Encoding and Decoding by Using Pell and modify Pell Matrices
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Abstract
In this paper, we study the Pell, modify Pell sequences, and the matrices whose entries are related to Pell and modify Pell sequences. Moreover, we apply these matrices to present a new algorithm for encoding, which transforms plain text into cipher text for secure transmission, and decoding, which involves decrypting the received cipher text back into its original message.
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References
Ercolano, J. (1979). Matrix generators of Pell sequences. Fibonacci Quart, 17(1), 71-77.
Flaut, C. (2019). Some application of difference equations in Cryptography and Coding Theory. Journal of Difference Equations and Applications, 25(7), 905-920.
Halici, S. and Daşdemir, A. (2010). On some relationships among Pell, Pell-Lucas and modified Pell sequences. Sakarya University Journal of Science, 14(2), 141-145.
Hoggatt Jr, V. E. and Ruggles, I. D. (1963). A Primer for the Fibonacci Numbers-Part IV. The Fibonacci Quarterly, 1(4), 39-45.
Horadam, A. F. (1994). Applications of modified Pell numbers to representations. Ulam Quarterly, 3(1),34-53.
Shtayat, J. and Al-Kateeb, A. (2019). An Encoding-Decoding algorithm based on Padovan numbers. arXiv preprint arXiv, 1907.02007.
Shtayat, J. and Al-Kateeb, A. (2022). The Perrin -matrix and more properties with an application. Journal of Discrete Mathematical Sciences and Cryptography, 25(1), 41-52.
Stakhov, A. P. (1999). A generalization of the Fibonacci -matrix. Reports of the National Academy of Sciences of Ukraine, 9, 46-49.
Sundarayya, P. and Vara Prasad, G. (2019). A public key cryptosystem using Affine Hill Cipher under modulation of prime number. Journal of Information and Optimization Sciences, 40(4), 919-930.
Sümeyra, U. Ç. A. R., Nihal, T. A. Ş. and Özgür, N. Y. (2019). A new application to coding theory via Fibonacci and Lucas numbers. Mathematical Sciences and Applications E-Notes, 7(1), 62-70.
Taş, N., Uçar, S., Özgür, N. Y. and Kaymak, Ö. Ö. (2018). A new coding/decoding algorithm using Fibonacci numbers. Discrete Mathematics, Algorithms and Applications, 10(02), 1850028.