Alice has a private channel with Bob.
Alice wants to receive a payment from Charlie, and so she sends him an LN invoice.
Can Charlie's node build a path to pay for that invoice that goes through the Alice<>Bob private channel? If the answer is yes, how does Charlie's node know about the existence of the channel? Doesn't that defeat the privacy of the channel?
Private channels aren't private. They should be called "unannounced channels".
They simply aren't included in your node's gossip. This means your node isn't telling all it's peer about the channel. The unannounced channel is excluded from the public network graph built by every node.
If Alice wants Charlie to use her unannounced channel with Bob, she can include a "route hint" in the invoice itself.
Then, anyone who sees that invoice knows Alice has an unannounced channel with Bob and can use it to route a payment on that channel
It's also possible to probe for unannounced channels and use them without any "permission" or route hint.
An unannounced channel is just a "suggestion" to the network that says, "hey, I'd prefer if none of you use this one."
But anyone who's determined enough can still use it.
Soon we will have short channel IDs (SCIDs) which will help hide unannounced channels better.
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Thanks a lot for the explanation, that helps a lot. I have a couple of questions if you don't mind helping a noobie.
It's also possible to probe for unannounced channels and use them without any "permission" or route hint.
Let's assume I'm Diana and I have a channel with Bob. How do I go about finding the Alice<>Bob unannounced channel to build a path?
And the second: imagine Diana's node has found the channel, regardless of how this happened. Can Diana gossip the Alice<>Bob channel around, effectively making it public?
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You can't gossip about a channel that isn't yours. The gossip has to be signed by both nodes making up the channel to be accepted and relayed. So both sides must agree to announce it.
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I could only add that Anton Kumaigorodsky tried to develop private channels routing for his IMMORTAN library but some threat vectors which may realize with such routing stopped him and as he said, it may require features not available yet. For example Eltoo.
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