Goal:  An alternative address format made possible by BIP 32, which allows one to specify a "Wallet ID" and "One-time payment" code, instead of the standard one-use Base58-Hash160 addresses.   This allows parties with a persistent relationship to be able to prove that payment addresses they provide each other are linked to a particular wallet, reducing exposure to MitM attacks without the need for SSL or a web of trust, and without compromising the privacy of either party.    For instance, this could be used between businesses that frequently do business, by exchanging and verifying public keys beforehand, or could be used by an exchange to identify if a customer withdrawal address is related to their last deposit address, and if not enforce extra authentication measures.

Background:
I haven't been following the payment protocol discussions/development much, so I apologize if this has already been addressed.   I'm calling it "wallet-linkable" addresses, which would be an optional second form for sending someone your address.   With BIP 32, the address is computed by the payee (the person sending the address to receive money):

   Standard Address ~ Base58(0x00 || hash160(PubKeyParent * Multiplier[i]) || checksum)

What I'd like to do is have the option, when specifying an address through the payment protocol, to send *just* the {PublicKeyParent, Multiplier[i]} and let the receiver of that address compute the address on their own.  This is no significant burden on the receiver, but it does provide the useful property that they can recognize when addresses specified in this way come from the same wallet -- because the PubKeyParent will be the same.  Remember, this is optional for the person providing the address.

One nice, accidental feature of BIP 32 is that the Multiplier[i] used above does not actually reveal the "chaincode" (I think Pieter started calling it the "tweak").   It is derived from the chaincode but doesn't reveal it.  Therefore, the payer sees the parent public key, but that's not useful to derive any of the other addresses unless they also have the chaincode.  But they can verify that the PublicKeyParent is identical between transactions, and thus is accessible only to that wallet.  It allows them validate a specific address provided by the payee, but not generate or identify any other addresses.

Use Cases:
(1)  So, just like with PGP/GPG, when two parties decide they will start a relationship, they can start by exchanging the public keys of their wallet and verify them in a reliable manner.  After that, when one party requests a payment address from the other, they can optionally send {PubKey, Multiplier}, and the payer's software will identify the owner of that address, or let you select who you think the address belongs to and it will verify it.  If the payee's system is compromised and address is replaced, the address received by the payer won't validate.  This doesn't help if the side sending the money is compromised.

(2)  When a customer first provides a deposit to an exchange, it will send money from an address in their wallet and the software will provide the exchange the {PubKey,Mult}.  When the customer later provides a withdrawal address, the site can automatically trust the address as long it is provided in the alternate form and the public keys match.  If they don't, it might be the same customer just requesting a withdrawal to a different wallet, which is fine, but they'll have to go through an extra verification step to do so. 


Downsides: 
Multi-sig/P2SH  - The only way this works with P2SH, violates one of the goals of P2SH slightly, but may not matter much if it's all done under the hood by the software.  Instead of providing a 20-byte hash of a script, you provide all the public keys and multipliers for the individual addresses.  The payer's software automatically verifies all addresses and creates the P2SH script itself (after a divine decree that public keys will always be sorted lexicographically in the multi-sig script).  The blockchain still benefits from the "compression" of moving the bulky scripts to the TxIn, but it does require revealing more information than is necessary for the payer to pay the payee.  But it may not really be a problem, given the benefits.  It might just be slightly longer strings to exchange during initialization and for each transaction.

I have various reasons I'd like to use this, and it'd be nice to have some community backing, so I don't have to twist anyone's arm to trust me that it's legit.

-Alan