Asymptotically Ideal Hierarchical Secret Sharing Based on CRT for Integer Ring

Fuente: arXiv
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Autores principales: Ding, Jian, Wang, Cheng, Li, Hongju, Shu, Cheng, Yu, Haifeng
Formato: Preprint
Publicado: 2026
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author Ding, Jian
Wang, Cheng
Li, Hongju
Shu, Cheng
Yu, Haifeng
author_facet Ding, Jian
Wang, Cheng
Li, Hongju
Shu, Cheng
Yu, Haifeng
contents In Shamir's secret sharing scheme, all participants possess equal privileges. However, in many practical scenarios, it is often necessary to assign different levels of authority to different participants. To address this requirement, Hierarchical Secret Sharing (HSS) schemes were developed, which partitioned all participants into multiple subsets and assigned a distinct privilege level to each. Existing Chinese Remainder Theorem (CRT)-based HSS schemes benefit from flexible share sizes, but either exhibit security flaws or have an information rate less than $\frac{1}{2}$. In this work, we propose a disjunctive HSS scheme and a conjunctive HSS scheme by using the CRT for integer ring and one-way functions. Both schemes are asymptotically ideal and are proven to be secure.
format Preprint
id arxiv_https___arxiv_org_abs_2603_22011
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Asymptotically Ideal Hierarchical Secret Sharing Based on CRT for Integer Ring
Ding, Jian
Wang, Cheng
Li, Hongju
Shu, Cheng
Yu, Haifeng
Cryptography and Security
Information Theory
In Shamir's secret sharing scheme, all participants possess equal privileges. However, in many practical scenarios, it is often necessary to assign different levels of authority to different participants. To address this requirement, Hierarchical Secret Sharing (HSS) schemes were developed, which partitioned all participants into multiple subsets and assigned a distinct privilege level to each. Existing Chinese Remainder Theorem (CRT)-based HSS schemes benefit from flexible share sizes, but either exhibit security flaws or have an information rate less than $\frac{1}{2}$. In this work, we propose a disjunctive HSS scheme and a conjunctive HSS scheme by using the CRT for integer ring and one-way functions. Both schemes are asymptotically ideal and are proven to be secure.
title Asymptotically Ideal Hierarchical Secret Sharing Based on CRT for Integer Ring
topic Cryptography and Security
Information Theory
url https://arxiv.org/abs/2603.22011