I do not understand: "Every monero transaction leaks the amount received by the recipient to the sender"
Which payment method on the planet does not "leak" the amount the sender is paying to the receiver?
Discussion
lightning
LN has prisms and atomic tx chaining, so the following scenario is doable: I buy the latest album for $10, not knowing that $5 of it went to the original artist and $5 went to the merchant. Thus, the sender doesn't know how much money went to the receiver and how much went to one or more other folks. Which is good, that's none of his business. But XMR needlessly exposes that private info to him.
where does that happen in real world?
Fountain App is a podcasting service with a feature called Splits where users pay a single invoice to "zap" a podcast they liked and the app automatically splits up the money to multiple recipients: https://support.fountain.fm/article/68-what-are-splits
See also Lightning Prisms: https://dergigi.com/2023/03/12/lightning-prisms/
Thanks. Whats the big advantage compared to the platform splitting up the payment? I pay 1000 sats to fountain and they split it up themselves, that way i also do not know how much each creator and the platform gets.
I think that is currently how fountain app does it
There are two possible advantages to doing it atomically, depending on how you do it: you can do it by atomically forwarding the funds to different destinations without telling the sender where the funds end up, which is better for receiver privacy, but allows the "middleman" server to steal by giving the sender an invoice that pays himself, without forwarding the money to the real would-be recipients.
Another way you can do it is, do the same thing except you *do* tell the sender where the funds end up, and include a signature from each recipient confirming that they will only reveal the payment preimage if they get their cut. By doing that, you give up on some of the receiver privacy, because now the sender knows the number of recipients, or at least a number of people who "claim" to be recipients (they could inflate this number), though he still doesn't know what amounts they get.
Whichever way you do it, you additionally break a heuristic that some routing nodes use to guess how much money was received in an LN payment; the heuristic they use is to guess that the ultimate recipient basically receives the full amount sent, minus some routing fees; but if you do an atomic payment split, how much the ultimate recipient gets depends on how the split is done, so the assumption no longer holds.