Cryptanalysis of a Class of Ideal Secret Sharing Schemes Based on the CRT for Polynomial Rings
Cryptanalysis shows an ISIT 2026 CRT polynomial-ring secret-sharing scheme lets unauthorized subsets reconstruct the secret.
Yang, Zhu, Fu and Xia proposed at ISIT 2026 a compartmented secret-sharing scheme based on the Chinese Remainder Theorem for polynomial rings and claimed it can be ideal. Cryptanalysis identifies three families of unauthorized subsets that can reconstruct the secret. The construction is insecure except for a degenerate parameter choice in which the only authorized subset is the full set of participants. The paper says the original security argument ignored some published polynomials and that similar flaws appear in the first author's hierarchical schemes from ISIT 2024 and 2026.
- The ISIT 2026 CRT polynomial-ring scheme was claimed to be ideal.
- Three families of unauthorized subsets can reconstruct the secret.
- It is secure only if the sole authorized subset is every participant.
- The original analysis did not account for all published polynomials.
- Similar flaws affect the first author's ISIT 2024 and 2026 hierarchical schemes.
From the original article
1 min read at arxiv.orgBased 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.
By Jian Ding · arxiv.org
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