What are the chances of generating identical onion domains?

Question

Tor

Good afternoon, for the sake of curiosity, I would like to know what are the chances of generating two identical onion domains? And by what principle are they generally generated (v3)?

Answer 1

And by what principle are they generally generated (v3)?

A 256-bit key pair is generated using the ed25519 algorithm. The public key is then encoded in base32 along with some service data - version number (3) and checksum. The resulting string is the domain in the onion zone.
If you do a full search (and I don’t see any other options), then you need to generate up to ^2,256 key pairs. If we take a billion computers that will simultaneously and without crossing each other generate a key pair every nanosecond, then all pairs can be sorted out in about 36 * 10 ⁴¹ billion years, which seems to me a rather small chance, given that the age of the universe is only a little less than 14 billion years.
It should be noted that not all variants from the 256-bit space satisfy ed25519. But even if we discard 99% of the options as invalid and do not spend time generating them, then enumeration of the remaining 1% will still be unimaginably longer than the age of the universe.