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If a Tor browser makes a request of a server on the Internet, it will be encrypted several times by the Tor browser before it leaves the client. The destination server, however, will receive only the message that the user input to the client (with or without TLS encryption). When that server replies it will only encrypt if a secure connection was established. When the server's reply enters the Tor system will the Tor system encrypt in reverse order or send the reply using reverse headers without encryption? Assuming the Tor nodes have retained state regarding their successor and predecessor nodes they have enough information to simply reverse the headers and do not need to use encryption to return the reply without exposing the complete path. This approach, however, could leave the response message in the clear as it transits the Tor system and that would be a serious security hole to the client's anonymity.

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If a Tor browser makes a request of a server on the Internet, it will be encrypted several times by the Tor browser before it leaves the client.

Correct. Once for each Tor relay, which is a default of 3. As it passes to each relay, one of the layers of encryption is removed, like an onion being peeled.

The destination server, however, will receive only the message that the user input to the client (with or without TLS encryption). When that server replies it will only encrypt if a secure connection was established.

Correct. Which is why the Tor Browser, at least, attempts to enforce the use of HTTPS Everywhere, and blocks connections to sites that don't support HTTPS/TLS. If you're just using the Tor client, rather than the Browser, then it's up to you and the server to negotiate security (or not).

When the server's reply enters the Tor system will the Tor system encrypt in reverse order or send the reply using reverse headers without encryption?

The response is encrypted in the same way as the request, with 3 layers. However, in this case the layers of encryption are added back on, like an onion having its peel put back on.

Have a read of these previous threads:

Assuming the Tor nodes have retained state regarding their successor and predecessor nodes they have enough information to simply reverse the headers and do not need to use encryption to return the reply without exposing the complete path.

The encryption is required to prevent the operators of the Tor nodes - who may be Bad People - from eavesdropping on your data. (Which may or may not have any additional TLS encryption.)

This approach, however, could leave the response message in the clear as it transits the Tor system and that would be a serious security hole to the client's anonymity.

It would, yes.

Have a look at this handy EFF/Tor infographic. It doesn't differentiate between forward and back communication, but gives you an idea of who can see with regards to your traffic.

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