You can tell the blindsigner what a and b are, but he can't guarantee that you're not lying to him without also knowing c and d.
Also, there is another problem with using oleganza's scheme as an ordinary split-key scheme: it is not publically verifiable. That is, without revealing enough parameters to expose the private key, you cannot prove to others that the blind signer was actually involved in creating the signature.
Also, there is another problem with using oleganza's scheme as an ordinary split-key scheme: it is not publically verifiable. That is, without revealing enough parameters to expose the private key, you cannot prove to others that the blind signer was actually involved in creating the signature.
I agree, the public verification is a problem. But it seems so close to a threshold scheme I am wondering if a similar construction could be used to achieve this. Maybe revealing T and showing that it could only have been constructed with the knowledge of p and q. Probably needs a lot more thinking about.
