Identity-based threshold (multi) signature with private accountability for privacy-preserving blockchain

Identity-based threshold signature (IDTHS) allows a threshold number of signers to generate signatures to improve the deterministic wallet in the blockchain. However, the IDTHS scheme cannot determine the identity of malicious signers in case of misinformation. To solve this challenge, we propose an identity-based threshold (multi) signature with private accountability (for short AIDTHS) for privacy-preserving blockchain. From the public perspective, AIDTHS is completely private and no user knows who participated in generating the signature. At the same time, when there is a problem with the transaction, a trace entity can trace and be accountable to the signers. We formally define the syntax and security model of AIDTHS. To address the issue of identifying malicious signers, we improve upon traditional identity-based threshold signatures by incorporating zero-knowledge proofs as part of the signature and leveraging a tracer holding tracing keys to identify all signers. Additionally, to protect the privacy of signers, the signature is no longer achievable by anyone, which requires a combiner holding the keys to produce a valid signature. We give a concrete construction of AIDTHS and prove its security. Finally, we implement the AIDTHS scheme and compare it with existing schemes. The key distribution algorithm of AIDTHS takes 34.60 $\mu s$ and the signature algorithm takes 13.04 ms. The verification algorithm takes 1 $s$, which is one-third of the time the TAPS scheme uses.