Cryptographic algorithm involving the matrix $Q^{p*}$
Main Article Content
Abstract
Cryptography is one of the most essential developing areas, which deals with the secure transfer of messages. In recent days, there are more number of algorithms have been evolved to provide better security. This work is also such an attempt. In this paper, an algorithm is presented for encryption and decryption which employs the matrix $Q^{p*}$ and the well- known equation $x^2 -py^2 =1$ where $p$ is a prime.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.
References
[1] Andreescu, T., Andrica, D., and Cucurezeanu, I, An Introduction to Diophantine Equations a Problem- Based Approach, Birkhauser Boston, 2010. Google Scholar
[2] Gould, H. W, A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart, 19(3) (1981), 250–257. Google Scholar
[3] J. Kannan, Manju Somanath, M. Mahalakshmi and K. Raja, Remodeled RSA Algorithm for Mes- sages of Length Two Employing G- Primes, International Journal of Mathematics and Computer Research, 10(2)(2022), 2555–2558. Google Scholar
[4] J. Kannan, Manju Somanath, M. Mahalakshmi and K. Raja, Encryption Decryption Algorithm Using Solutions of Pell Equation, International Journal of Mathematics and its Applications, 10(1) (2022), 1–8. Google Scholar
[5] M. Mahalakshmi, J. Kannan, Manju Somanath, K. Raja, and K. Kaleeswari, Cryptographic Algorithm Based on Prime Assignment, International Journal for Research in Applied Science & Engineering Technology, 10(1) (2022),1744–1751, DOI: 10.22214/ijraset.2022.40138. Google Scholar
[6] Manju Somanath, K. Raja, J. Kannan and M. Mahalakshmi,On a Class of Solutions for a Quadratic Diophantine Equation, Advances and Applications in Mathematical Sciences, 19(11) (2020),1097–1103. Google Scholar
[7] Sumeyra, U. C. A. R., Nihal, T. A. S., & Ozgur, N. Y, A new application to coding theory via Fibonacci and Lucas numbers, Mathematical Sciences and Applications E-Notes, 7(1) (2019), 62–70. Google Scholar
[8] Tas, N., Ucar, S., Ozgur, N. Y., & Kaymak, O. O, A new coding/decoding algorithm using Fibonacci numbers, Discrete Mathematics, Algorithms and Applications, 10(02) (2018), 1850028. Google Scholar
[9] Tekcan, A, Continued fractions expansion of$sqrt{D}$ and Pell equation $x^2 -Dy^2 =1$, Mathematica Moravica, 15 (2) (2011), 19--27. Google Scholar
[10] Trappe, W., & Washington, L. C, Introduction to Cryptography. Prentice Hall, 2006. Google Scholar