Yes, wraps can hide the identity of the signer from the relay too. But that doesn't mean the relay doesn't know who they are. The relay can see all filters and can guess really well who is asking for that data from that IP and use that to guess who is the owner/signer of the GiftWrap.

nostr:npub12262qa4uhw7u8gdwlgmntqtv7aye8vdcmvszkqwgs0zchel6mz7s6cgrkj might add NIP-42 AUTH to make that more clear. The signer of the connection doesn't necessarily mean that it's the writer of the GiftWrap. But it can always be guessed by the relay.

Relays are always trusted services for authors. They know everything coming out of your machine.

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Yes, AUTH is a fine solution if you don't care about the relay knowing about you. But a VPN or proxy and single-use connection would also obscure the identity of the sender (assuming the relay doesn't mind accepting the note for some other reason than authentication).

Agree. GiftWraps alone don't protect users against their relays. They must turn on a VPN, and the client app must create single-use connections to get to that level of security.

Even with all that, the anonymity set will be too small today to avoid guessing who the sender pubkey is.

Doesn’t e-cash solve the issue of how to pay for private notes?

Yeah, that's what I'm thinking. What does e-cash have over lightning in this scenario?

Zero fee*, simpler/faster transaction, full anonimity.

https://github.com/cashubtc/xcashu

*If the service accepts tokens from another mints it may incur in a LN fee if/when decides to swap them.

nostr:npub12rv5lskctqxxs2c8rf2zlzc7xx3qpvzs3w4etgemauy9thegr43sf485vg correct me if I'm wrong, please

Guess I'll have to look into it, I didn't know cheaper fees was part of the value prop