Key Exchange Using Passwords and Long Keys

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					 Key Exchange Using
         Passwords
      and Long Keys
            Vladimir Kolesnikov
               Charles Rackoff

Comp. Sci. University of Toronto
Communication Setting




                                …

      Full Control   Insecure
                     network
Secure Communication from
Shared Random Key
            Trusted Party
               k 2R DK      • Simple
                            • Very efficient




              k2 2R DK
            Trusted Party
Key Exchange (KE)
A protocol between two parties
 Both output (the same) randomly chosen k 2 DK


Security
 Adv does not know anything about k even if it sees
  all other exchanged keys
 Adv cannot mismatch players
     If Alice instance ``thinks’’ she exchanged a key with Bob,
      then at most one instance of “Bob talking to Alice” may
      have the same key
     Players must have secret credentials
Defining KE
   Large amount of prior work
   An intuitive notion, but hard to define

   We want our definition to:
       Be intuitive and easy to use
       Reject “bad” protocols (allow powerful adversaries)
       Accept “good” protocols (avoid unnecessary
        restrictions)
Simulation Style KE Definition
       Real               Ideal




                 ¼




   8      9
                     • Powerful
                     • But complicated
Game Style KE Definition

                                     Plays the game:

                            • challenge a completed
                              honest player


                         Challenge:
                         • Present either a key
                           or a random string
                         Adversary guesses which
                         • Should not do too well

         • Seems to be almost as powerful
         • Self-contained
         • Simpler
Our Setting
• Asymmetric – Server (e.g. Bank) and Clients




 • Large secure storage            • Key on storage card
   of credentials                      • can be lost or stolen
                                   • Memorized password
                                       • low entropy
                                       • guessing attack possible
  • if card not stolen
       • have full security. Password guessing not possible
  • If card is stolen, still have password security
Some of Related Work
   Hybrid model (C has a pwd and pk of S)
       Halevi Krawczyk 99, Boyarsky 99
   Simulation- vs game-style KE
       Simulation-style KE
           Shoup 99, Boyko MacKenzie Patel 00
           Universally Composable (UC) Canetti Halevi Katz
            Lindell MacKenzie 05
       Game-style KE
           Bellare Pointcheval Rogaway 00
Denial of Access (DoA) Attack
   In Password-Authenticated KE, it is
    necessary to stop service if “too many”
    password failures P?
       Adv can deny access for good guys
   We can protect against such attacks
       Require that Adv cannot cause P?, unless he
        stole key card
       Don’t know of previous formalizations of DoA
           Complements Denial of Service notion
Our Protocol




Note: No Mutual Authentication
Password updates
   Usually handled externally to the definition
   If C updates his pwd, then DoA attack is
    possible (Adv can replay old msgs)
       Problem: have users with related credentials
   Solutions
       Update long key as well
       Have a challenge-response protocol
       Keep password update counters
       In the last two cases also need to update definition
Can a definition allow for
mistyping passwords?
   We don’t model this
   What if we allowed Adv to create instances
    with mistyped passwords?
       Adv specifies the password
           Is this how people mistype?
             can behave badly on pwd’ = pwd+1
       Adv specifies a mistyping function
           Only f that has 0,1,|D|-1 or |D| fixed points is allowed
   UC-based definitions can handle this
    [CHKLM05]
Definitional Choices: Counting
passwords attacks
   Adv can guess passwords
   Quantify advantage; “password attack”
   Previously
       Act of Adv interfering with traffic
       (Insignificant change? Successful guess?)
   In our definition
       Count failed password attacks – player outputs P?
Summary
   Define Key Exchange (KE) in a new model
       Generalization of the hybrid model of Halevi-
        Krawczyk (HK)
       (Some of) our discussion applies to other models
        (password-only and hybrid model of HK)
   Give a new efficient KE protocol
   Discuss a potential flaw in the HK protocols
       Some members of the family of the HK protocols
        are vulnerable to password guessing attacks
Other
Extended version is on Eprint. Contains:
     Proofs
     Discussion on storing passwords on the server
     Discussion on password updates

             http://eprint.iacr.org/2006/057

				
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