Fast Two-Party ECDSA With Online-Efficient Signing

초록

Two-party ECDSA enables two participants, each holding a share of the signing key, to collaboratively generate an ECDSA signature. With the rise of the blockchain technology, it has received significant attention as a method to enhance the security of digital assets. Distributed ECDSA signing is divided into an offline phase and an online phase, depending on whether the computation involves the message or not. Since blockchain applications prefer minimal on-chain computation, optimizing the online phase is highly desirable. In CRYPTO 2017, Lindell proposed an efficient two-party ECDSA protocol based on additively homomorphic encryption (AHE). Using the Paillier cryptosystem as AHE, the protocol has remained the fastest in overall signing performance to date. However, it incurs high computational costs during the online phase due to expensive Paillier operations. In this paper, we propose a new two-party ECDSA scheme inspired by Lindell’s protocol. Our construction is online-efficient, meaning that the online phase requires computational effort essentially equivalent to that of a single signature verification, while nearly preserving the overall signing efficiency of Lindell’s protocol. We empirically evaluate the performance of our proposed construction. The experimental results demonstrate that: 1) our protocol completes the online signing phase in only 0.07 ms, whereas Lindell’s protocol requires 22.30 ms, and 2) both protocols require approximately 23 ms in total, including both the offline and online phases.

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