Well, how to make a client SSL certificate, which doesn't need an (external) certification authority?
Is there a way and is any profit to use elliptic curves for that?
What should i do to use it on a server? How to make a server accept a certificate? How does a server know which user has logged in?
A self-signed client certificate for SSL is just a self-signed certificate with a key suitable for signatures. Just about any self-signed certificate will do, as long as you do not explicitly restrict it to encryption (i.e. don't insist on including a Key Usage extension, and you'll be fine).
Elliptic curves are massively spiffy. But not everybody supports them yet. Advantages of elliptic curves are that they yield shorter public keys and smaller and faster signatures than RSA. Not that it matters much anyway (as a human being, you cannot make the difference between 50 and 1000 µs). More importantly, using elliptic curves confers early adopter status. It is the cryptographic equivalent of buying a red sports car.
