Multi-signatures for ECDSA and Its Applications in Blockchain.

Multi-signatures enable a group of t signers to sign a message jointly and obtain a single signature. Multi-signatures help validating blockchain transactions, such as transactions with multiple inputs or transactions from multisig addresses. However, multi-signatures schemes are always realised naively in most blockchain systems by directly concatenating t ECDSA signatures. In this paper, we give the first multi-signature scheme for ECDSA. Technically, we design a new ephemeral group public key for the set of signers and introduce an interactive signing protocol to output a single ECDSA signature. The signature can be validated by the ephemeral group public key. Then, we instantiate the ECDSA multi-signature scheme with class group, for which we design a secret exchanging mechanism that ensures the hiding content is well-constructed. Moreover, our scheme is able to identify the malicious party in the signing phase and help to minimize unnecessary resource consumption. This ECDSA multisignatures can be used in blockchain to reduce the transaction cost and provide accountability for signers and backward compatibility with existing ECDSA addresses.