On the application of hypergraph theory in modeling multi-party cryptographic protocols with enhanced security guarantees
G. Vijaya Kumargvijayakumar@outlook.comDepartment of Computer Science and EngineeringPragati Engineering CollegeSurampalem, Kakinada District, Andhra Pradesh, 533437, IndiaView full profile → , *Amit KumarCorresponding authoramit.kumar.orp@chitkara.edu.inCentre for Research Impact & OutcomeChitkara University Institute of Engineering and TechnologyChitkara UniversityRajpura, Punjab, 140401, India0009-0001-9561-2768View full profile → , Varya Agarwalvaryaaggarwal@gmail.comQuantum University Research CenterQuantum UniversityRoorkee, Uttarakhand, 247667, India0009-0000-3792-1565View full profile → , Khushbookhushboo@niu.edu.inSchool of Fine Arts & DesignNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Pochampalli Deepthipochampallideepthi@proton.meCentre for Multidisciplinary ResearchAnurag UniversityHyderabad, Telangana, 500088, India0009-0002-8728-0879View full profile → , Nitinkumar M. Patelnmpatel.gen.hcet@gokuluniversity.ac.inFaculty of EngineeringGokul Global UniversitySidhpur, 384151, Gujarat, India0009-0001-9140-5964View 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-3083
- Pages:
- 4683–4692
Abstract
The paper discusses the application of hypergraph theory to the analysis of multi-party cryptographic protocols that can provide a high level of security. The traditional graph-based models fail to capture the interaction between two or more participants at higher orders and therefore cannot be used to conduct accurate security analysis. A solution is a hypergraph-based model, in which both the vertices and hyperedges represent entities and multi-party communication and computation steps. The protocol implementation is formalized as hypergraph transformations, enabling a finesse tuning of the modeling of the concurrency, dependency and adversarial influence. Analytical analysis demonstrates a more expressiveness in which it is demonstrated that there is an increase of approximately 28.6 in the efficiency of the interaction modeling and the ability to detect attack is improved by 21.3% with respect to the conventional graph models. The proposed methodology improves protocol checking, scale-ability and resiliency. It provides a mathematically well-founded foundation in the development of efficient and secure multi-party cryptographic systems in distributed environment.
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References
[1] C. Qu, M. Tao, and R. Yuan, “A hypergraph-based blockchain model and application in Internet of Things-enabled smart homes,” Sensors, vol. 18, no. 9, Art. no. 2784 (2018), doi: 10.3390/s18092784.
[2] J. Fenner-López, C. Castillo-Muñoz, F. Escobar-Jara, A. Bustamante-Mora, and M. Burgos-López, “Enhancing secure multi-party computation with Damgård–Jurik and NIZK proofs: A lightweight protocol for scalable aggregation,” Appl. Sci., vol. 15, no. 19, Art. no. 10357 (2025), doi: 10.3390/app151910357.
[3] J. Zhou, Y. Feng, Z. Wang, and D. Guo, “Using secure multi-party computation to protect privacy on a permissioned blockchain,” Sensors, vol. 21, no. 4, Art. no. 1540 (2021), doi: 10.3390/s21041540.
[4] W. Rajaian, K. Velayutham, S. Moni, and S. Nazarudeen, “On the b-chromatic number of 3-petal graph families,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 4, pp. 1609–1627 (2026), doi: 10.47974/JDMSC-2345.
[5] A. Kulshrestha, A. Rampuria, M. Denton, and A. Sreenivas, “Cryptographically secure multiparty computation and distributed auctions using homomorphic encryption,” Cryptography, vol. 1, no. 3, Art. no. 25 (2017), doi: 10.3390/cryptography1030025.
[6] C. K. Sharma, L. Kaur, S. Mishra, S. Kulkarni, I. Khayrullayev, D. M. Mate, and P. Wakhare, “Unifying algebraic structures in mathematics for diverse theoretical applications,” J. Interdiscip. Math., vol. 29, no. 3, pp. 557–565 (2026), doi: 10.47974/JIM-2490.
[7] M. Xiao, W. Cheng, H. Fan, H. Shao, Z. Li, and Y. Zhong, “Formal analysis of EAP-TLS protocol based on logic of events,” Symmetry, vol. 17, no. 9, Art. no. 1456 (2025), doi: 10.3390/sym17091456.
[8] C.-C. Lee, D.-T. Do, and A. L. Imoize, “Advances in mathematical cryptography and information security toward Industry 5.0,” Mathematics, vol. 13, no. 16, Art. no. 2660 (2025), doi: 10.3390/math13162660.
[9] A. Liu, X.-B. Chen, S. Xu, Z. Wang, Z. Li, L. Xu, Y. Zhang, and Y. Chen, “A secure scheme based on a hybrid of classical-quantum communications protocols for managing classical blockchains,” Entropy, vol. 25, no. 5, Art. no. 811 (2023), doi: 10.3390/e25050811.
[10] W.-K. Yu, Y. Yang, Y.-X. Li, N. Wei, and S.-F. Wang, “Multi-party cryptographic key distribution protocol over a public network based on a quick-response code,” Sensors, vol. 22, no. 11, Art. no. 3994 (2022), doi: 10.3390/s22113994.
[11] R. C. Poonia, R. Almakki, A. K. J. Saudagar, A. Altameem, and M. Albathan, “A detailed examination of LSTM networks for large-scale text generation with optimizing sequence models,” J. Inf. Optim. Sci., vol. 45, no. 5, pp. 1477–1486 (2024), doi: 10.47974/JIOS-1769.
[12] D. Wu, B. Liang, Z. Lu, and J. Ding, “Efficient secure multi-party computation for multi-dimensional arithmetics and its applications,” Cryptography, vol. 9, no. 3, Art. no. 50 (2025), doi: 10.3390/cryptography9030050.
