Asymptotically Ideal Conjunctive Hierarchical Secret Sharing Scheme Based on CRT for Polynomial Ring

2026-03-23

AI Summary

Existing Chinese Remainder Theorem (CRT)-based conjunctive hierarchical secret sharing (CHSS) schemes either suffer from security flaws or achieve an information rate below 1/2. This work proposes a novel CHSS scheme leveraging the CRT over polynomial rings combined with one-way functions, achieving asymptotically perfect secrecy under the computational security model. Notably, the proposed scheme is the first to attain an information rate of 1 while maintaining equal-sized shares, thereby offering both high security and high efficiency. These advantages represent a significant improvement over all existing CRT-based CHSS constructions.

Technology Category

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

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Conjunctive Hierarchical Secret Sharing (CHSS) is a type of secret sharing that divides participants into multiple distinct hierarchical levels, with each level having a specific threshold. An authorized subset must simultaneously meet the threshold of all levels. Existing Chinese Remainder Theorem (CRT)-based CHSS schemes either have security vulnerabilities or have an information rate lower than $\frac{1}{2}$. In this work, we utilize the CRT for polynomial ring and one-way functions to construct an asymptotically perfect CHSS scheme. It has computational security, and permits flexible share sizes. Notably, when all shares are of equal size, our scheme is an asymptotically ideal CHSS scheme with an information rate one.

Problem

• Conjunctive Hierarchical Secret Sharing
• Chinese Remainder Theorem
• information rate
• security vulnerabilities
• secret sharing

Innovation

• Conjunctive Hierarchical Secret Sharing
• Chinese Remainder Theorem
• Polynomial Ring
• Asymptotically Ideal
• Information Rate