Enumeration of graph factorizations and cryptographic uses
Yogita Deepak Sinkaryogita.sinkar@vpkbiet.orgDepartment of Artificial Intelligence and Data ScienceVidya Pratikshan Kamalnayan Bajaj Institute of Engineering and TechnologyBaramati, Maharashtra, 413133, IndiaView full profile → , *Deepika DalaviCorresponding authordeepikadalvi18@gmail.comDepartment of Information TechnologyIndira College of Engineering & ManagementPune, Maharashtra, 410506, IndiaView full profile → , Aradhana Sahuaradhana@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, 490024, Chhattisgarh, IndiaView full profile → , Sheetal Kusalsheetal.borhade@sitpune.edu.inSymbiosis Centre for Applied Artificial Intelligence (SCAAI)Symbiosis Institute of TechnologySymbiosis International (Deemed University)Pune, Maharashtra, 412115, IndiaView full profile → , Ram Balbhim Ghogareramghogare@gmail.comDepartment of Civil EngineeringS. B. Patil College of EngineeringIndapur, Pune, Maharashtra, 413106, IndiaView full profile → , Akshay Hemant Gonganeshrikant.barkade@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , R. Shanthishanthir@maher.ac.inDepartment of MathematicsMeenakshi College of Arts and ScienceMeenakshi Academy of Higher Education & Research (Deemed to be University)Chennai, Tamil Nadu, 600078, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3067
- Pages:
- 4483–4496
Abstract
The problem of listing factorizations of graph is a computationally expensive problem, and has not been successfully applied in the design of cryptographic systems up to date. This paper will solve this challenge by coming up with a systematic plan of listing graph factorizations and harnessing the combinatorics of graph factorizations to create secure cryptography systems. The main target of it is to create a powerful enumeration model and prove that it can be used in key generating, safe communication, and structural randomness. It is a mixture of algebraic graph theory, algorithms of combinatoric decomposition and enumeration model and tested on benchmark graph datasets, such as regular, complete and bipartite graphs. The experimental results indicate that the time of enumeration is reduced by 31.6 percent and structural uniqueness is also enhanced by 24.8 percent than the traditional brute-force computations and the diversity of cryptographic keys has been boosted by 27.3. The features that would be able to be differentiated in the comparative analysis are enhanced protection against structural attacks, and scalability. The solution introduces a new connection between the graph factorization theory and cryptographic primitives, which allow an effective, structure-based, security. This work establishes graph factorizations as a firm foundation for next-generation cryptographic systems.
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References
[1] J. Jin and Z. Tu, “Graph antimagic labeling: A survey,” Discrete Mathematics, Algorithms and Applications, vol. 16, Art. no. 2330002 (2024).
[2] J. Bensmail, “Maximising 1’s Through Proper Labeling,” Discussiones Mathematicae Graph Theory, vol. 45, pp. 351–376 (2025).
[3] A. K. Handa, A. Gondinho, and T. Singh, “On local distance antimagic labeling of graphs,” AKCE International Journal of Graphs and Combinatorics, vol. 21, pp. 91–96 (2023).
[4] A. I. Hussein, M. I. Hussein, and O. S. Hlail, “AI-generated privacy-preserving protocols for cross-cloud data sharing and collaboration,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 4-B, pp. 1265–1279 (2025), doi: 10.47974/JDMSC-2265.
[5] S. S. Dari, D. Dhabliya, A. Dhablia, S. Dingankar, M. J. Pasha, and S. N. Ajani, “Securing micro transactions in the Internet of Things with cryptography primitives,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, pp. 753–762 (2024).
[6] S. O. Akindeinde and S. D. Yakubu, “Hybrid block method with quasilinearization for the dynamical simulation of a methamphetamine abuse model,” Journal of Interdisciplinary Mathematics, vol. 29, no. 2, pp. 399–412 (2026), doi: 10.47974/JIM-2337.
[7] S. Nandy, “An intrusion detection mechanism for secured IoMT framework based on swarm-neural network,” IEEE Journal of Biomedical and Health Informatics, vol. 26, no. 5, pp. 1969–1976 (2022).
[8] M. Zivkovic, “Novel hybrid firefly algorithm: An application to enhance XGBoost tuning for intrusion detection classification,” PeerJ Computer Science, vol. 8, Art. no. e956 (2022).
[9] J. M. Clark, R. Andersson, and S. Moreau, “A comprehensive review of secure embedding stabilization in federated learning: Security models, optimization techniques, and emerging computing applications,” International Journal on Advanced Computer Engineering and Communication Technology, vol. 14, no. 2, pp. 174–180 (2025), doi: 10.65521/ijacect.v14i2.2032.
[10] R. C. Poonia, T. Singh, C. K. Rajashri, D. Mondal, and S. M. Patil, “Optimizing communication system security through comprehensive testing and intelligent network configurations,” Journal of Information and Optimization Sciences, vol. 47, no. 5-A, pp. 1709–1717 (2026), doi: 10.47974/JIOS-2261.
