On 06/19/2013 02:36 PM, Adam Back wrote:
This maybe simpler and trivially compatible with existing type2 public keys
(ones that are multiples of a parent public key): send an ECDSA signature of
the multiplier, and as we know you can compute ("recover") the parent public
key from an the ECDSA signature made using it.

Adam

On Wed, Jun 19, 2013 at 05:28:15PM +0200, Adam Back wrote:
[q-th root with unknown no discrete log artefact]

If it was a concern I guess you could require a proof of knowledge of
discrete log.  ie as well as public key parent, multiplier the address must
include ECDSA sig or Schnorr proof of knowledge (which both demonstrate
knowledge of the discrete log of Q to base G.)

It's a cool trick but requiring a signature on each multiplier defeats one of the purposes of a deterministic wallet.  I don't want to have to explicitly export a whole bunch of signatures from my offline system just to exercise this address option.  The "observer wallet" should be able to do anything it needs to on its own, without help from the offline wallet. 

Unless you mean that there is a one-time signature from the offline computer that works for all addresses, that can be exported with the observer wallet...?  If all you want to do is prove that someone owns that private key, you could send {Sign(MagicString), Multiplier}.   So it becomes one signature operation per wallet, but creating new wallets would require going back to the offline computer for that one-time signature.  That's better than the alternative, but it's still extra bloat for the wallet apps.

Either way, I'm not convinced that these are a problem for the specified use cases I outlined.   In cases where you have a persistent business relationship, they need to verify the parent public key exchange anyway.  After that, the software doesn't technically require the transmission of the PubKey, it only needs the Name/ID of the party and the multiplier and it will fetch the PubKey from its data store.  Or it is transmitted and the payer verifies it's correct.  Computing an alternate {PubKey', Mult'} that produces the same address and then using it in a MitM attack doesn't work here if the two parties pre-verified the public keys. 

In the case that a business is checking whether the cashout address of a customer is the same as the last time:  if the first payout was not replaced by an attacker, then the business already has the correct public key in their DB and a replacement of further payout requests will fail validation.  If the first payout was replaced... well that could've been done anyway (with or without this alternate form), and the customer wouldn't have received their money and the whole process would be flagged and terminated before further transactions.

-Alan