Graph-theoretic approaches to post-quantum cryptographic protocols
S. Gayathrigayathri@avit.ac.inDepartment of Humanities and Sciences (Mathematics Division)Aarupadai Veedu Institute of TechnologyVinayaka Mission’s Research Foundation (Deemed to be University)Chennai, Tamil Nadu, 603104, IndiaView full profile → , Vundela SwathivundelaSwathi2024@protonmail.comCentre for Multidisciplinary ResearchAnurag UniversityHyderabad, Telangana, 500088, IndiaView full profile → , *Mohammed Hasan AldulaimiCorresponding authormohammed.hassan@uomus.edu.iqDepartment of Computer Techniques EngineeringCollege of EngineeringAl-Mustaqbal UniversityHillah, Babylon, 51001, IraqView full profile → , Sarvinoz Kasimovas_kasimova@proton.meDepartment of National Languages and LiteratureUniversity of Journalism and Mass Communications of UzbekistanTashkent, 100027, UzbekistanView full profile → , Qobil Hayitovqobilxayitov1@gmail.comDepartment of PsychologyNational University of Uzbekistan named after Mirzo UlugbekTashkent, 100174, UzbekistanView full profile → , Erdonov Bekmurodbekmurod.erdonov@mail.ruDepartment of Information Technology and Exact SciencesTermez University of Economics and ServiceTermez, 190111, UzbekistanView 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-3010
- Pages:
- 3803–3814
Abstract
The fast development of quantum computing poses a threat to the security of the classical cryptographic system, and so there is a need to have strong post-quantum systems that are hard to break. The issue discussed in this paper is how to develop secure and efficient cryptographic protocols, taking advantage of graph-theoretic constructions that are not vulnerable to quantum attacks. The initial goal is to create a cryptographic scheme based on graphs and with hard problems like Graph Isomorphism, Hamiltonian Path and expander graph properties. The suggested methodology combines combinatorial graph structures with algebraic transformations, which are backed up by hybrid models that combine graph embeddings and lattice-based inspired security mechanisms. The synthetic and benchmark graph datasets are experimented on and the performance is measured based on the strength of security, complexity of computation and the scale. The suggested scheme has 97.1% accuracy in attack resistance, decreases the time of key generation by 21.4% and enhances the structural security measures by 18.6% over lattice-only schemes. Compares and contrasts to show improved resilience against quantum adversaries with efficiency. The innovation in the framework is that it integrates graph-theorically to design cryptography in a hybrid manner. This research goes a long way in enhancing the security of communication between IoT, cloud and distributed systems.
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References
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