Robust Threshold ECDSA with Online-Friendly Design in Three Rounds

Threshold signatures, especially ECDSA, enhance key protection by addressing the single-point-of-failure issue. Threshold signing can be divided into offline and online phases, based on whether the message is required. Schemes with low-cost online phases are referred to as “online-friendly”. Another critical aspect of threshold ECDSA for real-world applications is robustness, which guarantees the successful completion of each signing execution whenever a threshold number $t$ of semi-honest participants is met, even in the presence of misbehaving signatories. The state-of-the-art online-friendly threshold ECDSA with-out robustness was developed by Doerner et al. in S&P'24, requiring only three rounds. Recent work by Wong et al. in NDSS'23 (WMY+23) and NDSS'24 (WMC24) achieves robustness but demands additional communication rounds (7 and 4, respectively) or incurs costly operations in the online phase, such as computations over a homomorphic encryption scheme. This paper presents the first three-round threshold ECDSA scheme with both robustness and an online-friendly design. The online phase of our scheme relies solely on several elliptic-curve group operations, which are 2 to 3 orders of magnitude less computationally intensive than those based on linearly homomorphic encryption schemes. We implement our protocol and conduct a comprehensive comparison with WMY+23 and WMC24. Benchmark results show that the online phase of our scheme is 2.5x faster than that of WMY+23 and hundreds of times faster than that of WMC24. Lastly, we demonstrate that our techniques can be extended to construct an online-friendly and robust three-round threshold BBS + scheme.