On the interplay between combinatorial designs and modern cryptography
S. Seethaladeviseethaladevi@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 → , *Suraj BhanCorresponding authorsuraj.bhan@niu.edu.inSchool of Engineering & TechnologyNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Dipti Ganesh Korwardeepti.korwar1@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Sandhya Onkar Ahiresandhyaahire@gmail.comDepartment of Electronics Engineering (VLSI Design & Technology)AISSMS College of EngineeringPune, Maharashtra, 411001, IndiaView full profile → , Ishita Guptaishita.gupta@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , V. Anantha Lakshmivananthalakshmi@gmail.comDepartment of CSE (Artificial Intelligence & Machine Learning)Pragati Engineering CollegeSurampalem, Kakinada District, Andhra Pradesh, 533437, 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-3074
- Pages:
- 4571–4582
Abstract
Combinatorial designs are a mathematical basis to build secure and effective cryptographic systems. They allow randomness to be well structured, uniformly distributed, and highly diffused, which is critical to the security primitives in the modern world. In this paper, the interaction between orthogonal arrays, Latin squares and quasigroup constructions in fortifying substitution permutation networks and S-box design is discussed. It provides a single analytical framework between combinatorial properties and algebraic hardness assumptions, which allow strong resistance to linear, differential and algebraic attacks. Also, hybridization with the current cryptography methods, and, in particular, post-quantum methods, is considered to improve scalability and resilience. The theoretical and experimental analyses show that it has better security measures, structural efficiency, and fault tolerances than the traditional constructions. The findings underscore the importance of the combinatorial design theory as an effective instrument to the next-generation cryptographic architecture. This book offers information on safe, scalable, and ground-based system design.
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References
[1] B. K. Roy and A. Roy, “IoT-applicable generalized frameproof combinatorial designs,” IoT, vol. 4, no. 3, pp. 466–485 (2023), doi: 10.3390/iot4030020.
[2] M. Karpinski, A. Sokolov, A. Tokkuliyeva, V. Radush, N. Kazakova, A. Shaikhanova, N. Zagorodna, and A. Korchenko, “Development of high-quality cryptographic constructions based on many-valued logic affine transformations,” Electronics, vol. 14, no. 10, Art. no. 2094 (2025), doi: 10.3390/electronics14102094.
[3] S. Hoque, A. Aydeger, and E. Zeydan, “Post-Quantum Secure UE-to-UE Communications,” 2024 15th International Conference on Network of the Future (NoF), Castelldefels, Spain, pp. 28-30 (2024), doi: 10.1109/NoF62948.2024.10741456.
[4] B. Zolfaghari, K. Bibak, and T. Koshiba, “The odyssey of entropy: Cryptography,” Entropy, vol. 24, no. 2, Art. no. 266 (2022), doi: 10.3390/e24020266.
[5] D. Commey, S. G. Hounsinou, and G. V. Crosby, “Post-Quantum Secure Blockchain-Based Federated Learning Framework for Healthcare Analytics,” in IEEE Networking Letters, vol. 7, no. 2, pp. 126-129 (June 2025), doi: 10.1109/LNET.2025.3563434.
[6] S. Thakur, L. Yadav, K. T. Punj, Y. Sood, V. K. Bhosale, and S. K. Swarnkar, “Addressing quantum threats to cryptographic security systems with advanced quantum-resistant algorithms,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 2-B, pp. 839–847 (2026), doi: 10.47974/JDMSC-2534.
[7] S. S. Vellela, P. Anusha, N. R. Vullam, J. Jala, V. S. Bellapu, and A. S. Vindhya, “Quantum Cryptography and Key Distribution for Secure Communication in the Post Quantum World,” 2025 International Conference on Sustainable Communication Networks and Application (ICSCN), Theni, India, pp. 619-624 (2025), doi: 10.1109/ICSCN67106.2025.11308316.
[8] J. M. Jose and V. Panchami, “A Survey on Consensus Algorithms in Blockchain Based on Post Quantum Cryptosystems,” 2022 5th International Conference on Computational Intelligence and Networks (CINE), Bhubaneswar, India, pp. 1-6 (2022), doi: 10.1109/CINE56307.2022.10037353.
[9] M. B. Chittem and A. K. Pradhan, “Hybrid Quantum-Classical Encryption (HQCE) Algorithm: A Post-Quantum Secure Solution for Data Encryption,” 2024 OITS International Conference on Information Technology (OCIT), Vijayawada, India, pp. 321-326 (2024), doi: 10.1109/OCIT65031.2024.00063.
[10] J. Wu, M. Xu, Y. Guo, and J. Jin, “A High-Speed 3-bit/cycle SAR ADC Employing Combinatorial Redundancy Offset Calibration Technique,” 2025 7th International Conference on Circuits and Systems (ICCS), Huzhou, China, pp. 146-150 (2025), doi: 10.1109/ICCS66653.2025.11569712.
[11] S. Fink, N. Fomin-Thunemann, F. Kamari, Y. Kovalchuk, and O. Garaschuk, “Glomerulus-specific inhomogeneity of the basal activity map in the olfactory bulb,” Int. J. Mol. Sci., vol. 27, no. 8, Art. no. 3684 (2026), doi: 10.3390/ijms27083684.
[12] P. Prabu, M. Alsulami, D. Alsadie, A. K. J. Saudagar, M. Alkhathami, and R. C. Poonia, “Utilizing behavioral deep learning models to monitoar and alert physicians regarding trauma cases,” J. Inf. Optim. Sci., vol. 44, no. 5, pp. 983–995 (2023), doi: 10.47974/JIOS-1461.
