You don't have to generate a matching key or anything like that at all.

The matching private key is often stored in a digital wallet or mobile device and protected by a password or other means of authentication.

The public key is placed on all computers that must allow access to the owner of the matching private key (the owner keeps the private key secret).

SSH only verifies whether the same person offering the public key also owns the matching private key.

And only the server that has the matching private keys, which are those two prime numbers, essentially, is able to decrypt what we sent.

And so the recipient is able to get the matching public key and use that to verify that domain's signing of the envelope of email.

The matching private key is not made available publicly, but kept secret by the end user who generated the key pair.

This searches the entire 56-bit DES keyspace and returns "1" if it probably finds a matching key.

You can never prove that a given public key was yours unless you have the matching private key.

This time no one had a matching key.