Number-theoretic foundations of post-quantum cryptographic protocols
Osama Al Rawidr.osama.alrawi@gulfuniversity.edu.bhDepartment of Electrical & Electronic EngineeringCollege of EngineeringGulf UniversitySanad, 26489, Kingdom of BahrainView full profile → , M. Thamizhsudarthamizhsudar@avit.ac.inDepartment of Humanities and Sciences (Mathematics Division)Aarupadai Veedu Institute of TechnologyVinayaka Mission’s Research Foundation (Deemed to be University)Paiyanoor, Chennai, Tamil Nadu, 603104, IndiaView full profile → , N. Nivethanivethan@maher.ac.inDepartment of Computer ScienceMeenakshi College of Arts and ScienceMeenakshi Academy of Higher Education and ResearchChennai, Tamil Nadu, 600078, IndiaView full profile → , *Vikram V. PatelCorresponding authorvikrampatel@gokuluniversity.ac.inFaculty of EngineeringGokul Global UniversitySidhpur, Gujarat, 384151, IndiaView full profile → , Mrunmai Mandar Ranademrunmai.ranade@vupune.ac.inDepartment of Engineering SciencesVishwakarma UniversityPune, Maharashtra, 411048, IndiaView full profile → , Alisher Abduvokhidovalisherabdulvohidovl@gmail.comFaculty of Physics and MathematicsAndijan State University129 University Street, Andijan, 170100, UzbekistanView full profile → , Sardor Sabirovsabirov_sardor@mamunedu.uzDepartment of General Professional SciencesMamun UniversityKhiva, 220900, 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-3012
- Pages:
- 3827–3838
Abstract
Conventional cryptographic systems such as factorization and discrete logarithm problems are threatened by the quick development of quantum computing. This paper offers a thorough study of number-theoretic problems and structures underlying post-quantum cryptographic protocols based on modular arithmetic, algebraic structures, lattices and computational hardness assumptions. The research is based on the mathematical problems of Learning with Errors (LWE) and Short Integer Solution (SIS) which are used for secure quantum-resistant encryption, digital signature and key exchange mechanisms. In secure communication scenarios, a framework of structured protocol is analyzed, which combines lattice-based operations and modular polynomial transformations. Experimental comparisons show that these schemes are not only practically efficient in computation but also have a level of security greater than 95% against the quantum attack, both for the LWE and SIS schemes. The results point towards the scalability, robustness and future applicability of number theoretic post quantum cryptographic systems.
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References
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