The combination of password authentication and secret sharing in Password-Protected Secret Sharing(PPSS)schemes presents a distributed solution that aligns with practical user needs.This protocol allows a user to share secrets among multiple servers,only requiring the memorization of a short password for subsequent simultaneous authentication and secret reconstruction.The security ensures that as long as the adversary does not corrupt servers beyond a threshold,it cannot reveal any information related to password or the secrets from the protocol.The PPSS schemes were initially based on discrete-log-hardness assumptions and their variants,making them vulnerable to quantum attacks.Finding a quantum-secure construction has thus become an urgent problem to address.Roy et al.introduced a quantum-secure construction against malicious adversaries,but its communication rounds are not optimal and even not be constant in the presence of malicious adversaries.Addressing the issue of optimizing protocol rounds,this paper firstly introduced a lattice-based quantum-secure construction with optimal rounds,using a Verifiable Oblivious Pseudorandom Function(V-OPRF)primitive and then rigorously proved security of the protocol.Furthermore,the protocol ensured that in scenarios with a majority of honest servers,an honest user will always successfully reconstruct the correct secret within the optimal number of rounds,demonstrating strong robustness.
password authenticationsecret sharingpost-quantum cryptographyverifiable oblivious pseudorandom function
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