Tor is a network of computers connected together USING the internet. Together they act to anonymize connections through the network through a process called Onion routing where sending a message involves adding multiple layers of encryption to it so that no computer in the chain can know both who sent it, and what it contained.
There are things “hosted on Tor” because it IS the internet still, you can access a Tor routing computer because it IS ON THE INTERNET, a Tor router can just host an internal website, and the masking of Tor helps hid where that website is.
Anyone can host whatever this way, just like anyone can host whatever the normal way, its just harder to locate.
TOR (The Onion Router) is a private network that exists on top (or within) of the regular internet. It is similar to a VPN in that regard. The difference is that your traffic is encrypted and routed through various computers in layers (like an onion) in such a way that the first computer in the layer knows your IP but doesnt know what site you are accessing and the last layer knows what site you are accessing but doesn’t know your IP. In this way, your browsing is completely private.
Let’s say you want to browse reddit. Your computer sends a message addressed to Reddit that says “gimme page XYZ”. The message you send has the address you are trying to talk to (Reddits address) and your address so Reddit knows who to send the message back to. But you aren’t (likely) connected directly to the Reddit servers, so your message gets passed from computer to computer until it reaches the Reddit server, and then Reddits reply gets sent back in a similar way (though not necessarily the same computers). Your address is basically the return address.
The thing is, along the way everyone can see where the message was from (or almost) and who its going to. Most of the time that’s not a problem. But sometimes (especially for illegal transactions) people don’t want others to know who they are talking to.
That’s where TOR comes in. TOR is a series of nodes that allow participating users to re-route their traffic so that by the time a message reaches its destination ONLY the most recent return address is on the outside.
Let’s say you send your letter to me. I take your letter and seal it in another envelope that only I can open. I send the letter to another person who does the same. Etc. Etc. Eventually a limit is reached and the message gets passed from what’s called a TOR exit node to the normal Internet again, then eventually it reaches Reddit who replies and the whole cycle goes in reverse. Reddits response goes to the exit Node. The Exit node then unwraps the message it sent and checks who it is supposed to reply to, they do the same, until eventually the message reaches the TOR node that you first connected to who gives you the message.
The key point is that each step inside the TOR network, each node only knows the address of the node that sent it the message. It does not know the address of any previous nodes that the message passed through before that.
TOR adds additional steps and encoding of part of the message at each step so that can slow traffic down. Also since TOR nodes may be running on individual peoples personal computers they might operate slower than dedicated internet routers and nodes, which can also slow traffic down. The tradeoff is speed for increased privacy/anonymity.
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