Novel CRT-based Asymptotically Ideal Disjunctive Hierarchical Secret Sharing Scheme

TL;DR

This paper introduces a new CRT-based disjunctive hierarchical secret sharing scheme that is asymptotically ideal, supports flexible share sizes, and offers computational security, improving upon previous insecure or less efficient schemes.

Contribution

It proposes the first asymptotically perfect CRT-based DHSS scheme with optimal information rate and security, addressing prior scheme limitations.

Findings

Scheme is asymptotically ideal with equal share sizes

Achieves an information rate of one

Provides computational security

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.