This logic desribes the knowledge and aims at exhibiting provable properties. Each new system often introduces its own primitives. Kerberpos Basically, a N-S key server for logins. No hope to apply formal logic to Kerberos. Code too big.
Encryption is quite easy to break.
G and p must be chosen carefully. Variant of El-Gamal. RSA can be used to encrypt or to sign. EC are young and so we do not know if they can be crackes easily. The bank signs your message.