This discussion took place at Pizza Day Prague 2022 after a brief discussion on Silent Payments. The main points have been summarized below.
The discussion was mainly between Alekos Filini, Martin Habovštiak, and Ruben Somsen, as well as Daniela Brozzoni, Eric Sirion, Pavol Rusnak, Salvatore Ingala, and others.
This was also posted to the the bitcoin-dev mailing list.
BIP47 requires a notification transaction prior to making payments. This transaction takes up on-chain space and can easily leak privacy if not handled with extreme caution. In practice this is quite hard.
The discussion revolved around whether we can a.) minimize the on-chain space required and b.) outsource the notification transaction so the link between the sender and recipient is no longer apparent on-chain.
As currently implemented, BIP47 (V1/V2) requires an input key for blinding, the blinded sender payment code in an op_return, and the recipient key in an output.
The first question that came up was whether it is necessary for the recipient to learn the payment code of the sender. The benefit is that this enables the recipient to send a notification transaction and subsequent payment to the sender, but in practice this never happens. It therefore seems acceptable to forego this requirement, as this potentially saves space. The minimum notification payload that seems required is a fresh sender key and a static recipient key.
The sender key should ideally be deterministically derived from the sender xpub based on the recipient key. If the user checks all the keys that were registered with the recipient prior to notification, it can statelessly find out whether the sender key was already previously registered. This step can be skipped, which is easier for light clients, but means the notification transaction will have to be resent if the user ever forgets they already sent a notification (such as when restoring from backup).
The next part of the discussion revolved around the idea of putting multiple notifications in a single transaction that can be outsourced to a third party in order to break the sender/recipient link. This third party could be paid over the Lightning Network for their services.
One idea was to use the taproot annex to insert the notification payload as (discounted) witness data. One downside with this approach is that it requires custom software for the recipient to notice the notification, since it's not tied to an easily noticeable output. The middle ground solution would be to put the sender keys there but still create an output for each recipient key.
One interesting point that came up was that you could represent the recipient key using e.g. only 4 bytes (provided you put it in the annex). This leaves a window of 1 in ~4.3 billion for a collision, but the extra work that needs to be performed when it does happen is negligible (essentially expecting a payment while there is none). This would reduce the payload from 64 bytes to 36 bytes of witness data.
While this did not come up in the discussion, it should be noted that using the annex makes the transaction non-standard. It could either be standardized as the first use case for the annex, or perhaps an alternative method should be considered.
Instead of the annex, the person to whom the notification payloads are being outsourced could put them in a p2wsh. This would mean it takes two transactions before the data appears on-chain (so the sender has to wait for this before making the actual payment), but this causes no additional overhead if we assume this person repeatedly publishes transactions (spending the p2wsh while creating a new one).