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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Ding, Jian, Wang, Cheng, Li, Hongju, Shu, Cheng, Yu, Haifeng
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917358100021248
author Ding, Jian
Wang, Cheng
Li, Hongju
Shu, Cheng
Yu, Haifeng
author_facet Ding, Jian
Wang, Cheng
Li, Hongju
Shu, Cheng
Yu, Haifeng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_22001
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Asymptotically Ideal Conjunctive Hierarchical Secret Sharing Scheme Based on CRT for Polynomial Ring
Ding, Jian
Wang, Cheng
Li, Hongju
Shu, Cheng
Yu, Haifeng
Cryptography and Security
Information Theory
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.
title Asymptotically Ideal Conjunctive Hierarchical Secret Sharing Scheme Based on CRT for Polynomial Ring
topic Cryptography and Security
Information Theory
url https://arxiv.org/abs/2603.22001