When you run skype binary, following network actions is made:
Step 1. Login stage.
Skype binary checks if saved profile exists, and try to find private/public keys and skype issued certificate in it (also called credentials).
If its first run (i.e. no profile in %APPDATA%/skype/ found), skype do generation of private/public RSA keypair 1024 bits (128 bytes or 0x80 in hex) long.
Then, its make connection to skype 'login' servers. And send skypename, MD5(password) bytes, and you public key. If authorization OK, skype will issue personal certificate for you skypename and public key. This is 0x104 bytes array signed by skype network public key, also known as CA (certification of authority) in PKI (Public Key Infrastructure). Getting we skype signed certificate means that you now successfully "login" in skype network.
By the way, certificate will be issued on 30 days only. So, after that 30 days, you MUST login again (i.e. get new skype signed certificate).
Skype User Certificate Example: