Let's imagine you have a client C and a server S. 

the machine C connects to server S with ssh, using a RSA key to enable no passord connection. So C owns his private key, and have given to S the public key.

Giving that, can I use RSA keys to certifiate S ? I would like each time C tries to connect to S in ssh, it can be sure that he's really talking to S. So exactly like certificate X509, but with RSA keys ?

If i'm not wrong, it would be a double authentication ?

Thank you