Algebraic graph models for secure distributed networks and cryptographic systems

Sharma, Surbhi; Rathi, Preeti; Popli, Ranjeeta Kaur; Tanwar, Sushama; Vats, Prashant

doi:10.47974/JDMSC-2468

Open Access Research Article

Algebraic graph models for secure distributed networks and cryptographic systems

Surbhi Sharmasurbhi.sharma@jaipur.manipal.eduDepartment of Computer Science and EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Preeti Rathipreeti.rathi@krmangalam.edu.inSchool of Engineering and TechnologyK R Mangalam UniversityGurgaon, Haryana, IndiaView full profile → , Ranjeeta Kaur Popliranjeetapopli@gmail.comDepartment of Computer Science(Affiliated to Guru Gobind Singh Indraprastha University)Kamal Institute of Higher Education and Advanced TechnologyMohan Garden, New Delhi, 110059, IndiaView full profile → , ^*Sushama TanwarCorresponding authorsushama.tanwar@jaipur.manipal.eduDepartment of Computer Science and EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Prashant Vatsprashant.vats@jaipur.manipal.eduDepartment of Computer Science and EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile →

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pp. 3071–3080Vol. 28Issue 8December 2025DOI: 10.47974/JDMSC-2468 Crossmark XML

Received:: 08 Apr 2025
Published Online:: 08 Dec 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2468
Pages:: 3071–3080

Abstract

The growing complexity of distributed networks and the increasing demand for robust cryptographic systems necessitate advanced mathematical frameworks for ensuring secure communication. This paper proposes an integrated approach using algebraic graph models to analyze, design, and evaluate security mechanisms within distributed networks. By leveraging tools from discrete mathematics, particularly graph theory, and applied algebra such as group theory, finite fields, and matrix algebra, we construct formal models that capture the structural and functional aspects of network security. These models provide a foundation for developing efficient cryptographic protocols, identifying network vulnerabilities, and enhancing data confidentiality, integrity, and authentication mechanisms. Additionally, we explore how algebraic graph structures such as Cayley graphs, lattice-based networks, and polynomial-based key distributions can be employed to design resilient and scalable network architectures. The proposed framework is validated through case studies and complexity analyses, demonstrating its applicability to real-world secure communication environments. This research contributes to the development of mathematically grounded, scalable solutions for contemporary challenges in network cryptography and secure distributed systems.

Keywords

Algebraic graph theory Cryptographic systems Secure distributed networks Applied algebra Discrete mathematics Network security Graph-based cryptography Cayley graphs Finite fields Key distribution models Group theory in cryptography Network topology modeling Lattice-based security Mathematical network modeling Cryptographic protocol design

Subject Classifications

Primary 93A30Secondary 49K15

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Journal of Discrete Mathematical Sciences and Cryptography

Algebraic graph models for secure distributed networks and cryptographic systems

Abstract

Keywords

Subject Classifications

References