The paper describes how the system works by working through scenarios where A and B are trying to communicate securely. Ron Rivest has said that he came up with the names Alice and Bob so he could use A and B in mathematical notation. Having one male and one female also meant that "he" and "she" could be used in the scenarios and people would know which "person" the authors were talking about. The introduction of the most famous couple in cryptography is as follows:
For our scenarios we suppose that A and B (also known as Alice and Bob) are two users of a public-key cryptosystem. We will distinguish their encryption and decryption procedures with subscripts: EA,DA,EB,DB.Now Alice and Bob were soon joined by others. Eve is an eavesdropper on the conversations between Alice and Bob. Mallory is a malicious attacker. The list goes on and on.
Only 6 years after the original RSA cryptography paper John Gordon was able to give an after dinner speech where, tongue firmly in cheek, he gave more details and insights into Alice and Bob. John Gordon's The Alice and Bob After Dinner Speech covers Alice and Bob, how mathematicians share jokes, how to represent the alphabet with words, and even why you should be nice to your calculator.