Paper 2024/1463

Asynchronous Verifiable Secret Sharing with Elastic Thresholds and Distributed Key Generation

Abstract

Distributed Key Generation (DKG) is a technique that enables the generation of threshold cryptography keys among a set of mutually untrusting nodes. DKG generates keys for a range of decentralized applications such as threshold signatures, multiparty computation, and Byzantine consensus. Over the past five years, research on DKG has focused on optimizing network communication protocols to improve overall system efficiency by reducing communication complexity. However, SOTA asynchronous distributed key generation (ADKG) schemes (e.g., Kokoris-Kogias ADKG, CCS 2020 and Das ADKG, S\&P 2022, and others) only support recovery thresholds of either $f$ or $2f$, where $f$ is the maximum number of malicious nodes. This paper proposes an asynchronous verifiable secret sharing protocol featuring an elastic threshold, where $t \in [f,n-f-1]$ and $n \ge 3f+1$ is the total number of parties. Our protocol enables a dealer to share up to $t+1$ secrets with a total communication cost of O($\lambda n^3$), where $\lambda$ is the security parameter, and the protocol relies on the hardness of the $q$-SDH problem. We further modified the Schnorr protocol to enable simultaneous commitments to multiple secrets, which we refer to $m$-Schnorr.