Cryptanalysis of a Class of Ideal Secret Sharing Schemes Based on the CRT for Polynomial Rings

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).