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I'm interested to understand in detail how the lightning network works over Tor. Implementations like lnd, c-lightning etc. offer an extension which allow running TOR with Lightning. I would like to understand how running Lightning with TOR works in practice. In particular I'm interested in the following cases:

1) I am the sender, but I enabled Tor in my node. How does sending to a node R outside Tor network looks like?

2) I am the recipient node, and I do not advertise an IP address, but an onion address. How do I receive payments?

3) The sender node S is a regular LN node, without any Tor connections. As a sender, I want to send a payment to node R and my LN node finds the best path to send my payment to R. Is it possible that this path will at any hop go thought Tor or go through onion node, because any of the nodes in the selected path happens to be onion or has access to Tor? And if yes, how the routing looks then?

Running lightning node over TOR is no different than running it over normal IP connection. Sending payment, fulfilling incoming payment, sending error messages etc. would happen in the exact same way in both cases. The only difference is that the above messages that you send to your peer will now happen over TOR network rather than a direct IP package.

If you are using only TOR without any public IP address then to route your payment to a node that is using only public IP address you will need to have a node in your path to the receiver that is (1) running TOR and public IP or (2) or running public IP and can connect to TOR nodes using the socks5 proxy. If you do not have this node in between you would not be able to send the payment.

When Tor service starts it creates a socks5 proxy which is by default at address 127.0.0.1:9050. If a node with public IP is started with the option --proxy=127.0.0.1:9050 (or including it in the config file) the node will be able to connect to nodes running TOR (like yours).

If you are running TOR and have a public IP address then you can directly connect with nodes that run tor or public IP nodes via the tor service socks5 proxy.

I am the sender, but I enabled TOR in my node. How does sending to a node R outside TOR network looks like?

The network routing happens according to what I mentioned above. However, the path calculation for sending the payment to the receiver happens on your node so it does not involve what network routing you are using. You would construct the onion routing packet with the path to the receiver (the channels you will use to send the payment), and try to send this onion and the payment_hash to your peer via the update_add_htlc message. This message will then go over TOR nodes before reaching your peer, instead of a directly reaching your peer.

I am the recipient node, and I do not advertise an IP address, but an onion address. How do I receive payments?

You can receive payments from nodes directly that are running TOR. If you want to receive payments from nodes that have only public IP, then you would need to have a node in your path that has the proxy option set so that it can connect to TOR nodes via socks5 proxy.

The sender node S is a regular LN node, without any Tor connections. As a sender, I want to send a payment to node R and my LN node finds the best path to send my payment to R. Is it possible that this path will at any hop go thought Tor or go through onion node, because any of the nodes in the selected path happens to be onion or has access to Tor? And if yes, how the routing looks then?

Assume you the path from S to R looks like this: S -> T -> U -> V -> R. Number of cases can arise:

• 
  S and R do not run TOR: It depends
  
  
  • All the nodes could be on public IP and your payment goes through.
  
  
  • T could be node running public IP and TOR. It has a public IP channel with you, and TOR channel with U. U can then have a proxy option set that allow it to have TOR based channels with T and public IP channel with U. V is a public IP node and U routes payment to V in normal way.
  
  


• 
  R runs TOR: At least one node in between should run/understand TOR
  
  
  • T/U/V has a public IP, and have TOR so that they can make channels with TOR nodes and public IP nodes
  
  
  • T/U/V are all public IP nodes but V has a proxy option set which allows it to have a tor based channel connection with R.