Suppose Alice wants to communicate with Bob using symmetric key cryptography with a session key KS.
They have no public key cryptography and they intend to use a key distribution center (KDC).
The KDC is a server that shares a unique secret symmetric key with each registered user. For Alice and Bob, denote these keys by KA-K and KB-K.
Design a scheme that uses the KDC to distribute KS to Alice and Bob. Assume that KS is assigned by the KDC and is initially unknown to Alice and Bob.
Your scheme should use three messages to distribute the session key: a message from Alice to the KDC; a message from the KDC to Alice; and finally a message from Alice to Bob. The first message is KA-K(A, B).
Assume that the KDC and Bob know that they should use KA-K and KB-K, respectively, to decrypt the messages they receive from Alice. Using the notation: KA-K, KB-K, KS, A, and B to answer the following questions.
a. What is the second message?
b. What is the third message?
c. What is the main advantage of first distributing a session key and then using symmetric-key cryptography rather than using public-key cryptography techniques for the whole communication?