To me it seems that the only thing Tor is doing for anonymity (not security!) is

Question

To me it seems that the only thing Tor is doing for anonymity (not security!) is the fact that it does not record the traffic in and out, because obviously if every router was recording the traffic going through it (let alone publish that information), every pathway would be clearly visible and then anyone could backtrace anyone.

But how does Tor guarantee that nodes do not log their traffic and/or send them to an adversary? I would bet that all NSA-helded routers would keep track of this and I bet that most of private-held routers would also do this since Tor is open-source and since people are naturally driven for evil.

Anonymity would still work if the nodes did not cooperate with each other (sharing traffic logs) or if the data passed through one honest node that does not log any information, but it's still a major flaw if most of the network you don't know if you can trust.

So how does the Tor network know whether to trust a node not to send traffic information to an adversary or to make it publically available?

Explanation / Answer

It doesn't guarantee anonymity if enough of the network is controlled by a single adversary. There's no general way you can do so; if your whole connection goes entirely through adversary-run computers, your adversary is going to be able to track it, no matter what system you're using.

What Tor does is make it really, really, really hard for an adversary to control enough of the network to make this happen. It passes each connection through multiple nodes, so you have to control enough nodes that not just one but at least three nodes selected from the list are yours (it can have to be more than three; three is the minimum circuit length). The reason Tor works is that with a single Tor network, you have lots and lots of people running Tor servers; an adversary has to compete with tons of legitimate nodes. It's the same basic idea as Bitcoin - make it so an attacker inherently has to compete with legitimate users, and then the bigger the system gets the harder it is to attack.

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