Key exchange can be facilitated by a Trusted Third Party. Suppose that there are n that want to communicate with each other securely.

a) Is there any advantage in having a Trusted Third Party to facilitate key exchange between the n parties? Explain briefly.

b) Suppose Alice, Bob, and Carol are three users that each have a secret key with the TTP, respectively k a , k b , kc. . Alice , Bob, and Carol wish to establish a group session key KABC which would be known to all three of them but not to an eavesdropper. Which of the following alternatives would be secure against an eavesdropper? Select all that would be secure, and Justify briefly why:

b1) Alice contacts the TTP. TTP generates a random k AB and a random k AC and send to Alice E(ka , k AB),ticket1=E(k b , k AB),ticket 2=E(k c , k AC) . Alice sends ticket 1 to Bob and ticket 2 to Carol.

b2) Bob contacts the TTP. TTP generates a random k AB and a random k BC It sends to Bob E(ka , KAB),ticket 1=E(k a , k AB),ticket 2=E(k c , k BC ). Bob sends ticket 1 to Alice, and ticket 2 to to Carol.

b3) Alice contacts the TTP. TTP generates random k ABC and sends to Alice E(k a , k ABC ) ,ticket1=E(k b , k ABC )andticket 2=E(k c , k ABC).Alice sends ticket 1 to Bob and ticket 2 to Carol.

b4) Alice contacts TTP, who generates a random k ABC and sends to Alice E(k a , k ABC ), and ticket 1=k ABC , and ticket 2=k ABC. Alice sends ticket 1 to Bob and ticket 2 to Carol.