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.
