Design of a Secret Sharing Scheme with Mandatory Subgroup Participation
Source abstract
Abstract
This paper proposes an approach based on a secret sharing scheme with the mandatory participation of predefined subgroups. The proposed scheme allows secret reconstruction only when representatives from each designated group of participants (e.g., cloud providers, legally independent parties, etc.) are present. This mechanism enhances resistance to internal collusion, strengthens access control, and enables distributed management. The structure and mathematical foundations of the proposed scheme are presented, along with an analysis of its properties. A cryptanalysis is conducted, evaluating the scheme’s resilience to various types of attacks, and the results are discussed. The computational complexity of the algorithm is also analyzed, and its resource efficiency is confirmed.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Cryptography and Data Security · Advanced Steganography and Watermarking Techniques · Privacy-Preserving Technologies in Data
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan
Faculty of Languages and Humanities, Egyptian University of Islamic Culture Nur-Mubarak, Almaty 050016, Kazakhstan
Funding
Ministry of Science and Higher Education of the Republic of Kazakhstan
References (20)
Show source-provided references
1. Čuřík, P., Ploszek, R., and Zajac, P. (2022). Practical Use of Secret Sharing for Enhancing Privacy in Clouds. Electronics, 11.10.3390/electronics11172758 ↗
2. Huang, C.-W., and Juan, J.S.-T. (2025). New (t, n)-Threshold P-VSS Schemes Using Fewer Types of Polarizers. Eng. Proc., 92.10.3390/engproc2025092049 ↗
3. Liu, Y., Sun, Q., Yang, Z., Zhou, Y., Zhao, W., and Shi, D. (2024). Progressive Reconstruction on Region-Based Secret Image Sharing. Electronics, 13.10.3390/electronics13081529 ↗
4. Progressive (k,n) secret image sharing scheme with meaningful shadow images by GEMD and RGEMD10.1016/j.jvcir.2018.08.003 ↗
5. Threshold File Sharing Based on Bit Masks: Ideas and Possible Applications
6. A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption10.1063/5.0270220 ↗
7. A new method of threshold secret sharing based on residue class systems
8. How to share a secret10.1145/359168.359176 ↗
9. Buchanan, W.J. (2024, April 30). Shamir Secret Sharing (SSS). Asecuritysite.com. Available online: https://asecuritysite.com/shares.
10. Alam, I., Alali, A.S., Ali, S., and Asri, M.S.M. (2024). A Verifiable Multi-Secret Sharing Scheme for Hierarchical Access Structure. Axioms, 13.10.20944/preprints202405.2061.v1 ↗
11. An information theoretic approach to secret sharing10.1109/TIT.2015.2421905 ↗
12. Watanabe, Y., and Shikata, J. (2014). Timed-release secret sharing scheme with information theoretic security. arXiv.10.1007/978-3-319-21356-9_15 ↗
13. Revisiting Group Oriented Secret Sharing Schemes10.1016/j.ins.2021.12.053 ↗
14. Binu, V.P., and Sreekumar, A. (2016). Threshold multi-secret sharing using elliptic curve and pairing. arXiv.
15. Modification of Asmuth-Bloom data sharing scheme using the fractal geometry method
16. A verifiable threshold secret sharing scheme based on lattices10.1016/j.ins.2018.11.004 ↗
17. A Parallel Color Image Encryption Algorithm Based on a 2-D Logistic-Rulkov Neuron Map10.1109/JIOT.2025.3540097 ↗
18. Cheating identifiable polynomial based secret sharing scheme for audio and image10.1007/s11042-023-15625-1 ↗
19. Tsai, Y.-Y., Jhou, J.-Y., You, T.-Y., and Lu, C.-T. (2025). Advancing Secret Sharing in 3D Models Through Vertex Index Sharing. Electronics, 14.10.3390/electronics14081675 ↗
20. Du, J., Dai, C., Mao, P., Dong, W., Wang, X., and Li, Z. (2024). An Efficient Lightweight Authentication Scheme for Smart Meter. Mathematics, 12.10.3390/math12081264 ↗