Asymptotically Ideal Hierarchical Secret Sharing Based on CRT for Integer Ring
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866913023818465280 |
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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 |