Weakly Private Distributed Multi-User Secret Sharing

Distributed multi-user secret sharing is a cryptographic primitive for secure distributed computing. Khalesi et al. (2021) provided a full information-theoretic characterization of the capacity region under weak privacy and correctness constraints. Their encoding and decoding scheme relied on a randomized Monte-Carlo procedure whose success probability depended on the choice of a very large finite field. A gap remains between their information-theoretic characterization and deterministic design