Keywords and phrases: elliptic curve cryptography, extended generalized Fibonacci sequences, key space.
Received: July 4, 2023; Revised: September 15, 2023; Accepted: September 26, 2023
How to cite this article: Vaishali Billore, Naresh Patel and Hemant Makwana, Implementation of extended generalized Fibonacci matrices as a key in modified elliptic curve cryptography, JP Journal of Algebra, Number Theory and Applications 62(2) (2023), 123-140. http://dx.doi.org/10.17654/0972555523025
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References: [1] R. Balamurugan, V. Kamalakannan, G. D. Rahul and S. Tamilselvan, Enhancing security in text messages using matrix based mapping and Elgamal method in elliptic curve cryptography, 2014 International Conference on Contemporary Computing and Informatics (IC3I) IEEE, 2014, pp. 103-106. [2] V. Billore and N. Patel, Cryptography utilizing the affine-hill cipher and extended generalized Fibonacci matrices, Electronic Journal of Mathematical Analysis and Applications 11(2) (2023), 1-12. [3] D. S. Dummit and R. M. Foote, Abstract Algebra, Vol. 3, Wiley, Hoboken, 2004. [4] T. Elgamal, A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Trans. Inform. Theory 31(4) (1985), 469-472. [5] G. Geetha and P. Jain, Implementation of matrix based mapping method using elliptic curve cryptography, International Journal of Computer Applications Technology and Research 3(5) (2014), 312-317. [6] D. Hankerson, A. J. Menezes and S. Vanstone, Guide to Elliptic Curve Cryptography, Springer Science & Business Media, 2004. [7] J. Hoffstein, J. Pipher and J. H. Silverman, An Introduction to Mathematical Cryptography, Springer, Vol. 1, 2008. [8] N. Koblitz, Elliptic curve cryptosystems, Math. Comp. 48(177) (1987), 203-209. [9] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2019. [10] M. Kumari and J. Tanti, On the role of the Fibonacci matrix as key in modified ECC, Available at https://arxiv.org/abs/2112.11013, 2021. [11] V. S. Miller, Use of elliptic curves in cryptography, Advances in Cryptology - Crypto 85 (1986), 417-426. [12] C. Paar and J. Pelzl, Understanding Cryptography: a Textbook for Students and Practitioners, Springer Science & Business Media, 2009. [13] K. Prasad and H. Mahato, Cryptography using generalized Fibonacci matrices with Affine-Hill cipher, Journal of Discrete Mathematical Sciences and Cryptography 25 (2022), 2341-2352. [14] U. Priyatharsan, P. L. Rupasinghe and I. Murray, A new elliptic curve cryptographic system over the finite fields, 2017 6th National Conference on Technology and Management (NCTM), IEEE, 2017, pp. 164-169. [15] L. D. Singh and T. Debbarma, A new approach to elliptic curve cryptography, 2014 IEEE International Conference on Advanced Communications, Control and Computing Technologies, IEEE, 2014, pp. 78-82.
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