It is also possible to generate a key pair, store your private key and public key in your browser, and send your public key to the server. The bigger-named browsers mostly allow you to import the keys, but not to generate them. Setting up the system on the server is left as an exercise. ;-)

If you're dealing with shared secret encryption or distributing a private key, the trick to getting the secret key to the intended party is to do so out of band or to transfer it along a channel already secured by some other encryption.