Fair blind threshold signatures based on discrete logarithm

In this paper, we propose a group-oriented fair blind (t; n) threshold signature scheme based on the discrete logarithm problem. By the scheme, any t out of n signers in a group can represent the group to sign fair blind threshold signatures, which can be used in anonymous e-cash systems. Since blind signature schemes provide perfect unlinkability, such e-cash systems can be misused by criminals, e.g. to safely obtain a ransom or to launder money. Our scheme allows the judge (or the government) to deliver information allowing anyone of the t signers to link his view of the protocol and the message-signature pair. In our scheme, the size of a fair blind threshold signature is the same as that of an individual fair blind signature and the signature veriication process is simpliied by means of a group public key. The security of our scheme relies on the diiculty of computing discrete logarithm.