In response to the threat posed by quantum computers, Pilaram and Eghlidos proposed the first lattice-based multi-stage secret sharing scheme which is the only post-quantum multi-stage secret sharing scheme. In this paper, we introduce an efficient attack on it and show that any adversary can easily reconstruct unrecovered secrets as long as it collects enough pseudo-secret shares. For the sake of complete, we further list two countermeasures to protect the scheme from such attack.

Abstract Replication is widely used in cloud storage systems to provide availability and reliability for outsourced cloud data. However, untrusted providers would like to maintain fewer replicas than promise for economic profits or other benefits. Since providers hardly ever offer remote checking tools, it becomes a challenge to validate from user side whether Providers are faithfully keeping enough replicas or not. Existing solutions have several disadvantages, including low efficiency, high computation overload, and lack of supporting for colluding attack. In this article, a collector‐based multiple replica storage model is introduced. Based on that, a novel multiple replica possession proving scheme public key segment is proposed in detail. Particularly, a public key is divided into several private segments, which will be distributed to corresponding storage servers for evidence generation. Only if every replica node shows its correct possession evidence, can the challenge be concluded as success. Theoretical analysis and prototype experiments show the correctness, security, and efficiency of the scheme.