Lightweight Asynchronous Verifiable Secret Sharing with Optimal Resilience

Abstract We present new protocols for Asynchronous Verifiable Secret Sharing for Shamir (i. e. , threshold t 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 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.