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Given the length and character set of .onion domains (e.g. DDG https://3g2upl4pq6kufc4m.onion/), how many possible Tor hidden-service addresses are there?

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v2 onion addresses are 16 characters long and each character has 32 possible values. Therefore, there are 32^16 == 1,208,925,819,614,629,174,706,176 unique v2 onion addresses.

There are many many MANY more possible v3 onion services, but the math required is not as straight forward. Since I'm not confident I got the math correct, I will not state the number I came to here.

The following blog post links to a website where I list all v2 onion services (and if I did the crypto correctly, all v3 onion services too)

https://matt.traudt.xyz/p/ZDJV8wxZ.html

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Probably as many as low quality questions...

There is really little point in counting these, and it isn't very logical either.

Onions are generated randomly, they can't be counted (or shouldn't be counted).

We'll never have all the onions that can be generated in front of us. We'll only ever use a small fraction of the total onions that may exist. The only thing we care about is that our onions, as hashes, won't collide with (i.e., match) other people's onions. As long as the chance of collision is negligible, we can keep using them without counting them.

Counting onions is like counting rational numbers. There is a case for saying that if we represent integers with three decimal digits and leave zero out there can be 999 of them. But it doesn't make sense to say that if we represent rational numbers under a thousand with three digits and three decimals and leave zero out there'll be 999,999 of them. That's not correct. There are infinite rational numbers between 0 and 999.999. Using our notation we can only count 999,999 of them, but that's our fault, not theirs.

In sum, there are more onions than 2^80, though we can expect that excess onions would collide. We will not be present to see the collision - or live long enough - so we won't know, and we don't care. Conversely, there could be fewer onions than 2^80, if some onions would never turn up. We can't prove every onion is possible (i.e., that for every onion a key exists whose hash returns that onion). Even if we proved it for one by finding one, it'd take us too long to prove it for the rest. Hence we'll never prove it. Only a mathematician could speak about his, not a Tor user.

After all of this, we're none the wiser. The onions haven't been counted. There's a number for it but it doesn't mean anything.

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