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Versions: 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 RFC 6628

Internet Engineering Task Force                                  S. Shin
Internet-Draft                                                 K. Kobara
Intended status: Standards Track                              RCIS, AIST
Expires: September 2, 2010                                 March 1, 2010


 Most Efficient Augmented Password-Only Authentication and Key Exchange
                      draft-shin-augmented-pake-00

Abstract

   This document describes an efficient augmented password-only
   authentication and key exchange (AugPAKE) protocol where a user
   remembers a low-entropy password and its verifier is registered in
   the intended server.  In general, the user password is chosen from a
   small set of dictionary whose space is within the off-line dictionary
   attacks.  The AugPAKE protocol described here is secure against
   passive attacks, active attacks and off-line dictionary attacks (on
   the obtained messages with passive/active attacks), and also provides
   resistance to server compromise (in the context of augmented PAKE
   security).

Status of this Memo

   This Internet-Draft is submitted to IETF in full conformance with the
   provisions of BCP 78 and BCP 79.

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   This Internet-Draft will expire on September 2, 2010.

Copyright Notice

   Copyright (c) 2010 IETF Trust and the persons identified as the



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   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
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   the Trust Legal Provisions and are provided without warranty as
   described in the BSD License.


Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Keywords . . . . . . . . . . . . . . . . . . . . . . . . .  4
   2.  AugPAKE Specification  . . . . . . . . . . . . . . . . . . . .  4
     2.1.  Underlying Groups  . . . . . . . . . . . . . . . . . . . .  4
     2.2.  Notation . . . . . . . . . . . . . . . . . . . . . . . . .  4
     2.3.  Protocol . . . . . . . . . . . . . . . . . . . . . . . . .  6
       2.3.1.  Initialization . . . . . . . . . . . . . . . . . . . .  6
       2.3.2.  Actual Protocol Execution  . . . . . . . . . . . . . .  6
   3.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . .  8
   4.  Security Considerations  . . . . . . . . . . . . . . . . . . .  8
     4.1.  General Assumptions  . . . . . . . . . . . . . . . . . . .  8
     4.2.  Security against Passive Attacks . . . . . . . . . . . . .  8
     4.3.  Security against Active Attacks  . . . . . . . . . . . . .  9
       4.3.1.  Impersonation Attacks on User U  . . . . . . . . . . .  9
       4.3.2.  Impersonation Attacks on Server S  . . . . . . . . . . 10
       4.3.3.  Man-in-the-Middle Attacks  . . . . . . . . . . . . . . 10
     4.4.  Security against Off-line Dictionary Attacks . . . . . . . 10
     4.5.  Resistance to Server Compromise  . . . . . . . . . . . . . 11
   5.  Implementation Consideration . . . . . . . . . . . . . . . . . 12
   6.  Intellectual Property  . . . . . . . . . . . . . . . . . . . . 12
   7.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 12
     7.1.  Normative References . . . . . . . . . . . . . . . . . . . 12
     7.2.  Informative References . . . . . . . . . . . . . . . . . . 13
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 14












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1.  Introduction

   In the real world, many applications such as web mail, Internet
   banking/shopping/trade require secure channels between participating
   parties.  Such secure channels can be established by using an
   authentication and key exchange (AKE) protocol, which allows the
   involving parties to authenticate each other and to generate a
   temporal session key.  The temporal session key would be used to
   protect the subsequent communications between the parties.

   Until now, password-only AKE (called, PAKE) protocols have attracted
   much attention because password-only authentication is very
   convenient to the users.  However, it is not trivial to design a
   secure PAKE protocol due to the existence of off-line dictionary
   attacks on passwords.  These attacks are possible since passwords are
   chosen from a relatively-small dictionary that allows for an attacker
   to perform the exhaustive searches.  This problem was brought forth
   by Bellovin and Merritt [BM92], and many following works have been
   conducted in the literature (see some examples in [IEEEP1363.2]).  A
   PAKE protocol is said to be secure if the best attack an active
   attacker can take is restricted to the on-line dictionary attacks,
   which allow to check a guessed password only by interacting with the
   honest party.

   An augmented PAKE protocol (e.g., [BM93], [RFC2945], [ISO]) provides
   extra protection for server compromise in the sense that an attacker,
   who obtained a password verifier from a server, cannot impersonate
   the corresponding user without performing off-line dictionary attacks
   on the password verifier.  This additional security is known as
   "resistance to server compromise".  The AugPAKE protocol described in
   this document is such an augmented PAKE one which also achieves most
   efficiency over the previous works.  In other words, the AugPAKE
   protocol is secure against passive attacks, active attacks and off-
   line dictionary attacks (on the obtained messages with passive/active
   attacks), and provides resistance to server compromise.  At the same
   time, the AugPAKE protocol has similar computational efficiency to
   the plain Diffie-Hellman key exchange [DH76] that does not provide
   authentication by itself.  Specifically, the user and the server need
   to compute 2 and 2.17 modular exponentiations, respectively, in the
   AugPAKE protocol.  After excluding pre-computable costs, the user and
   the server are required to compute only one and 1.17 modular
   exponentiations, respectively.  Compared with SRP [RFC2945] and AMP
   [ISO], the AugPAKE protocol is more efficient 1) than SRP in terms of
   the user's computational costs and 2) than AMP in terms of the
   server's computational costs.






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1.1.  Keywords

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [RFC2119].


2.  AugPAKE Specification

2.1.  Underlying Groups

   The AugPAKE protocol can be implemented over the underlying groups,
   defined in Discrete Logarithm Cryptography [SP800-56A].

   o  Let p and q be sufficiently large primes such that p = (2 * q) +
      1.  This p is called a "safe" prime.  We denote by G a
      multiplicative group of prime order q over the field GF(p), the
      integers modulo p.  Let g be a generator for the group G so that
      all the group elements are generated by g.  The group operation is
      denoted multiplicatively (in modulo p).

   o  Let p and q be sufficiently large primes such that q is a divisor
      of ((p - 1) / 2).  We denote by G a multiplicative subgroup of
      prime order q over the field GF(p), the integers modulo p.  Let g
      be a generator for the subgroup G so that all the subgroup
      elements are generated by g.  The group operation is denoted
      multiplicatively (in modulo p).

   o  Let p and q be sufficiently large primes such that q is a divisor
      of ((p - 1) / 2) and every factors of ((p - 1) / 2) are also
      primes comparable to q in size.  This p is called a "secure"
      prime.  We denote by G a multiplicative subgroup of prime order q
      over the field GF(p), the integers modulo p.  Let g be a generator
      for the subgroup G so that all the subgroup elements are generated
      by g.  The group operation is denoted multiplicatively (in modulo
      p).

   By using a secure prime p, the AugPAKE protocol has computational
   efficiency gains.  Specifically, it can save computational costs that
   would be needed for the order check of elements, received from the
   counterpart party.

2.2.  Notation

   The AugPAKE protocol is a two-party protocol where a user and a
   server authenticate each other and generate a session key.  The
   following notation is used in this document:




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   U
       The user's identity (e.g., defined in [RFC4282]).  It is a string
       in {0,1}^* where {0,1}^* indicates a set of finite binary
       strings.

   S
       The server's identity (e.g., defined in [RFC4282]).  It is a
       string in {0,1}^*.

   b = H(a)
       A binary string a is given as input to a secure one-way hash
       function H (e.g., SHA-2 family [FIPS180-3]) which produces a
       fixed-length output b.  The hash function H maps {0,1}^* to
       {0,1}^k where {0,1}^k indicates a set of binary strings of length
       k and k is a security parameter.

   b = H'(a)
       A binary string a is given as input to a secure one-way hash
       function H' which maps the input a in {0,1}^* to the output b in
       Z_q^* where Z_q^* is a set of positive integers modulo prime q.

   a | b
       It denotes a concatenation of binary strings a and b in {0,1}^*.

   0x
       A hexadecimal value is shown preceded by "0x".

   w
       The password remembered by the user.  This password may be used
       as an effective password (instead of itself) in the form of
       H'(0x00 | U | S | w).

   X * Y mod p
       It indicates a multiplication of X and Y modulo prime p.

   X = g^x mod p
       The g^x indicates a multiplication computation of g by x times.
       The resultant value modulo prime p is assigned to X. The discrete
       logarithm problem says that it is computationally hard to compute
       the discrete logarithm x from X, g and p.

   bn2bin(X)
       It indicates a conversion of a multiple precision integer X to
       the corresponding binary string.  If X is an element over GF(p),
       its binary representation MUST have the same bit length as the
       binary representation of prime p.





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   U -> S: msg
       It indicates a message transmission that the user U sends a
       message msg to the server S.

   U:
       It indicates a local computation of user U (without any out-going
       messages).

2.3.  Protocol

   The AugPAKE protocol consists of two phases: initialization and
   actual protocol execution.  The initialization phase SHOULD be
   finished in a secure manner between the user and the server, and it
   is performed all at once.  Whenever the user and the server need to
   establish a secure channel, they can run the actual protocol
   execution through an open network (i.e., the Internet) in which an
   active attacker exists.

2.3.1.  Initialization

   U -> S: (U, W)
           The user U computes W = g^w mod p, where w is the effective
           password, and transmits W to the server S. The W is
           registered in the server as the password verifier of user U.
           Of course, user U just remembers the password w only.

   As noted above, this phase SHOULD be performed securely and all at
   once.

2.3.2.  Actual Protocol Execution

   The actual protocol execution of the AugPAKE protocol allows the user
   and the server to share an authenticated session key through an open
   network (see Figure 1).

















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   +-----------------+                              +------------------+
   |     User U      |                              |  Server S (U,W)  |
   |                 |            (U, X)            |                  |
   |                 |----------------------------->|                  |
   |                 |                              |                  |
   |                 |            (S, Y)            |                  |
   |                 |<-----------------------------|                  |
   |                 |                              |                  |
   |                 |             V_U              |                  |
   |                 |----------------------------->|                  |
   |                 |                              |                  |
   |                 |             V_S              |                  |
   |                 |<-----------------------------|                  |
   |                 |                              |                  |
   +-----------------+                              +------------------+

                    Figure 1: Actual Protocol Execution

   U -> S: (U, X)
           The user U chooses a random element x from Z_q^* and computes
           its Diffie-Hellman public value X = g^x mod p.  The user
           sends the first message (U, X) to the server S.

   S -> U: (S, Y)
           If the received X from user U is 0, 1 or -1 (mod p), server S
           MUST terminate the protocol execution.  Otherwise, the server
           chooses a random element y from Z_q^* and computes Y = (X *
           (W^r))^y where r = H'(0x01 | U | S | bn2bin(X)).  Then,
           server S sends the second message (S, Y) to the user U.

   U -> S: V_U
           If the received Y from server S is 0, 1 or -1 (mod p), user U
           MUST terminate the protocol execution.  Otherwise, the user
           computes K = Y^z where z = 1 / (x + (w * r)) mod q and r =
           H'(0x01 | U | S | bn2bin(X)).  Also, user U generates an
           authenticator V_U = H(0x02 | U | S | bn2bin(X) | bn2bin(Y) |
           bn2bin(K)).  Then, the user sends the third message V_U to
           the server S.

   S -> U: V_S
           If the received V_U from user U is not equal to H(0x02 | U |
           S | bn2bin(X) | bn2bin(Y) | bn2bin(K)) where K = g^y mod p,
           server S MUST terminate the protocol execution.  Otherwise,
           the server generates an authenticator V_S = H(0x03 | U | S |
           bn2bin(X) | bn2bin(Y) | bn2bin(K)) and a session key SK =
           H(0x04 | U | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)).  Then,
           server S sends the fourth message V_S to the user U.




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   U:
           If the received V_S from server S is not equal to H(0x03 | U
           | S | bn2bin(X) | bn2bin(Y) | bn2bin(K)), user U MUST
           terminate the protocol execution.  Otherwise, the user
           generates a session key SK = H(0x04 | U | S | bn2bin(X) |
           bn2bin(Y) | bn2bin(K)).

   In the actual protocol execution, the sequential order of message
   exchanges is very important in order to avoid any possible attacks.
   For example, if the server S sends the second message (S, Y) and the
   fourth message V_S together, any attacker can easily derive the
   correct password w with off-line dictionary attacks.

   The session key SK, shared only if the user and the server
   authenticate each other successfully, MAY be generated by using a key
   derivation function (KDF) [SP800-108].


3.  IANA Considerations

   This document includes no request to IANA.


4.  Security Considerations

   This section shows why the AugPAKE protocol (i.e., the actual
   protocol execution) is secure against passive attacks, active attacks
   and off-line dictionary attacks, and also provides resistance to
   server compromise.

4.1.  General Assumptions

   o  An attacker is computationally-bounded.

   o  Any hash functions, used in the AugPAKE protocol, are secure in
      terms of pre-image resistance (one-wayness), second pre-image
      resistance and collision resistance.

4.2.  Security against Passive Attacks

   An augmented PAKE protocol is said to be secure against passive
   attacks in the sense that an attacker, who eavesdrops the exchanged
   messages, cannot compute an authenticated session key (shared between
   the honest parties in the protocol).

   In the AugPAKE protocol, an attacker can get the messages (U, X), (S,
   Y), V_U, V_S by eavesdropping, and then wants to compute the session
   key SK.  That is, the attacker's goal is to derive the correct K from



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   the obtained messages X and Y because the hash functions are secure
   and the only secret in the computation of SK is K = g^y mod p.  Note
   that

   X =     g^x mod p and

   Y =     (X * (W^r))^y = X^y * W^(r * y) = X^y * (g^y)^t = X^y * K^t

   hold where t = w * r mod q.  Though t is determined from possible
   password candidates and X, the only way for the attacker to extract K
   from X and Y is to compute X^y.  However, the probability for the
   attacker to compute X^y is negligible in the security parameter for
   the underlying groups since both x and y are random elements chosen
   from Z_q^*.  Therefore, the AugPAKE protocol is secure against
   passive attacks.

4.3.  Security against Active Attacks

   An augmented PAKE protocol is said to be secure against active
   attacks in the sense that an attacker, who completely controls the
   exchanged messages, cannot compute an authenticated session key
   (shared with the honest party in the protocol) with the probability
   better than that of on-line dictionary attacks.  In other words, the
   probability for an active attacker to compute the session key is
   restricted by the on-line dictioinary attacks where it grows linearly
   to the number of interactions with the honest party.

   In the AugPAKE protocol, the user (resp., the server) computes the
   session key SK only if the received authenticator V_S (resp., V_U) is
   valid.  There are three cases to be considered in the active attacks.

4.3.1.  Impersonation Attacks on User U

   When an attacker impersonates the user U, the attacker can compute
   the same SK (to be shared with the server S) only if the
   authenticator V_U is valid.  For a valid authenticator V_U, the
   attacker has to compute the correct K from X and Y because the hash
   functions are secure.  In this impersonation attack, the attacker of
   course knows the discrete logarithm x of X and guesses a password w'
   from the password dictionary.  So, the probability for the attacker
   to compute the correct K is bounded by the probability of w = w'.
   That is, this impersonation attack is restricted by the on-line
   dictionary attacks where the attacker can try a guessed password
   communicating with the honest server S. Therefore, the AugPAKE
   protocol is secure against impersonation attacks on user U.






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4.3.2.  Impersonation Attacks on Server S

   When an attacker impersonates the server S, the attacker can compute
   the same SK (to be shared with the user U) only if the authenticator
   V_S is valid.  For a valid authenticator V_S, the attacker has to
   compute the correct K from X and Y because the hash functions are
   secure.  In this impersonation attack, the attacker chooses a random
   element y and guesses a password w' from the password dictionary so
   that

   Y =     (X * (W'^r))^y = X^y * W'^(r * y) = X^y * (g^y)^t'

   where t' = w' * r mod q.  The probability for the attacker to compute
   the correct K is bounded by the probability of w = w'.  Also, the
   attacker knows whether the guessed password is equal to w or not by
   seeing the received authenticator V_U. However, when w is not equal
   to w, the probability for the attacker to compute the correct K is
   negligible in the security parameter for the underlying groups since
   the attacker has to guess the discrete logarithm x (chosen by user U)
   as well.  That is, this impersonation attack is restricted by the on-
   line dictionary attacks where the attacker can try a guessed password
   communicating with the honest user U. Therefore, the AugPAKE protocol
   is secure against impersonation attacks on server S.

4.3.3.  Man-in-the-Middle Attacks

   When an attacker performs the man-in-the-middle attack, the attacker
   can compute the same SK (to be shared with the user U or the server
   S) only if one of the authenticators V_U, V_S is valid.  Note that if
   the attacker relays the exchanged messages honestly, it corresponds
   to the passive attacks.  In order to generate a valid authenticator
   V_U or V_S, the attacker has to compute the correct K from X and Y
   because the hash functions are secure.  So, the attacker is in the
   same situation as discussed above.  Though the attacker can test two
   passwords (one with user U and the other with server S), it does not
   change the fact that this attack is restricted by the on-line
   dictionary attacks where the attacker can try a guessed password
   communicating with the honest party.  Therefore, the AugPAKE protocol
   is also secure against man-in-the-middle attacks.

4.4.  Security against Off-line Dictionary Attacks

   An augmented PAKE protocol is said to be secure against off-line
   dictionary attacks in the sense that an attacker, who completely
   controls the exchanged messages, cannot reduce the possible password
   candidates better than on-line dictionary attacks.  Note that, in the
   on-line dictionary attacks, an attacker can test one guessed password
   by running the protocol execution (i.e., communicating with the



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   honest party).

   As discussed in Section 4.2, an attacker in the passive attacks does
   not compute X^y (and the correct K = g^y mod p) from the obtained
   messages X, Y. This security analysis also indicates that, even if
   the attacker can guess a password, the K is derived independently
   from the guessed password.  Next, we consider an active attacker
   whose main goal is to perform the off-line dictionary attacks in the
   AugPAKE protocol.  As in Section 4.3, the attacker can 1) test one
   guessed password by impersonating the user U or the server S, or 2)
   test two guessed passwords by impersonating the server S (to the
   honest user U) and impersonating the user U (to the honest server S)
   in the man-in-the-middle attacks.  Whenever the honest party receives
   an invalid authenticator, the party terminates the actual protocol
   execution without sending any message.  In fact, this is important to
   prevent an attacker from testing more than one password in the active
   attacks.  Since passive attacks and active attacks cannot remove the
   possible password candidates efficiently than on-line dictionary
   attacks, the AugPAKE protocol is secure against off-line dictionary
   attacks.

4.5.  Resistance to Server Compromise

   We consider an attacker who has obtained a (user's) password verifier
   from a server.  In the (augmented) PAKE protocols, there are two
   limitations [BJKMRSW00]: 1) the attacker can find out the correct
   password from the password verifier with the off-line dictionary
   attacks because the verifier has the same entropy as the password;
   and 2) if the attacker impersonates the server with the password
   verifier, this attack is always possible because the attacker has
   enough information to simulate the server.  An augmented PAKE
   protocol is said to provide resistance to server compromise in the
   sense that the attacker cannot impersonate the user without
   performing off-line dictionary attacks on the password verifier.

   In order to show resistance to server compromise in the AugPAKE
   protocol, we consider an attacker who has obtained the password
   verifier W and then tries to impersonate the user U without off-line
   dictionary attacks on W. As a general attack, the attacker chooses
   two random elements c and d from Z_q^*, and computes

   X =     (g^c) * (W^d) mod p

   and sends the first message (U, X) to the server S. In order to
   impersonate user U successfully, the attacker has to compute the
   correct K = g^y mod p where y is randomly chosen by server S. After
   receiving Y from the server, the attacker's goal is to find out a
   value e satisfying Y^e = K mod p.  That is,



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           log_g (Y^e) = log_g K mod q

           (c + (w * d) + (w * r)) * y * e = y mod q

           (c + w * (d + r)) * e = 1 mod q

   where log_g K indicates the logarithm of K to the base g.  Since
   there is no off-line dictionary attacks on W, the above solution is
   that e = 1 / c mod q and d = -r mod q.  However, the latter is not
   possible since r is determined by X (i.e., r = H'(0x01 | U | S |
   bn2bin(X))) and H' is a secure hash function.  Therefore, the AugPAKE
   protocol provides resistance to server compromise.


5.  Implementation Consideration

   As discussed in Section 4, the AugPAKE protocol is secure against
   passive attacks, active attacks and off-line dictionary attacks, and
   provides resistance to server compromise.  However, an attacker in
   the on-line dictionary attacks can check whether one password
   (guessed from the password dictionary) is correct or not by
   interacting with the honest party.  Let N be a dictionary size of
   passwords.  Certainly, the attacker's success probability grows with
   the probability of (I / N) where I is the number of interactions with
   the honest party.  In order to provide a reasonable security margin,
   implementation SHOULD take a countermeasure to the on-line dictionary
   attacks.  For example, it would take about 90 years to test 2^(25.5)
   passwords with one minute lock-out for 3 failed password guesses (see
   Appendix A in [SP800-63]).


6.  Intellectual Property

   The National Institute of Advanced Industrial Science and Technology
   (AIST) has submitted a patent application about the AugPAKE protocol,
   described in this document.  For details of the patent application
   and its status, please contact the authors of this document.


7.  References

7.1.  Normative References

   [FIPS180-3]
              Information Technology Laboratory, "Secure Hash Standard
              (SHS)", NIST FIPS Publication 180-3, October 2008, <http:/
              /csrc.nist.gov/publications/fips/fips180-3/
              fips180-3_final.pdf>.



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   [RFC2119]  Bradner, S., "Key words for use in RFCs to Infdafdafdicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC4282]  Aboba, B., Beadles, M., Arkko, J., and P. Eronen, "The
              Network Access Identifier", RFC 4282, December 2005.

   [SP800-108]
              Chen, L., "Recommendation for Key Derivation Using
              Pseudorandom Functions (Revised)", NIST Special
              Publication 800-108, October 2009, <http://csrc.nist.gov/
              publications/nistpubs/800-108/sp800-108.pdf>.

   [SP800-56A]
              Barker, E., Johnson, D., and M. Smid, "Recommendation for
              Pair-Wise Key Establishment Schemes Using Discrete
              Logarithm Cryptography (Revised)", NIST Special
              Publication 800-56A, March 2007, <http://csrc.nist.gov/
              publications/nistpubs/800-56A/
              SP800-56A_Revision1_Mar08-2007.pdf>.

7.2.  Informative References

   [BJKMRSW00]
              Bellare, M., Jablon, D., Krawczyk, H., MacKenzie, P.,
              Rogaway, P., Swaminathan, R., and T. Wu, "Proposal for
              P1363 Study Group on Password-Based Authenticated-Key-
              Exchange Methods", IEEE P1363.2: Password-Based Public-Key
              Cryptography , Submissions to IEEE P1363.2 ,
              February 2000, <http://grouper.ieee.org/groups/1363/
              passwdPK/contributions/p1363-pw.pdf>.

   [BM92]     Bellovin, S. and M. Merritt, "Encrypted Key Exchange:
              Password-based Protocols Secure against Dictionary
              Attacks", Proceedings of the IEEE Symposium on Security
              and Privacy , IEEE Computer Society , 1992.

   [BM93]     Bellovin, S. and M. Merritt, "Augmented Encrypted Key
              Exchange: A Password-based Protocol Secure against
              Dictionary Attacks and Password File Compromise",
              Proceedings of the 1st ACM Conference on Computer and
              Communication Security , ACM Press , 1993.

   [DH76]     Diffie, W. and M. Hellman, "New Directions in
              Cryptography", IEEE Transactions on Information Theory
              Volume IT-22, Number 6, 1976.

   [IEEEP1363.2]
              IEEE P1363.2, "Password-Based Public-Key Cryptography",



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              Submissions to IEEE P1363.2 , <http://grouper.ieee.org/
              groups/1363/passwdPK/submissions.html>.

   [ISO]      ISO/IEC JTC 1/SC 27 11770-4, "Information technology --
              Security techniques -- Key management -- Part 4:
              Mechanisms based on weak secrets", May 2006, <http://
              www.iso.org/iso/iso_catalogue/catalogue_tc/
              catalogue_detail.htm?csnumber=39723>.

   [RFC2945]  Wu, T., "The SRP Authentication and Key Exchange System",
              RFC 2945, September 2000.

   [SP800-63]
              Burr, W., Dodson, D., and W. Polk, "Electronic
              Authentication Guideline", NIST Special Publication 800-63
              Version 1.0.2, April 2006, <http://csrc.nist.gov/
              publications/nistpubs/800-63/SP800-63V1_0_2.pdf>.


Authors' Addresses

   SeongHan Shin
   RCIS, AIST
   Akihabara Daibiru #1003, 1-18-13 Sotokanda, Chiyoda-ku
   Tokyo,   101-0021
   JP

   Phone: +81 3-5298-4723
   Email: seonghan.shin@aist.go.jp


   Kazukuni Kobara
   RCIS, AIST


   Phone:
   Email:














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