Post-quantum cryptographic schemes using lattice problems
*Mohammed Wahed Ali KhanCorresponding authormdwahedalikhan@gmail.comDepartment of CybersecurityVersos - Unleash the FutureRiyadh, 11353, Kingdom of Saudi ArabiaView full profile → , Afreen Rahmat Khatoona.rkhatoon15@gmail.comDepartment of Electronics & Communication EngineeringUniversity College of EngineeringOsmania UniversityHyderabad, Telangana, 500007, IndiaView full profile → , Hafiz Munaam Hussain Tariqmunaamhussaintariq@hotmail.comDepartment of Computer Science and Information TechnologyNED University of Engineering and TechnologyKarachi, 75330, PakistanView full profile → , Tahreem Khantahreem.tariq92@gmail.comDepartment of Computer Science and Information TechnologyNED University of Engineering and TechnologyKarachi, 75330, PakistanView 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-3032
- Pages:
- 4065–4074
Abstract
The quick progress of quantum computing is a considerable risk to the classical cryptography of the public key and, the creation of quantum-resistant analogs is necessary. This paper provides a generalized architecture of post-quantum cryptographic schemes, by using lattice problems, especially Learning with Errors (LWE) and Ring-LWE (RLWE). The suggested architecture combines the secure public-key encryption and key encapsulation mechanisms (KEMs) with the implementation in the IoT, blockchain, and cloud setup. An original lattice-based encryption design is developed that hybridizes with classical cryptographic primitives to improve security, efficiency and interoperability. It is a methodology that focuses on structured lattice formulations, noise based hardness models and parameter selection optimisation of real time performance. It is proved that experimental analysis has better resilience against quantum attacks and is computationally efficient. The outcomes confirm the high level of strength and scalability of the proposed solution, which can be implemented in the next generation secure communication systems.
Keywords
Subject Classifications
References
[1] M. E. Sabani, I. K. Savvas, and G. Garani, “Learning with errors: A lattice-based keystone of post-quantum cryptography,” Signals, vol. 5, no. 2, pp. 216–243 (2024), doi: 10.3390/signals5020012.
[2] D. S. Amirkhanova, M. Iavich, and O. Mamyrbayev, “Lattice-based post-quantum public key encryption scheme using ElGamal’s principles,” Cryptography, vol. 8, no. 3, Art. no. 31 (2024), doi: 10.3390/cryptography8030031.
[3] A. Ibrahim and F. Gebali, “Efficient serial systolic polynomial multiplier for lattice-based post-quantum cryptographic schemes in IoT edge node,” Network, vol. 6, no. 2, Art. no. 21 (2026), doi: 10.3390/network6020021.
[4] Y. Zhang, Y. Tang, C. Li, H. Zhang, and H. Ahmad, “Post-quantum secure identity-based signature scheme with lattice assumption for Internet of Things networks,” Sensors, vol. 24, no. 13, Art. no. 4188 (2024), doi: 10.3390/s24134188.
[5] R. Asif, “Post-quantum cryptosystems for Internet-of-Things: A survey on lattice-based algorithms,” IoT, vol. 2, no. 1, pp. 71–91 (2021), doi: 10.3390/iot2010005.
[6] M. E. Sabani, I. K. Savvas, D. Poulakis, G. Garani, and G. C. Makris, “Evaluation and comparison of lattice-based cryptosystems for a secure quantum computing era,” Electronics, vol. 12, no. 12, Art. no. 2643 (2023), doi: 10.3390/electronics12122643.
[7] S. Kulkarni, U. Kadam, D. K. Paswan, K. Shipra, B. C. Julme, and S. L. Dhondge, “Numerical stability analysis of nonlinear differential equations in engineering systems,” Journal of Interdisciplinary Mathematics, vol. 28, no. 6, pp. 2255–2261 (2025), doi: 10.47974/JIM-2367.
[8] M. Iavich, T. Kuchukhidze, and R. Bocu, “A post-quantum digital signature using Verkle trees and lattices,” Symmetry, vol. 15, no. 12, Art. no. 2165 (2023), doi: 10.3390/sym15122165.
[9] 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.
[10] J. Algar-Fernandez, A. Villacís-Vanegas, Y. Amaro-Aular, and M.-D. Cano, “Benchmarking post-quantum signatures and KEMs on general-purpose CPUs using a TCP client–server testbed,” Computers, vol. 15, no. 2, Art. no. 116 (2026), doi: 10.3390/computers15020116.
[11] A. Mulla, S. Dude, A. Pawar, K. Pharande, and S. Suryawanshi, “AI-powered cyber security protection tool,” IJRAET, vol. 14, no. 2s, pp. 226–230 (Dec. 2025).
[12] M. Á. González de la Torre, L. Hernández Encinas, and A. Queiruga-Dios, “Analysis of the FO transformation in the lattice-based post-quantum algorithms,” Mathematics, vol. 10, no. 16, Art. no. 2967 (2022), doi: 10.3390/math10162967.
[13] F. Movahedi, “Extremal trees and their properties for Sigma index with fixed degree sequence,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 3, pp. 1239–1248 (2026), doi: 10.47974/JDMSC-2198.
[14] V. L. R. da Costa, J. López, and M. V. Ribeiro, “A system-on-a-chip implementation of a post-quantum cryptography scheme for smart meter data communications,” Sensors, vol. 22, no. 19, Art. no. 7214 (2022), doi: 10.3390/s22197214.




