Instead of doing that, which would require rewriting all existing Nostr libraries, you could do some math with your keys such that users of that relay still know it's you, but everybody else don't.

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That's the whole point, everything currently has assumptions about what is a valid event. This breaks those assumptions, which means unless implementations opt-in, these events will not be propagated

I'm not sure I got the use case correctly, but if you hash the relay URL, turn that into a scalar and add the number to your private key you'll get a new private key.

The receiver can check who is the actual sender of that event by hashing the same relay URL, multiplying that with G and subtracting that from the pubkey that is written in the event.

Right, but what I want is for relays to reject the event as invalid unless they're specially configured. Because regardless of which key is used, the content may be something that shouldn't be shared (think patreon content, which is usually shared with a static access token)