Key Pre-distribution Scheme: Enhanced Security in Distributed Systems

Document Type : Original Research Manuscripts

Authors

1 Ph.D. Candidate, Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.

2 Professor, Department of Computer Engineering, Faculty of Engineering, Shahed University, Tehran, Iran.

10.22034/kps.2025.495040.1217
Abstract
This paper presents a novel key pre-distribution scheme designed to improve secure communication within distributed systems by using noncommutative ring theory and Linear Feedback Shift Registers (LFSRs). The use of noncommutative rings enables the creation of more complex and secure mathematical frameworks for cryptographic key generation, enhancing resilience against common security threats. LFSRs are selected for their efficiency and minimal overhead in key generation, making this approach particularly effective for resource-constrained environments, such as Internet of Things (IoT) and sensor networks. By combining noncommutative rings with LFSR-based generation techniques, the proposed scheme delivers a lightweight, scalable, and highly secure solution for key pre-distribution. Simulation results demonstrate notable improvements in both security and efficiency. In order to enhance scalability, it is advisable to explore optimizations within the Key Agreement and Link Setup phases, as well as the implementation of parallel processing strategies. Furthermore, conducting empirical testing in various IoT environments would yield valuable insights regarding the practicality of the approach and its capacity for further enhancements. This analysis highlights the algorithm's promise for secure and efficient key management in small to medium-scale IoT systems, while also identifying areas for refinement necessary to support larger networks.

Keywords

Subjects

Ahangar, A., Babalhavaeji, F., Hosseini Beheshti, M. S., Hariri, N., & Khademi, M. (2024). Semantic model of Information Security: Extracting Conceptual Network with Analysis Approach of Scientific Publications and Delphi. Scientometrics Research Journal, 9(2), 247-268. doi: 10.22070/rsci.2022.14656.1511
Anzani, M., Haj Seyyed Javadi, H. & Modirir, V. (2018), Key-management scheme for wireless sensor networks based on merging blocks of symmetric design. Wireless Netw 24, 2867–2879. doi: 10.1007/s11276-017-1509-y
Anshel, I., Anshel, M., & Goldfeld, D. (1999). An algebraic method for public-key cryptography. Mathematical Research Letters, 6(3), 287-291. ‏
 
Anshel, I., Goldfeld, D., & Gunnells, P. E. (2023). $\aleph$-structures: One-way Actions via Holomorphs and Split Extensions with Cryptographic Applications. In Analysis, Cryptography and Information Science (pp. 1-19). doi: 10.1142/9789811271922_0001
Arnault, F., Berger, T., Minier, M., & Pousse, B. (2011). Revisiting LFSRs for cryptographic applications. IEEE Transactions on Information Theory, 57(12), 8095-8113. ‏ doi:10.1109/TIT.2011.2164234
Azizi Nasrabadi, V., Haj Seyyed Javadi, H., & Moussavi, A. (2025). Secure data communication in IoT-based medical health systems using Frobenius rings. International Journal of Nonlinear Analysis and Applications. ‏16 (1),179-190. doi: 10.22075/ijnaa.2023.31921.4734.

Bahrami, PN., Haj Seyyed Javadi, H., Dargahi, T., Dehghantanha, A., & Raymond Choo, K. K. (2018). A hierarchical key pre-distribution scheme for fog networks. Concurrency and Computation: Practice and Experience. 31(22). doi: 10.1002/cpe.4776

Bechkit, W., Challal, Y., Bouabdallah, A., & Tarokh, V. (2013). A highly scalable key pre-distribution scheme for wireless sensor networks. IEEE Transactions on wireless Communications, 12(2), 948-959. ‏ doi: 10.1109/TWC.2012.010413.120732.
Bhat, G. M., & Ahmad, F. (2007). New lfsr based circuit for generating complex code sequences. Electronics world+ wireless world, 40-43.
Blundo, C., De Santis, A., Herzberg, A., Kutten, S., Vaccaro, U., & Yung, M. (1998). Perfectly secure key distribution for dynamic conferences. Information and Computation, 146(1), 1-23.‏
El-Hajj, M., & Beune, P. (2024). Lightweight public key infrastructure for the Internet of Things: A systematic literature review. Journal of Industrial Information Integration, 41, 100670. ‏ doi: 10.1016/j.jii.2024.100670
Eschenauer, L., & Gligor, V. D. (2002, November). A key-management scheme for distributed sensor networks. In Proceedings of the 9th ACM Conference on Computer and Communications Security (pp. 41-47).‏ doi: 10.1145/586110.586117.
Eschenauer, L., Gligor, V. D., & Baras, J. (2004). On trust establishment in mobile ad-hoc networks. In Security Protocols: 10th International Workshop, Cambridge, UK, April 17-19, 2002. Revised Papers 10 (pp. 47-66). Springer Berlin Heidelberg. doi:10.1007/978-3-540-39871-4_6‏
Farshid, R., Abedi, Y., & Jafari, S. (2022). Small-Data and Its Application among Various Scientific Areas: A Scientometric Study. Scientometrics Research Journal, 8(1), 255-281. doi: 10.22070/rsci.2020.5871.1440.
George, N., Nithin, S., & Kottayil, S. K. (2016). Hybrid key management scheme for secure AMI communications. Procedia Computer Science, 93, 862-869.‏ doi:10.1016/j.procs.2016.07.260.
Hanoymak, T., & Küsmüs, O. (2015). On construction of cryptographic systems over units of group rings. Int Electron J Pure Appl Math, 9, 37-43. ‏ doi:10.12732/iejpam.v9i1.5
Janani, M., Jeevitha, R., Jaikumar, R., Suganthi, R., & Jhansi Ida, S. (2023). Multivariate Cryptosystem Based on a Quadratic Equation to Eliminate the Outliers Using Homomorphic Encryption Scheme. In Homomorphic Encryption for Financial Cryptography: Recent Inventions and Challenges (pp. 277-302). Cham: Springer International Publishing. ‏ doi:10.1007/978-3-031-35535-6_13

Javanbakht, M., Erfani, H., Haj Seyyed Javadi, H., & Daneshjoo, P. (2014). Key Predistribution Scheme for Clustered Hierarchical Wireless Sensor Networks based on Combinatorial Designs. doi: 10.1002/sec.914

Kendall, M., Martin, K. M., Ng, S. L., Paterson, M. B., & Stinson, D. R. (2014). Broadcast-enhanced key predistribution schemes. ACM Transactions on Sensor Networks (TOSN), 11(1), 1-33. ‏ doi:10.1145/2629661
Kumar, G., & Saini, H. (2017). On Security and Performance in ECC Noncommutative Cryptography and Signcryption (Doctoral dissertation, Jaypee University of Information Technology, Solan, HP).‏
Lam, T. Y. (1991). A first course in noncommutative rings. Graduate Texts in Mathematics/Springer-Verlag, 131.‏
Malik, M., Dutta, M., & Granjal, J. (2019). A survey of key bootstrapping protocols based on public key cryptography in the Internet of Things. IEEE Access, 7, 27443-27464.‏ doi:10.1109/ACCESS.2019.2900957
Masaeli, N., Haj Seyyed Javadi, H., & Erfani, S. H. (2020). Key pre-distribution scheme based on transversal design in large mobile fog networks with multi-clouds. Journal of Information Security and Applications, 54, 102519. doi:10.1016/j.jisa.2020.102519
Modiri, V., Haj Seyyed Javadi, H., & Anzani, M. (2017). A Novel Scalable Key Pre-Distribution Scheme for Wireless Sensor Networks Based on Residual Design. Wireless Personal Communication, 96, 2821–2841. doi: 10.1007/s11277-017-4326-9.
Morshed Aski, A., Haj Seyyed Javadi, H. & Shirdel, G.H. (2020).  A Full Connectable and High Scalable Key Pre-Distribution Scheme Based on Combinatorial Designs for Resource-Constrained Devices in IoT Network. Wireless Personal Communication, 114, 2079–2103. doi: 10.1007/s11277-020-07466-0
Moussavi, A., & Shamsi, M. (2018). A Polynomial-Based Key Distribution Approach for Wireless Sensor Networks. Iranian Journal of Science and Technology, Transactions A: Science, 42, 13-20.‏ doi: 10.22099/ijsts.2015.3219
Myasnikov, A. G., Shpilrain, V., & Ushakov, A. (2011). Non-commutative cryptography and complexity of group-theoretic problems (No. 177). American Mathematical Soc.
Savir, J., & McAnney, W. H. (1990, September). A multiple seed linear feedback shift register. In Proceedings. International Test Conference 1990 (pp. 657-659). IEEE. ‏
Shi, Y., & Zhang, B. (2016). Recent advances in transition metal phosphide nanomaterials: synthesis and applications in hydrogen evolution reaction. Chemical Society Reviews, 45(6), 1529-1541.‏ doi:10.1039/c5cs00434a
Siraparapu, S. R., & Azad, S. M. A. K. (2024). Securing the IoT Landscape: A Comprehensive Review of Secure Systems in the Digital Era. e-Prime-Advances in Electrical Engineering, Electronics and Energy, 100798.‏ doi: 10.1016/j.prime.2024.100798
Solari Esfehani, N., & Haj Seyyed Javadi, H. (2021). A survey of key pre-distribution schemes based on combinatorial designs for resource-constrained devices in the IoT network. Wireless Networks, 27(4), 3025-3052.‏ doi:10.1007/s11276-021-02629-8
Swan, R. G. (1962). Factorization of polynomials over finite fields. Pacific J. Math., 12, 1099-1106.
Tajeri, M., Javadi, H. H. S., Bayat, M., & Shiri, M. E. (2022). Pre-Distribution Encryption Key Scheme for Communicating between IoT Device Layer and Fog Layer. Cybernetics and Systems, 55(8), 2093–2117. doi:10.1080/01969722.2022.2145665
Yao, Y., Duan, J., Xu, K., Cai, Y., Sun, Z., & Zhang, Y. (2024). A survey on large language model (llm) security and privacy: The good, the bad, and the ugly. High-Confidence Computing, 4(2), 100211.‏ doi:10.1016/j.hcc.2024.100211.

  • Receive Date 20 December 2024
  • Revise Date 03 January 2025
  • Accept Date 24 February 2025