Novel CRT-based Asymptotically Ideal Disjunctive Hierarchical Secret Sharing Scheme

Computer Science > Cryptography and Security [Submitted on 17 Mar 2026] Novel CRT-based Asymptotically Ideal Disjunctive Hierarchical Secret Sharing Scheme Hongju Li, Jian Ding, Fuyou Miao, Cheng Wang, Cheng Shu Disjunctive Hierarchical Secret Sharing (DHSS)} scheme is a type of secret sharing scheme in which the set of all participants is partitioned into disjoint subsets, and each subset is said to be a level with different degrees of trust and different thresholds. In this work, we focus on the Chinese Remainder Theorem (CRT)-based DHSS schemes due to their ability to accommodate flexible share sizes. We point out that the ideal DHSS scheme of Yang et al. (ISIT, 2024) and the asymptotically ideal DHSS scheme of Tiplea et al. (IET Information Security, 2021) are insecure. Consequently, existing CRT-based DHSS schemes either exhibit security flaws or have an information rate less than \frac{1}{2}. To address these limitations, we propose a CRT-based asymptotically perfect DHSS scheme that supports flexible share sizes. Notably, our scheme is asymptotically ideal when all shares are equal in size. Its information rate achieves one and it has computational security. Subjects: Cryptography and Security (cs.CR); Information Theory (cs.IT) Cite as: arXiv:2603.16267 [cs.CR]   (or arXiv:2603.16267v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2603.16267 Focus to learn more Submission history From: Jian Ding [view email] [v1] Tue, 17 Mar 2026 08:56:21 UTC (13 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)