Lightweight Asynchronous Verifiable Secret Sharing with Optimal Resilience

We present new protocols for Asynchronous Verifiable Secret Sharing for Shamir (i.e., threshold $$t<n$$ t < n ) sharing of secrets. Our protocols: Use only “lightweight” cryptographic primitives, such as hash functions; Can share secrets over rings such as Z/(pᵏ) Z / ( p k ) as well as finite fields Fq F q ; Provide optimal resilience , in the sense that they tolerate up to $$t < n/3$$ 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 in n , at least on the “happy path”, where no party provably misbehaves.