Efficient Asymmetric Threshold ECDSA for MPC-based Cold Storage

Motivated by applications to cold-storage solutions for ECDSA-based cryptocurrencies, we present a new threshold ECDSA protocol between $n$ ``online\u27\u27 parties and a single ``offline\u27\u27 (aka.~cold) party. The primary objective of this protocol is to minimize the exposure of the offline party in terms of connected time and bandwidth. This is achieved through a unique asymmetric signing phase, in which the majority of computation, communication, and interaction is handled by the online parties. Our protocol supports a very efficient non-interactive pre-signing stage; the parties calculate preprocessed data for future signatures where each party (offline or online) sends a single independently-generated short message per future signature. Then, to calculate the signature, the offline party simply receives a single short message (approx.~300B) and outputs the signature. All previous ECDSA protocols either have high exposure for all parties, or rely on non-standard coding assumptions. (We assume strong RSA, DCR, DDH and enhanced unforgeability of ECDSA.) To achieve the above, we present a new batching technique for proving in zero-knowledge that the plaintexts of practically any number of Paillier ciphertexts all lie in a given range. The cost of the resulting batch proof is very close to that of the non-batch proof for a single ciphertext, and the technique is applicable to arbitrary Schnorr-style protocols