What we need is a way to generate additional blinded variations of a public key. The blinded variations would have the same properties as the root public key, such that the private key could generate a signature for any one of them. Others could not tell if a blinded key is related to the root key, or other blinded keys from the same root key.
What are the desireable properties of a blinded public key which are not achievable by generating a new public key? I'm not clear on what were trying to do.
As an example, say some unpopular military attack has to be ordered, but nobody wants to go down in history as the one who ordered it. If 10 leaders have private keys, one of them could sign the order and you wouldn't know who did it.
Obviously this could be achieved by them all having the same keys but that's presumably unsuitable for some reason. It looks like you're trying to hide some information while trying to make it still available for other people or under certain circumstances but I'm not sure what.
ByteCoin