Novel CRT-based Asymptotically Ideal Disjunctive Hierarchical Secret Sharing Scheme

2026-03-17

AI Summary

Existing Chinese Remainder Theorem (CRT)-based disjunctive hierarchical secret sharing (DHSS) schemes either suffer from security vulnerabilities or achieve an information rate below 1/2. This work proposes a novel CRT-based DHSS scheme that models hierarchical access structures and integrates a computational security mechanism, thereby achieving an information rate of 1 under equal-share-size conditions while supporting flexible share sizes. To the best of our knowledge, this is the first DHSS construction that simultaneously satisfies asymptotic ideality, high information rate, and computational security, offering a significant improvement over existing approaches.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Cognitive Modeling & Cognitive Systems: (Computational) Cognitive Architectures
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

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.

Problem

• Disjunctive Hierarchical Secret Sharing
• Chinese Remainder Theorem
• information rate
• security
• asymptotically ideal

Innovation

• CRT-based
• Asymptotically Ideal
• Disjunctive Hierarchical Secret Sharing
• Information Rate
• Computational Security