Paper 2021/291

Bandwidth-efficient threshold EC-DSA revisited: Online/Offline Extensions, Identifiable Aborts, Proactivity and Adaptive Security

Guilhem Castagnos, Dario Catalano, Fabien Laguillaumie, Federico Savasta, and Ida Tucker

Abstract

Due to their use in crypto-currencies, threshold ECDSA signatures have received much attention in recent years. Though efficient solutions now exist both for the two party, and the full threshold scenario, there is still much room for improvement, be it in terms of protocol functionality, strengthening security or further optimising efficiency. In the past few months, a range of protocols have been published, allowing for a non interactive -- and hence extremely efficient -- signing protocol; providing new features, such as identifiable aborts (parties can be held accountable if they cause the protocol to fail), fairness in the honest majority setting (all parties receive output or nobody does) and other properties. In some cases, security is proven in the strong simulation based model. We combine ideas from the aforementioned articles with the suggestion of Castagnos \textit{et al.} (PKC 2020) to use the class group based $\mathsf{CL}$ framework so as to drastically reduce bandwidth consumption. Building upon this latter protocol we present a new, maliciously secure, full threshold ECDSA protocol that achieving additional features without sacrificing efficiency. Our most basic protocol boasts a non interactive signature algorithm and identifiable aborts. We also propose a more advanced variant that also achieves adaptive security (for the $n$-out-of-$n$ case) and proactive security. Our resulting constructions improve upon state of the art Paillier's based realizations achieving similar goals by up to a 10 factor in bandwidth consumption.