Graph - Based Innovations in Cryptographic Security

Abstract

Cryptography focuses on securely transmitting messages from one party to another, ensuring that an unauthorized third party cannot comprehend them. To achieve this, various mathematical concepts, particularly from Graph Theory, have been incorporated into cryptographic techniques for more secure data transmission. The process of converting the original plain-text message into an unreadable cipher-text is known as encryption, while converting the cipher-text back to the original plain-text is referred to as decryption. Graph Theory is essential in numerous fields, particularly in cryptography, where its properties and straightforward matrix representation in computers make it highly valuable. In this paper the encryption and decryption process has been made more safer by using adjacent matrix of complement graph.
Introduction: In today's digital communication landscape, ensuring secure data transmission is essential, and cryptography plays a vital role in safeguarding sensitive information. Graph theory, with its intricate structures and concepts, offers innovative frameworks for creating robust encryption methods. This research explores using adjacency matrices, graph complements, and disjoint graphs to develop secure cryptographic systems. By leveraging graph complements and structural complexities, these methods obscure messages, enhancing resistance to cryptographic attacks. Applications range from securing communication channels to enhancing blockchain privacy. Building on previous studies, this work demonstrates the potential of graph-theory-based cryptography in addressing modern security challenges effectively.