Post-quantum access control with application to secure data retrieval

Servan-Schreiber et al. [IEEE S& P, 2023] presented a new notion called private access control lists (PACL) for function secret sharing (FSS), where the FSS evaluators can ensure that the FSS dealer is authorized to share the given function. Their construction relies on costly non-interactive secret-shared proofs and is not secure in the post-quantum setting. We give a construction of PACL from publicly verifiable secret sharing (PVSS) under the short integer solution (SIS) problem. Our construction adapts the Gentry et al.'s scheme [EUROCRYPT, 2022] for the post-quantum setting based on the learning with error (LWE) assumption aimed at ensuring that database access control policies are enforced by FSS evaluators, who verify that the FSS dealer is authorized to share the specified database query function. The benchmarks of our PACL show a trade-off between proving and verification efficiency, making the optimal choice dependent on application requirements. This construction has many applications for access control by applying FSS. We also present a secure data retrieval scheme using DPF-PACL for access control, which complements the PACL framework while providing independent utility.