PreprintCC BY 4.0arXiv
Cryptanalysis of a Class of Ideal Secret Sharing Schemes Based on the CRT for Polynomial Rings
Abstract
Based on the CRT for polynomial rings, Yang, Zhu, Fu and Xia (ISIT 2026) proposed a compartmented secret sharing scheme for the compartmented access structure with lower bounds, claiming it can be ideal. We exhibit three families of unauthorized subsets that reconstruct the secret. The scheme is therefore insecure, except for a degenerate choice of parameters in which the only authorized subset is the whole participant set. The flaw in the security analysis is that it does not take all published polynomials into account. Similar flaws appear in the same first author's hierarchical schemes (ISIT 2024, 2026).
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BibTeX
@misc{ding2026cryptanalysis,
title = {{Cryptanalysis of a Class of Ideal Secret Sharing Schemes Based on the CRT for Polynomial Rings}},
author = {Jian Ding and Zhiyuan Guo and Hongju Li and Yuying Man},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06312},
eprint = {2610.06312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06312},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cryptanalysis of a Class of Ideal Secret Sharing Schemes Based on the CRT for Polynomial Rings
AU - Jian Ding
AU - Zhiyuan Guo
AU - Hongju Li
AU - Yuying Man
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06312
UR - https://arxiv.org/abs/2610.06312
AB - Based on the CRT for polynomial rings, Yang, Zhu, Fu and Xia (ISIT 2026) proposed a compartmented secret sharing scheme for the compartmented access structure with lower bounds, claiming it can be ideal. We exhibit three families of unauthorized subsets that reconstruct the secret. The scheme is therefore insecure, except for a degenerate choice of parameters in which the only authorized subset is the whole participant set. The flaw in the security analysis is that it does not take all published polynomials into account. Similar flaws appear in the same first author's hierarchical schemes (ISIT 2024, 2026).
ER -