squares and superimposed codes", Discrete Mathematics, Algorithms and Applications, 4(3) (2012)
  19. S. K. Pal, "Design of strong cryptographic schemes based on Latin Squares", Journal of Discrete Mathematical Sciences and Cryptography, 13(3), pp.233~256 (2010)

관련 논문AI추천

The Construction Study of v-self-orthogonal Latin SquareMeng, Qian, Zheng장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제3호EXPLICIT CLASSES OF PERMUTATION AND COMPLETE PERMUTATION POLYNOMIALS OVER FINITE FIELDSABDALLAH DERBAL, ABDELMEJID BAYAD, BELHOUT BOUSALMI장전수학회 · Advanced Studies in Contemporary Mathematics2021 · 제31권 제1호Permutation functions arising from interpolationsHyeonok Lee, Sangtae Jeong대한수학회 · 대한수학회논문집2009 · 제24권 제2호SKEW(β1+υβ2+νβ3+υνβ4+ν2β5+υν2β6)-CONSTACYCLIC CODES OVER Fq+υFq+νFq+υνFq+ν2Fq+υν2FqG. Ismail, M. Al-Ashker, R. Al-Shorbassi장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제1호Cryptographic algorithm involving the matrix $Q^{p*}$A. Deepshika, J. Kannan, M. Mahalakshmi강원경기수학회 · 한국수학논문집2022 · 제30권 제3호CYCLIC AND CONSTACYCLIC CODES OVER Z4 + wZ4Abdullah Dertli, Nuh Aydin, Yasemin Cengellenmis대한수학회 · 대한수학회보2024 · 제61권 제6호

이 간행물의 다른 논문 (11건)

A CRITERION FOR A LIE GROUP TO ADMIT A CONTINUOUS EMBEDDING IN A MOTION GROUPA. I. Shternpp. 129-132ON WEAKLY SYMMETRIC GENERALIZED (k,μ)-SPACE FORMSP. SIVA KOTA REDDY, G. SOMASHEKHARA, PRABHAVATI G ANGADI, G. S. SHIVAPRASANNApp. 133-144STUDY ON SOME IDENTITIES ARISING FROM HIGHER ORDER CHANGHEE POLYNOMIALS BASES김혜경pp. 145-158On r-dynamic coloring on Mycielskian graphsGOMATHI C S, MOHANAPRIYA Npp. 173-186THE PIVOT NUMBER OF A GRAPHSHADI IBRAHIM KHALAF, SULTAN SENAN MAHDE, Ismail Naci CANGUL, Veena Mathadpp. 187-196
원문 보기