1 Authenticated Key Exchange Rocky K. C. Chang 20 March 2007

Rocky, K. C. Chang2 Outline  The secure key exchange problem  Recall the Diffie-Hellman protocol  Designing an authenticated Diffie-Hellman protocol Several versions  The perfect forward secrecy property

Rocky, K. C. Chang3 The secure key exchange problem  Before two users can use a private key for encryption or for message authentication, how did they come up the key? Out-of-band, in-band, or a hybrid  How do two IPSec nodes set up their security associations (SAs)? Encryption algorithms, authentication algorithms, session keys, etc.  In general, the problem is how to derive a secret (key, identity, etc) between two users over an insecure network? The second problem is how to use the secret (keys) to secure their messages from a certain layer up.

Rocky, K. C. Chang4 The secure key exchange problem  An acceptable solution (a secure key exchange protocol) to this problem is required to handle Source authentication Message authentication Data confidentiality Protection against denial-of-service attacks, such as, flooding of messages, replay messages, etc.

5 Recall from the DH slides

Rocky, K. C. Chang6 The basic DH protocol

Rocky, K. C. Chang7 The man in the middle attack

Rocky, K. C. Chang8 The final (unauthenticated) DH protocol

9 Designing an authenticated DH protocol

Rocky, K. C. Chang10 Authenticated DH protocol: v.1

Rocky, K. C. Chang11 Problems with v. 1  Let Alice and Bob choose the DH parameters (p, q, g).  The number of messages can be reduced.  The session key k is used as an argument in authentication. A good rule of thumb is to use a secret for a single thing.  The 2 authentication messages are too similar. Subject to the replay or similar attacks

Rocky, K. C. Chang12 Problems with v. 1  Fix the (p, q, g) in a key exchange protocol would shorten the protocol’s life. Management of versions  Can shorten the number of messages to 2.  The data in AUTH A and AUTH B consists of all the data exchanged so far.

Rocky, K. C. Chang13 Authenticated DH protocol: v.2

Rocky, K. C. Chang14 Problems with v. 2  What if Bob wants a larger prime than Alice? Bob will have to abort the protocol and send back an error message. Alice has to restart again with new DH parameters.  AUTH A in the first message cannot securely authenticate Alice. Why? The purpose of the nonce in the first message?

Rocky, K. C. Chang15 Authenticated DH protocol: v.3

Rocky, K. C. Chang16 The final authenticated DH protocol

Rocky, K. C. Chang17 Alice’s view  She receives a single message from Bob. She is sure that the message is from Bob because of the AUTH B which includes N a.  Alice checks that the DH parameters are properly chosen. When she sends out Y, she knows that only persons who know x such that X = g x mod p can compute k.  Bob authenticated X, and he does that when he is following the protocol. Thus, Bob knows the appropriate x.  Therefore, Alice is sure that only Bob knows the final key k that she derives.

Rocky, K. C. Chang18 Bob’s view  The first message that he receives gives him almost no useful information.  The third message is definitely from Alice based on the AUTH A which includes a random value chosen by Bob. Bob also knows that the first message was proper too.  Bob knows that the DH parameters are safe.  The rest is similar to the case for Alice.

Rocky, K. C. Chang19 Key compromise  If Alice loses her authentication key without it becoming known to an attacker, She loses the ability to run the key exchange protocol. She still can use the session keys that have been established.  If Alice loses the session key without it becoming known to an attacker, She will have to run the key exchange protocol to obtain a new session key.

Rocky, K. C. Chang20 Perfect forward secrecy  If Alice’s authentication key is compromised, the attacker can impersonate Alice. However, the past communications between Alice and Bob still remain secret. The attacker cannot recover the session key k even if he recorded all messages.  If the session key is compromised, It does not provide information about any other key, including the authentication keys.

Rocky, K. C. Chang21 Perfect forward secrecy  PFS: “disclosure of long-term secret keying material does not compromise the secrecy of exchanged keys from earlier runs.” For example, using public-key to exchange secret keys does not have PFS. There is currently no other solution to provide the PFS except for the Diffie-Hellman exchange.  As a result, the DH protocol has been included in all well-designed key exchange protocols.

Rocky, K. C. Chang22 Summary  We have strengthened the basic DH protocol to an authenticated DH protocol.  At the end of the protocol, each side is authenticated and come up a secret session key.  The DH protocol possesses the perfect forward secrecy property.  The DH protocol has been used in a number of key exchange protocols, such as Photuris, SKIP, and of course IKE.

Rocky, K. C. Chang23 Acknowledgments  The notes are prepared mostly based on N. Ferguson and B. Schneier, Practical Cryptography, Wiley, 2003.