Lightweight Asynchronous Verifiable Secret Sharing with Optimal Resilience

We present new protocols for Asynchronous Verifiable Secret Sharing for Shamir (i.e., threshold t < n) sharing of secrets. Our protocols: - Use only "lightweight" cryptographic primitives, such as hash functions; - Can share secrets over rings such as Z/(p(k)) as well as finite fields F-q; - Provide optimal resilience, in the sense that they tolerate up to t < n/3 corruptions, where n is the total number of parties; -Are complete, in the sense that they guarantee that if any honest party receives their share then all honest parties receive their shares; - Employ batching techniques, whereby a dealer shares many secrets in parallel and achieves an amortized communication complexity that is linear inn, at least on the "happy path", where no party provably misbehaves.