A Lightweight and High-Security Graph Cryptosystem for Smart Cities and Cyber Physical Systems

Abstract

This chapter explores the integration of graph theory and cryptographic design within intelligent digital ecosystems, including smart cities and cyber-physical systems. A novel graph structure termed the Fifth root Biquadrate Mean Cordial Graph (FBMCG) is introduced, and its structural properties are analyzed on the splitting graph Spl(Cn) where n ≡ 0( 𝑚𝑜𝑑6). Based on this graph foundation, the chapter presents a lightweight, high security modular graph-based cryptosystem, designated as the Fifth root Biquadrate Mean Modular Cryptography (FBMMC), developed using modular arithmetic and a multi-key encryption mechanism. The proposed cryptographic scheme achieves linear computational complexity, maintains low collision probability, and establishes strong resistance to brute-force and structural attacks. Owing to the lightweight design, the scheme can be efficiently deployed in IoT devices and smart-card systems, while its high-security configuration supports advanced communication infrastructures. The analysis further indicates that for a splitting graph Spl(Cn) of order 𝑛 = 72 and a plaintext of 24 characters, the achieved bit-security is approximately 188 bits, which corresponds to a high-security level suitable for applications such as smart grids and secure IoT networks.