List the five messages that Alice (A) and Bob (B) exchange in order for Bob to authenticate himself to Alice, by using his private key K_{B_pri} to decrypt to prove that he is the owner of the private key, and for Alice to authenticate herself to Bob using a shared secret K_AB with Bob.

Here is are some similar examples:

A, B, C

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Assuming that Alice and Bob have the necessary shared secret, trusted public keys, and private keys: A List the three messages that Alice and Bob exchange in order for Alice to authenticate herself to Bob, by using her private key to decrypt to prove that she is the owner of the private key. Briefly explain how exactly authentication is done. Message 1 Message 2 encrypt(KAlice Public, NBob) Alice uses her private key to decrypt encrypt(KAlice Public, NBob) to get NBob. Alice Hello Message 3 Bob compares NBob sent from Alice and his copy of NBob. If they are the same, it proves that Alice has the private key and NBob is not a replay if it is unique wrt time. Message 4 Message 5 NBob B List the five messages that Alice and Bob exchange in order for Bob to authenticate himself to Alice, by using his private key to encrypt to prove that he is the owner of the private key, and for Alice to authenticate herself to Bob using a shared secret with Bob. Message 1 Message 2 Message 3 Bob Message 1 Message 2 Message 3 encrypt(KBobPrivate, NAlice) Hello Page 5 of 7 NBob Bob uses his private key to encrypt NAlice. If Alice uses his public key to successfully decrypt encrypt(KBobPrivate, NAlice) to produce the same NAlice, this proves that Bob has the private key. This has been discussed in the lecture slides. Bob Bob Hello, NBob hash(KAB, NBob) C Can the five-message mutual authentication in b) be reduced to a three-message mutual authentication? If yes, list the three messages. Yes, by packing as many items as possible into a message. encrypt(KBobPrivate, NAlice) Alice NAlice Alice NAlice, hash(KAB, NBob) Comments: NBob is independent of any other items. So, it can be moved from Message 4 to 1. Once Alice has NBob, she can send hash(KAB, NBob) in Message 2 instead of 5. With these two items sent in earlier messages, Messages 4 and 5 can be removed. Assuming that Alice and Bob have the necessary shared secret, trusted public keys, and private keys: A List the three messages that Alice and Bob exchange in order for Alice to authenticate herself to Bob, by using her private key to decrypt to prove that she is the owner of the private key. Briefly explain how exactly authentication is done. Message 1 Message 2 encrypt(KAlice Public, NBob) Alice uses her private key to decrypt encrypt(KAlice Public, NBob) to get NBob. Alice Hello Message 3 Bob compares NBob sent from Alice and his copy of NBob. If they are the same, it proves that Alice has the private key and NBob is not a replay if it is unique wrt time. Message 4 Message 5 NBob B List the five messages that Alice and Bob exchange in order for Bob to authenticate himself to Alice, by using his private key to encrypt to prove that he is the owner of the private key, and for Alice to authenticate herself to Bob using a shared secret with Bob. Message 1 Message 2 Message 3 Bob Message 1 Message 2 Message 3 encrypt(KBobPrivate, NAlice) Hello Page 5 of 7 NBob Bob uses his private key to encrypt NAlice. If Alice uses his public key to successfully decrypt encrypt(KBobPrivate, NAlice) to produce the same NAlice, this proves that Bob has the private key. This has been discussed in the lecture slides. Bob Bob Hello, NBob hash(KAB, NBob) C Can the five-message mutual authentication in b) be reduced to a three-message mutual authentication? If yes, list the three messages. Yes, by packing as many items as possible into a message. encrypt(KBobPrivate, NAlice) Alice NAlice Alice NAlice, hash(KAB, NBob) Comments: NBob is independent of any other items. So, it can be moved from Message 4 to 1. Once Alice has NBob, she can send hash(KAB, NBob) in Message 2 instead of 5. With these two items sent in earlier messages, Messages 4 and 5 can be removed.