Paper 2024/1950 Original: eprint.iacr.org/2024/1950 ↗

Two-Round 2PC ECDSA at the Cost of 1 OLE

Abstract

We present a novel protocol for two-party ECDSA that achieves two rounds (a single back-and-forth communication) at the cost of a single oblivious linear function evaluation (OLE). In comparison, the previous work of Boneh et al.~(EUROCRYPT 2025) achieves two rounds but requires expensive zero-knowledge proofs on top of the OLE. We demonstrate this by proving that in the generic group model, any adversary capable of generating forgeries for our protocol can be transformed into an adversary that finds preimages for the ECDSA message digest function (e.g., the SHA family). Interestingly, our analysis is closely related to, and has ramifications for, the `presignatures' mode of operation---Canetti et al.~(CCS 2020), Groth and Shoup (EUROCRYPT 2022). Motivated by applications to embedded cryptocurrency wallets, where a single server maintains distinct, shared public keys with separate clients (i.e., a star-shaped topology), and with the goal of minimizing communication, we instantiate our protocol using Paillier encryption and suitable zero-knowledge proofs. To reduce computational overhead, we thoroughly optimize all components of our protocol under sound cryptographic assumptions, specifically small-exponent variants of RSA-style assumptions. Finally, we implement our protocol and provide benchmarks. At the 128-bit security level, the signing phase requires approximately 50ms of computation time on a standard linux machine, and 2KB of bandwidth.