Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 19 (2024), 301 -- 316

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

A NEW PUBLIC KEY CRYPTOGRAPHY USING GENERALIZED FIBONACCI MATRICES

Jyoti Panchal, Harish Chandra and Akanksha Singh

Abstract. This work presents a new public key cryptography encryption-decryption scheme based on generalized Fibonacci matrices and the Hill cipher. This scheme proposes using Fibonacci sequences under prime modulo for key establishment. This scheme exchanges the key matrix X = Mθp of order p × p for encryption and decryption. As an alternative to a key matrix, our scheme only requires the exchange of a pair of numbers (p,θ), resulting in a small key space and reduced time and space complexity. We also implemented our scheme with the help of java script and established better security.

2020 Mathematics Subject Classification: 94A60, 68P25
Keywords: Cryptography, Hill Cipher, Fibonacci Sequence, Generalized Fibonacci Matrices, Key exchange ElGamal

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Jyoti Panchal
Department of Mathematics and Scientific Computing
Madan Mohan Malaviya University of Technology
Gorakhpur U.P. (273010).



Harish Chandra
Department of Mathematics and Scientific Computing
Madan Mohan Malaviya University of Technology
Gorakhpur U.P. (273010).
e-mail:hcmsc@mmmut.ac.in


Akanksha Singh
Department of Mathematics and Scientific Computing
Madan Mohan Malaviya University of Technology
Gorakhpur U.P. (273010).




http://www.utgjiu.ro/math/sma