An approach of encryption that combines ECC and the adjacency matrices of graphs using extended generalized Lucas matrix as key matrix

Billore, Vaishali; Patel, Naresh; Makwana, Hemant

doi:10.47974/JDMSC-2045

Open Access Research Article

An approach of encryption that combines ECC and the adjacency matrices of graphs using extended generalized Lucas matrix as key matrix

^*Vaishali BilloreCorresponding authorvaishali.billore20@gmail.comInstitute of Engineering and TechnologyIndore, Madhya Pradesh, 452001, IndiaView full profile → , Naresh Pateln_patel_1978@yahoo.co.inAutonomous) Science CollegeGovernment Holkar (Model, Indore, Madhya Pradesh, 452001, IndiaView full profile → , Hemant Makwanahmakwana@ietdavv.edu.inDepartment of Information and TechnologyInstitute of Engineering and TechnologyIndore, Madhya Pradesh, 452001, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 809–825Vol. 28Issue 3April 2025DOI: 10.47974/JDMSC-2045 Crossmark XML

Received:: 07 Feb 2024
Published Online:: 26 Feb 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2045
Pages:: 809–825

Abstract

These days, the best way to secure our data and conversations is to use message encryption techniques. Thanks to the proliferation of network and internet communications, advancements in message encryption technologies have picked up speed. When personal, sensitive information is transmitted via unsecured networks, it opens the door to possible hacking attempts, theft, and eavesdropping on conversations. In order to shorten this term, cryptographic methods are essential. Along with the conventional matrix algebra, we created a higher-order recursive matrix called an Extended generalised Lucas matrix and linked it to Extended generalised Fibonacci sequences in this paper. Elliptic curve cryptography and graph theory are the foundations of our proposed public key cryptography, which employs these matrices as keys for an affine cypher and key agreement for encryption-decryption using a mix of terms from Extended generalised Lucas sequences and residue operations. By reducing key transmission to the exchange of a small set of numbers (parameters) rather than the full key matrix, this method offers a large key space while simultaneously reducing the space and time complexity of key transmission. On top of that, it’s secure and dependable since it’s built on the challenging Elliptic Curve-Discrete Logarithm algorithm.

Keywords

Extended generalized lucas sequence & matrices Affine hill cipher Elliptic curve cryptography Adjacency matrix

Subject Classifications

11B3711T7111B3914H5294A60

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