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

TL;DR

This paper introduces a new CRT-based polynomial ring secret sharing scheme that is asymptotically ideal, secure, and allows flexible share sizes, improving on previous schemes with security flaws or low information rates.

Contribution

It presents an asymptotically perfect CHSS scheme using CRT for polynomial rings, achieving an information rate of one with equal share sizes.

Findings

Scheme is asymptotically ideal with information rate one.

Provides computational security and flexible share sizes.

Improves security and efficiency over previous CRT-based CHSS schemes.

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.