Proof of ownership of an account number? Or of funds in an account? Proof of ownership of an account number can be done with pgp.
I meant the funds. But even the account number, how do you prove it's yours? The account numbers go to the chain somehow?
Also, being able to split/merge wallets is interesting too. Today maybe not much, since transfers are free. But they won't remain free forever, and even today, each transfer does imply in a small cost to the entire network. Merging/splitting wallets would be a way to move money around without using the chain. It's also a good feature to have.
Perhaps, but I see this as an issue separate from signatures.
Well, if you can export keys, you can sign with them using an external tool at least.
You can associate a public key to an arbitrary identity, not just a name or email address. Gpg allows this.
As far as I understand, the link "gpg key" => "arbitrary identity" is possible, since proof of gpg key ownership is possible though signature.
But "arbitrary identity" => "gpg key" I can't see how, since there's no generic way to prove ownership of an arbitrary identity.
Like, I can create a GPG key and link it to your name. But that isn't my name. See what I mean?
If you want to prove you hold certain funds in an account, I am not sure how extending bitcoin to perform cryptographic signatures can help.
You just sign something with the same private key that owns the coins and that's it, you prove you own such coins. The other party just need to check the block chain to confirm.