Cryptosystem Using the Generalized Petersen Graph πΊπ (ππ + π, π)
C Beaula, P. Venugopal Β· Indian Journal of Science and Technology Β· 2024
Objective: In the digital era, data transfer in a network without external interference is one of the challenging problems. External interference can be minimized by creating a strong cryptosystem. For this purpose, different mathematical concepts are incorporated to construct a cryptosystem. Recently, techniques in graph theory, a branch of mathematics, are also employed in cryptography. The objective of this paper is to propose a new cryptosystem to encrypt and decrypt an alphabetical string of lengths less than equal to 16 using graph decomposition and edge labeling on a generalized Petersen graph. Method: The edges of the decomposed graphs of the union of the generalized Petersen graph are labelled using the technique of vertex strongly*-graph and these labels are used to encrypt and decrypt the alphabetical string. Findings: A graph is a vertex strongly*-graph if there exists a bijection such that are distinct for every vertex where are the edges incident to a vertex . The Generalized Petersen graph is proved to be a vertex strongly*-graph. Using this concept, a new cryptosystem is proposed. Novelty: The usage of the decomposition of the union of the generalized Petersen graph in the cryptosystem is the novelty of this paper. Application: To encrypt and decrypt an alphabetical string of size up to 16. Keywords: Encryption, Decryption, Generalized Petersen Graph, Edge Labeling, The Union of Graphs, Graph Decomposition.