发表机构
School of Mathematics and Big Data, Chaohu University; School of Mathematics and Statistics, Hefei University（巢湖大学数学与大数据学院; 合肥大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文破解了基于多项式环CRT的分隔秘密共享方案，指出其存在未授权子集可重构秘密的漏洞，并揭示安全分析忽略部分公开多项式的根本缺陷。
AI 中文摘要
基于多项式环上的中国剩余定理（CRT），Yang、Zhu、Fu和Xia（ISIT 2026）提出了一种针对带下界的分隔访问结构的 compartmented 秘密共享方案，并声称该方案可以是理想的。我们展示了三个未授权子集族能够重构秘密。因此，该方案是不安全的，除非参数选择退化到仅当授权子集为全体参与者集合的情形。安全分析中的缺陷在于它没有考虑所有已公开的多项式。类似缺陷也出现在同一第一作者的分层方案（ISIT 2024、2026）中。
英文摘要
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).
