Asymptotically Ideal Conjunctive Hierarchical Secret Sharing Scheme Based on CRT for Polynomial Ring
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917358100021248 |
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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 | 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 |