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Construction of Maximum Distance Separable Rhotrices using Cauchy Rhotrices over Finite Fields

by P. L. Sharma, Shalini Gupta, Neetu Dhiman
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 168 - Number 9
Year of Publication: 2017
Authors: P. L. Sharma, Shalini Gupta, Neetu Dhiman
10.5120/ijca2017914489

P. L. Sharma, Shalini Gupta, Neetu Dhiman . Construction of Maximum Distance Separable Rhotrices using Cauchy Rhotrices over Finite Fields. International Journal of Computer Applications. 168, 9 ( Jun 2017), 8-17. DOI=10.5120/ijca2017914489

@article{ 10.5120/ijca2017914489,
author = { P. L. Sharma, Shalini Gupta, Neetu Dhiman },
title = { Construction of Maximum Distance Separable Rhotrices using Cauchy Rhotrices over Finite Fields },
journal = { International Journal of Computer Applications },
issue_date = { Jun 2017 },
volume = { 168 },
number = { 9 },
month = { Jun },
year = { 2017 },
issn = { 0975-8887 },
pages = { 8-17 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume168/number9/27901-2017914489/ },
doi = { 10.5120/ijca2017914489 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:15:40.010997+05:30
%A P. L. Sharma
%A Shalini Gupta
%A Neetu Dhiman
%T Construction of Maximum Distance Separable Rhotrices using Cauchy Rhotrices over Finite Fields
%J International Journal of Computer Applications
%@ 0975-8887
%V 168
%N 9
%P 8-17
%D 2017
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Maximum distance separable (MDS) matrices are important in cryptography and particularly used in block ciphers due to their properties of diffusion. Rhotrices are represented by the coupled matrices. Therefore, maximum distance separable rhotrices are of much interest in the context of cryptography. In this paper, we define Cauchy rhotrix and then use it to construct MDS rhotrices over finite fields.

References
  1. Ajibade, A. O. (2003). The concept of rhotrices in mathematical enrichment, Int. J. Math. Educ. Sci. Tech., Vol. 34, No. 2, pp.175-179.
  2. Mohammed, A., Ezugwu, E.A. and Sani, B. (2011). On generalization and algorithmatization of heart-based method for multiplication of rhotrices, International Journal of Computer Information Systems, Vol. 2, pp. 46-49.
  3. Mohammed, A. (2011). Theoretical development and applications of rhotrices, Ph. D. Thesis, Ahmadu Bello University, Zaria.
  4. Sani, B. (2004). An alternative method for multiplication of rhotrices, Int. J. Math. Educ. Sci. Tech., Vol. 35, No. 5, pp. 777-781.
  5. Sani, B. (2007). The row-column multiplication for high dimensional rhotrices, Int. J. Math. Educ. Sci. Technol, Vol. 38, pp. 657-662.
  6. Tudunkaya, S.M. and Makanjuola, S.O. (2010). Rhotrices and the construction of finite fields, Bulletin of Pure and Applied Sciences, Vol. 29 E, No. 2, pp. 225-229.
  7. Aminu, A. (2009). On the linear system over rhotrices, Notes on Number Theory and Discrete Mathematics, Vol. 15, pp. 7-12.
  8. Aminu, A. (2012). A note on the rhotrix system of equation, Journal of the Nigerian association of Mathematical Physics, Vol. 21, pp. 289-296.
  9. Sani, B. (2008). Conversion of a rhotrix to a coupled matrix, Int. J. Math. Educ. Sci. Technol., Vol. 39, pp. 244-249.
  10. Tudunkaya, S. M. (2013). Rhotrix polynomial and polynomial rhotrix, Pure and Applied mathematics Journal, Vol. 2, pp. 38-41. http://dx.doi.org/10.11648/j.pamj.20130201.16
  11. Absalom, E. E., Sani, B. and Sahalu, J. B. (2011). The concept of heart-oriented rhotrix multiplication, Global J. Sci. Fro. Research, Vol. 11, No. 2, pp. 35-42.
  12. Sharma, P. L. and Kanwar, R. K. (2011). A note on relationship between invertible rhotrices and associated invertible matrices, Bulletin of Pure and Applied Sciences, Vol. 30 E (Math & Stat.), No.2, pp. 333-339.
  13. Sharma, P. L. and Kanwar, R. K. (2012a). Adjoint of a rhotrix and its basic properties, International J. Mathematical Sciences, Vol. 11, No. (3-4), pp. 337-343.
  14. Sharma, P. L. and Kanwar, R. K. (2012b). On inner product space and bilinear forms over rhotrices, Bulletin of Pure and Applied Sciences, Vol. 31E, No. 1, pp. 109-118.
  15. Sharma, P. L. and Kanwar, R. K. (2012c). The Cayley-Hamilton theorem for rhotrices, International Journal Mathematics and Analysis, Vol. 4, No. 1, pp. 171-178.
  16. Sharma, P. L. and Kanwar, R. K. (2013). On involutory and pascal rhotrices, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 7, No. IV, pp. 133-146.
  17. Sharma, P. L. and Kumar, S. (2013). On construction of MDS rhotrices from companion rhotrices over finite field, International Journal of Mathematical Sciences, Vol. 12, No. 3-4, pp. 271-286.
  18. Sharma, P. L. and Kumar, S. (2014a). Some applications of Hadamard rhotrices to design balanced incomplete block. International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 8, No. II, pp. 389-406.
  19. Sharma, P. L. and Kumar, S. (2014b). Balanced incomplete block design (BIBD) using Hadamard rhotrices, International J. Technology, Vol. 4, No. 1, pp. 62-66.
  20. Sharma, P. L. and Kumar, S. (2014c). On a special type of Vandermonde rhotrix and its decompositions, Recent Trends in Algebra and Mechanics, Indo-American Books Publisher, New Delhi, pp. 33-40.
  21. Sharma, P. L., Kumar, S. and Rehan, M. (2014). On construction of Hadamard codes using Hadamard rhotrices, International Journal of Theoretical & Applied Sciences, Vol. 6, No. 1, pp. 102-111.
  22. Sharma, P. L., Kumar, S. and Rehan, M. (2013a). On Hadamard rhotrix over finite field, Bulletin of Pure and Applied Sciences, Vol. 32 E (Math & Stat.), No. 2, pp. 181-190.
  23. Sharma, P. L., Kumar, S. and Rehan, M. (2013b). On Vandermonde and MDS rhotrices over GF(2q), International Journal of Mathematics and Analysis, Vol. 5, No. 2, pp. 143-160.
  24. Sharma, P. L., Gupta, S. and Rehan, M. (2015). Construction of MDS rhotrices using special type of circulant rhotrices over finite fields, Himachal Pradesh University Journal, Vol. 03, No. 02, pp. 25-43.
  25. Sharma, P. L., Gupta, S. and Rehan, (2017). On circulant like rhotrices over finite fields, Accepted for publication in Applications and Applied Mathematics: An International Journal (AAM).
  26. Alfred J. Menezes, Paul C. Van Oorschot and Scott A. Vanstone. (1996, Third Edition). Hand book of Applied Cryptography, CRC Press.
  27. Junod, P. And Vaudenay, S. (2004). Perfect diffusion primitives for block ciphers building efficient MDS matrices, Lecture notes in computer science, Vol. 9-10.
  28. Sajadieh, M., Dakhilian, M., Mala, H. and Omoomi, B. (2012). On construction of involutry MDS matrices from Vandermonde matrices, Des. Codes and Cry., Vol. 64, pp. 287-308.
  29. Lacan, J. and Fimes, J. (2004). Systematic MDS erasure codes based on Vandermonde matrices, IEEE Trans. Commun. Lett. Vol. 8, No. 9, pp. 570-572.
  30. Gupta, K. C. and Ray, I. G. (2013). On constructions of MDS matrices from companion matrices for lightweight cryptography, Cryptography Security Engineering and Intelligence Informatics, Lectures Notes in Computer Science, Vol. 8128, pp. 29-43.
  31. Gupta, K. C. and Ray, I. G. (2014). On constructions of MDS matrices from circulant-like matrices for lightweight cryptography, ASU/2014/1.
  32. Tzeng, K. K. and Zimmermann, K. (1975). On extending Goppa codes to cyclic codes, IEEE Transactions on Information Theory, Vol. 21, pp. 721-716.
  33. Nakahara, J. and Abrahao, E. (2009). A new involutory MDS matrix for the AES. In: International Journal of Computer Security, Vol. 9, pp. 109-116.
Index Terms

Computer Science
Information Sciences

Keywords

Cauchy rhotrix Finite field Maximum distance separable rhotrix Circulant rhotrix Vandermonde rhotrix.

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