Quantum-resistant cryptographic constructions using discrete structures
Pallavi Vilas Mhaskepallavi.mhaske@mituniversity.edu.inDepartment of Ethical Science and Food TechnologyMIT School of Food TechnologyMIT Art, Design and Technology UniversityPune, Maharashtra, 412201, IndiaView full profile → , *Debanjana PrasadCorresponding authordebanjana.prasad@niu.edu.inDepartment of BiotechnologyNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Namrata Somnath Bajarenamrata.bajare@vit.eduDepartment of Computer EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Rubi Kamborubi.kambo@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , D. Raghavendra Gowdaraghavendrag@outlook.comDepartment of Computer Science and EngineeringVardhaman College of EngineeringShamshabad, Hyderabad, Telangana, 501218, 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-3075
- Pages:
- 4583–4594
Abstract
Conventional cryptographic constructions have to meet the challenge of the quick development of quantum computing, and they require the creation of efficient constructions resistant to quantum attack. In this paper, the authors suggest a hybrid cryptographic model that combines lattice-based hardness assumptions, such as Learning with Errors (LWE) with graph theoretical and combinatorial structures to provide greater security, efficiency and scalability. This framework is a hybrid of lattice trapdoor functions, expander graphs, and discrete optimization methods, aiming to enhance structural robustness against classical and quantum attackers. The performance is compared with the conventional methods of RSA/ECC and lattice and graph-based cryptographic methods. The results reported in this work shows that, the proposed hybrid framework provides the security level of 256 bits and quantum attack resistance as 96.8%, whereas the lattice-based approach provides 82.4%. Moreover, the hybrid construction has the key generation time 21.1ms, encryption time 14.1ms and throughput of 183Mbps. These values represent a decrease of 14.92% for the key generation time, 10.19% for the encryption time and 27.96% for the memory usage when compared to the baseline which is based on lattices. These results indicate that a combination of complementary discrete mathematical models could be a potential way to design efficient, scalable post-quantum cryptographic systems.
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References
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