Fast secure two-party ECDSA signing

Abstract

ECDSA is a standard digital signature schemes that is widely used in TLS, Bitcoin and elsewhere. Unlike other schemes like RSA, Schnorr signatures and more, it is particularly hard to construct efficient threshold signature protocols for ECDSA (and DSA). As a result, the best-known protocols today for secure distributed ECDSA require running heavy zero-knowledge proofs and computing many large-modulus exponentiations for every signing operation. In this paper, we consider the specific case of two parties (and thus no honest majority) and construct a protocol that is approximately two orders of magnitude faster than the previous best. Concretely, our protocol achieves good performance, with a single signing operation for curve P-256 taking approximately 37 ms between two standard machine types in Azure (utilizing a single core only). Our protocol is proven secure under standard assumptions using a game-based definition. In addition, we prove security by simulation under a plausible yet non-standard assumption regarding Paillier.