Secure joint Bitcoin trading with partially blind fuzzy signatures

Bitcoin has recently received considerable attentions in both academia and industrial areas. It is an appealing anonymous electronic cash system-based peer-to-peer computer networks and does not rely on any centralized trusted authority. The Bitcoin is associated with a public/secret key pair where the security key is only known by its Bitcoin account owner. It is usually hosted on some platform and can only be spent after its owner and the platform sign on it. In this paper, we investigate how to jointly manage the Bitcoin trading when the Bitcoin account is possessed by multiple participants and how to simultaneously guarantee the anonymity of the multiple owners. We first consider the scenario where a single dealer possesses the Bitcoin account but authorizes multiple participants to jointly manage it. For instance, a company authorizes its several departments to manage its account. We next consider the scenario where the Bitcoin account is shared by some peers, e.g., joint investigators each of whom independent possesses a part of the account. The main challenge is that the signers are uncertain in different transactions. We propose partially blind threshold signatures with uncertain signers and their extensions to address this challenge. Analysis shows that our proposals are secure and efficient.