SSL Hankshake

client – hello server -> server
client <- here is my pub cert - server client - encrypts a random text with server pub cert and sends to server (prove it) -> server
clinet <- server decrypts to get random text and then encrypts it with private key and sends to client (here is the proof) - server client - decrypts and verifies the random message (ok) client - encrypts a symmetric key and sends to server -> server
client <- both client and server encrypts message with common symmetric key -> server