Topological cryptography using radio arithmetic mean labelling and Playfair matrix with radio mean number integration forsymmetric encryption

Abstract

Graph labeling applies in a variety of fields such as computer science, communication, and cryptography which plays a main role in modelling structural and numerical relationships among networks. Using graph-theoretic labeling in cryptographic systems can guide both strong security and a solid mathematical foundation for encryption. This work proposes a symmetric encryption technique that blends Radio Arithmetic Mean Labeling (RAML) on cycle graphs with an extended Playfair cipher operating on a 6×6 matrix, which includes both letters of the English alphabet and digits. An alternative labelling method improves efficiency without complex calculations, which is created by getting the help of the RAML method. In RAML approach positive integers are assigned to the vertices of a graph G such that: l f (u)+f (v) 2 m ≥diam(G)+1− d (encryption shift is computed as u,v) for all different vertices u and v. Here,f(u) is the label of vertexu, d(u,v) is the shortest path distance between u and v, and diam(G) is the diameter of the graph. The Radio Mean Number (RMN) refers to the highest label used under RAML. The encryption process begins by breaking the plaintext into digraphs, adding padding where needed and removing duplications. Each digraph is then mapped onto the vertices of the cycle graph which is labelled using the RAML scheme. After that, the digraphs are arranged in order of increasing values of labeling f to introduce randomness. A 6×6 Playfair matrix constructed from a secret keyword is used to transform each digraph based on the usual spatial rule for row, column, and rectangle. The RMN value is then used to set the positional shift for each digraph, calculated as:shifti = (ΣASCII values of digraph letters) mod (RMN). Each digraph is encrypted using the extended Playfair matrix. These shifts add extra topological diffusion more advanced than classical substitution. Decryption uses the shared key and the same graph structure and labeling to restore the original text. This method is a structured symmetric encryption scheme. It is more secure than traditional Playfair and other graph-based methods. It provides better diffusion and high labeling efficiency. It can be applied in secure communications, network security, topological cryptography, and may resist quantum computing attacks. Future work will test its applications in communications and network security, and will assess and enhance its security.