Lightweight Asynchronous Verifiable Secret Sharing with Optimal Resilience

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2024年6月6日

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Victor Shoup,
Nigel P. Smart

摘要

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 ${\mathbb {Z}}/(p^k)$ $Z / (p^{k})$ as well as finite fields $\mathbb {F}_q$ $F_{q}$ ;

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.