Fast 2-out-of-n ECDSA Threshold Signature
Lin Zhong, Yujue Wang, Jun Du, Daji Liang, Ziyuan Zhong, Kevin He, J. Andrew Zhang · 2023
The majority of research in threshold signatures has focused on configurations requiring either 2-out-of-2 (2-2) or t out-of$- n (t-n)$ participants. However, schemes involving 2-outof$- n (2- n)$ participants have been comparatively underexplored. Although one could theoretically employ $\mathrm{a}t-n$ threshold signature system and set $t =2$ to create a $2- n$ configuration, this workaround results in increased computational and communication overhead, thereby reducing signing speed. To tackle this issue, we present an optimized extension of Li17’s two-party signature to facilitate fast $2- n$ ECDSA threshold signatures. During the Decentralized Key Generation (DKG) phase, we replace Li17’s inefficient range proof with a more streamlined version, which minimizes both proof size and computational demands. Additionally, we introduce a Decentralized Key Refresh (DKR) protocol that updates the key shares of participants, enhancing the proactive security of each participant’s key share. Unlike Li17’s two-party signature, which only precomputes part of r, our scheme can also precalculate a portion of s, thereby reducing computational requirements during the Sign-online phase. Experimental data confirms the viability of our scheme; compared to Li17, our scheme speeds up the DKG phase by 83% and improves the Sign-online phase by 33%.