Asymptotically Ideal Conjunctive Hierarchical Secret Sharing Scheme Based on CRT for Polynomial Ring
This work addresses security and efficiency issues in hierarchical secret sharing for applications like secure multi-party computation, though it appears incremental as it builds on existing CRT-based methods.
The authors tackled the problem of constructing a secure and efficient Conjunctive Hierarchical Secret Sharing (CHSS) scheme by using the Chinese Remainder Theorem (CRT) for polynomial rings and one-way functions, resulting in an asymptotically ideal scheme with an information rate of one when shares are equal-sized.
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.