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Let's say that someone moves a Tor instance [1] from one internet access point [2] to another one. And let's say that an adversary is logging traffic from both access points. The adversary could log, that some user Tor client has chosen X entry guards out of Y available entry guards.

How unique is that Tor instance's set of entry guards?

When the user moves to another internet access point, couldn't the adversary be pretty sure, that it's the same user?

This is getting problematic if the adversary can at some point link the identity of a specific user to a set of entry guards, because the adversary can now monitor from which location this user connects to the Tor network?

Would it be better to have a separate installation of Tor (and therefore set of entry guards) per internet access point?

[1]: For example an installation of TBB on a flash drive or so.
[2]: Different ISP's, WiFi hotspots, VPNs etc.

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Currently Tor chooses 3 entry guards. There may be much fewer entry guards than Tor users, but as you fear, when combining 3 randomly chosen entry guards they indeed become a unique fingerprint for you. At least very very few users have the same set of entry guards as you do, and probably no one else at your geographical location.

It will be very easy for an adversary to conclude or guess that it is the same Tor user that is connecting to the network.

For this reason the Tor developers have expressed the wish to reduce the number of entry guards to 1 (there was a ticket I believe). But this is not as easy as it sounds, partly due to performance reasons.

However, even if you move around and the adversary knows you are the same Tor user, it will still not make it any easier for the adversary to link your anonymous user identities to your computer or you.

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How is this adversary figuring out what entry guards you are using?

Assuming it does from you connecting to Tor on an access point owned by them.

There are more Tor users than entry guards, so one entry guard is used by multiple people which will help with matters.

Also, how is he logging where data from the entry guard is going? (this is just a technical question that I do no know the answer to)

And finally, how will he know if the data from the entry guard is going to a Tor user and not just another Tor relay (the data is encrypted after all) (though Tor relays locations are public knowledge)

I wouldn't say that you need a separate installation of Tor per access point. It would require huge amounts of work to track your location from this, and the tracking would only give an estimation.

The way they would do it would be to ignore any access from locations that were constant (other Tor users), ignore any locations that are relays, and then they can find you if no one else using that entry guard is also changing location. So for certainty, you may want to use a new installation when using an untrusted access point.

sorry for the rambling.

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