[Cfrg] Status of DragonFly

"Igoe, Kevin M." <kmigoe@nsa.gov> Thu, 13 December 2012 18:42 UTC

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From: "Igoe, Kevin M." <kmigoe@nsa.gov>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: Status of DragonFly
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Date: Thu, 13 Dec 2012 18:42:54 +0000
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Cc: Dan Harkins <dharkins@arubanetworks.com>
Subject: [Cfrg] Status of DragonFly
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I'd like the reading list's input on DragonFly (hereafter called DF), Dan Harkins' Password Authenticated
Key Exchange design (draft-irtf-cfrg-dragonfly-00).  I'd like to point out that draft-harkins-tls-pwd-03
is a proposal to use DF in  TLS that differs slightly from the CFRG draft.

Here is where I believe we stand:

1)      Confidentiality: The proof that the confidentiality of the key generated by the DF
      protocol is reducible to the standard Diffie-Hellmann problem is quite straight
      forward, so the resulting shared secret value is at least as secure as with  standard DH/ECDH.

2)      Authentication: Obviously the system can be no more secure than the password
      being used. I believe the most viable attack is to guess a password, use this password
      to initiate the  DF protocol with the endpoint being attacked, and see if it works.
      Monitoring the system logs should easily detect such an attack.

3)      Timing: I'm particularly concerned about the method used to generate the PE (password
dependent base point) in the ECDH case. Inside a while loop, several parameters,
 including the identities of the two endpoints, the shared password, and a counter are
passed to a KDF to produce an n-bit output, where the curve is mod an n-bit prime p.
The resulting n-bit value X is checked to see if 0 <= X < p and X^3+a*X+b is a quadratic
residue mod p (an event of probability ½).  If both these tests are passed, the while
loop is exited and X is used as the x-coordinate of our PE.

The problem I see with (3) is that the number of times through the loop gives an opponent a
check  on any putative value for the password.  E.g.  if their current guess for the password
takes many passes through the while loop to generate the PE, but they observe that the DF response
 time is inconsistent with that, they have eliminated that guess for the password.

      When DF is applied to TLS in as described in draft-harkins-tls-pwd-03, two nonces are used as
      inputs to the KDF, which has two consequences:
a.      the PE MUST be computed online
b.      each DF exchange gives an independent timing check on the password.
      The opponent can passively sit back, monitoring the timing of DF exchanges on various links until
      they stumble across one where the timings match up with the timings associated with one of the
      passwords they are testing. They've now are able to bypass the authentication provided by DF.

      A possible fix is to use the KDF to generate a random X, 1<X<q, where q is the size of the cryptographic
      subgroup of the curve, and take PE = X*G, where G is the generator of the cryptographic subgroup.  For
      most cryptographic curves,  q  is very, very close to 2^n, so it is VERY unlikely that more than 1 call to the
      KDF will be needed.

      Another fix would be to require PE generation be done offline, which would eliminate any possibility of
      using nonces in the DF protocol.  One could, however, mix the nonces in after the completion to the
      DF based Diffie-Hellmann exchange.

Kevin M. Igoe   | "We can't solve problems by using the same kind
kmigoe@nsa.gov<mailto:kmigoe@nsa.gov>  | of thinking we used when we created them."
                |              - Albert Einstein -