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Unfortunately, I couldn't find any reference to that question. Does Tor implement an own key generation for the RSA keys (and the other keys) or does the OR use an external implementation for that?

And if they implement it by themselves, how does the algorithm work exactly?

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It uses external libraries. Specifically OpenSSL, curve25519-donna, and ed25519 (either donna or ref10).

The code for key generation can be found in:

curve25519 - gitweb.torproject.org/tor.git/tree/src/common/crypto_curve25519.c?id=tor-0.2.7.6#n130

ed25519 - gitweb.torproject.org/tor.git/tree/src/common/crypto_ed25519.c?id=tor-0.2.7.6#n99

RSA - gitweb.torproject.org/tor.git/tree/src/common/crypto.c?id=tor-0.2.7.6#n553

(I can't post >2 links)

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