Encryption Decryption Algorithm Using Solutions of Pell Equation

# J. Kannan^{1}, Manju Somanath^{2}, M. Mahalakshmi^{1} and K. Raja^{2}

^{1}Department of Mathematics, Ayya Nadar Janaki Ammal College (Autonomous, Affiliated to Madurai Kamaraj University, Madurai), Sivakasi, Tamil Nadu, India.

^{2}Department of Mathematics, National College (Autonomous, Affiliated to Bharathidasan University, Trichy), Trichy, Tamil Nadu, India.**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.

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

**Cite this article as:** J. Kannan, Manju Somanath, M. Mahalakshmi and K. Raja, *Encryption Decryption Algorithm Using Solutions of Pell Equation*, Int. J. Math. And Appl., vol. 10, no. 1, 2022, pp. 1-8.

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