Encryption Decryption Algorithm Using Solutions of Pell Equation


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Authors

  • J. Kannan Department of Mathematics, Ayya Nadar Janaki Ammal College (Autonomous, Affiliated to Madurai Kamaraj University, Madurai), Sivakasi, Tamil Nadu, India.
  • Manju Somanath Department of Mathematics, National College (Autonomous, Affiliated to Bharathidasan University, Trichy), Trichy, Tamil Nadu, India.
  • M. Mahalakshmi Department of Mathematics, Ayya Nadar Janaki Ammal College (Autonomous, Affiliated to Madurai Kamaraj University, Madurai), Sivakasi, Tamil Nadu, India.
  • K. Raja Department of Mathematics, National College (Autonomous, Affiliated to Bharathidasan University, Trichy), Trichy, Tamil Nadu, India.

Keywords:

Pell equation, Encryption-decryption algorithm, $Q^{3*}$ matrix, Cryptography

Abstract

Cryptography is a concept of protecting information and conversations which are transmitted through a public source, so that the intended persons only read and process it. There are several encryption and decryption algorithm which involves mathematical concepts to provide more security to the text which has to be shared through a medium. In this paper, the algorithm is written on the basis of the Pell equation $x^2-3y^2=1$ whose solutions are given by the recurrence relations from which the matrix $Q^{3*}$ is defined. The central theme is to convert the taken message into a matrix of even size which is later divided into blocks.

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Published

02-04-2022

How to Cite

J. Kannan, Manju Somanath, M. Mahalakshmi, & K. Raja. (2022). Encryption Decryption Algorithm Using Solutions of Pell Equation. International Journal of Mathematics And Its Applications, 10(1), 1–8. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/7

Issue

Vol. 10 No. 1 (2022)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.