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Versions: 00 01 02

Internet Research Task Force                                     S. Shin
Internet-Draft                                                 K. Kobara
Intended status: Informational                                      AIST
Expires: August 8, 2014                                February 04, 2014


        Augmented Password-Authenticated Key Exchange (AugPAKE)
                       draft-irtf-cfrg-augpake-01

Abstract

   This document describes a secure and highly-efficient augmented
   password-authenticated 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).  Also, this
   protocol provides resistance to server compromise in the context that
   an attacker, who obtained the password verifier from the server, must
   at least perform off-line dictionary attacks to gain any advantage in
   impersonating the user.  The AugPAKE protocol is not only provably
   secure in the random oracle model but also the most efficient over
   the previous augmented PAKE protocols (SRP and AMP).

Status of This Memo

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

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on August 8, 2014.

Copyright Notice

   Copyright (c) 2014 IETF Trust and the persons identified as the
   document authors.  All rights reserved.




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   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
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Keywords  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  AugPAKE Specification . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Underlying Group  . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .   4
       2.2.1.  Password Processing . . . . . . . . . . . . . . . . .   6
     2.3.  Protocol  . . . . . . . . . . . . . . . . . . . . . . . .   6
       2.3.1.  Initialization  . . . . . . . . . . . . . . . . . . .   7
       2.3.2.  Actual Protocol Execution . . . . . . . . . . . . . .   7
   3.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
     3.1.  General Assumptions . . . . . . . . . . . . . . . . . . .   9
     3.2.  Security against Passive Attacks  . . . . . . . . . . . .   9
     3.3.  Security against Active Attacks . . . . . . . . . . . . .   9
       3.3.1.  Impersonation Attacks on User U . . . . . . . . . . .  10
       3.3.2.  Impersonation Attacks on Server S . . . . . . . . . .  10
       3.3.3.  Man-in-the-Middle Attacks . . . . . . . . . . . . . .  11
     3.4.  Security against Off-line Dictionary Attacks  . . . . . .  11
     3.5.  Resistance to Server Compromise . . . . . . . . . . . . .  12
   4.  Implementation Consideration  . . . . . . . . . . . . . . . .  12
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  13
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  13
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .  13
     6.2.  Informative References  . . . . . . . . . . . . . . . . .  13
   Appendix A.  Features of AugPAKE  . . . . . . . . . . . . . . . .  15
   Appendix B.  Test Vector of AugPAKE . . . . . . . . . . . . . . .  16
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  18

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
   authenticated key exchange (AKE) protocol, which allows the involving
   parties to authenticate each other and to generate a temporary
   session key.  The temporary session key is used to protect the
   subsequent communications between the parties.



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   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], [ISOIEC11770-4],
   [IEEEP1363.2]) 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 an augmented PAKE
   which also achieves highly efficiency over the previous works (SRP
   [RFC2945], [ISOIEC11770-4], and AMP [ISOIEC11770-4]).  In summary, 1)
   The AugPAKE protocol is secure against passive attacks, active
   attacks and off-line dictionary attacks on the obtained messages with
   passive/active attacks (see [SKI10] for the formal security proof),
   and 2) It 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 1 and 1.17 modular
   exponentiations, respectively.  Compared with SRP [RFC2945],
   [ISOIEC11770-4], and AMP [ISOIEC11770-4], 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.

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].








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2.  AugPAKE Specification

2.1.  Underlying Group

   The AugPAKE protocol can be implemented over the following group.

   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 does not require the order check
   of elements, received from the counterpart party.  Note that the
   groups, defined in Discrete Logarithm Cryptography [SP800-56A] and
   RFC 5114 [RFC5114], are not necessarily the above secure prime
   groups.

   Alternatively, one can implement the AugPAKE protocol over the
   following groups.

   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 subgroup of prime order q over the field GF(p), the
      integers modulo p. Let g be any element of G other than 1.  For
      example, g = h^2 mod p where h is a primitive element.  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).  If p is not a "secure" prime, the
      AugPAKE protocol MUST perform the order check of received
      elements.

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:

   U



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       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.  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".

   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.

   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).

   W
       The password verifier registered in the server.  This password
       verifier is computed as follows: W = g^w mod p where the user's
       password w is used itself, or W = g^w' mod p where the effective
       password w' = H'(0x00 | U | S | w) is used.

   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),



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       its binary representation MUST have the same bit length as the
       binary representation of prime p.

   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).

2.2.1.  Password Processing

   The input password MUST be processed according to the rules of the
   [RFC4013] profile of [RFC3454].  The password SHALL be considered a
   "stored string" per [RFC3454] and unassigned code points are
   therefore prohibited.  The output SHALL be the binary representation
   of the processed UTF-8 character string.  Prohibited output and
   unassigned code points encountered in SASLprep pre-processing SHALL
   cause a failure of pre-processing and the output SHALL NOT be used
   with the AugPAKE protocol.

   The following table shows examples of how various character data is
   transformed by the rules of the [RFC4013] profile.

   #  Input            Output     Comments
   -  -----            ------     --------
   1  I<U+00AD>X       IX         SOFT HYPHEN mapped to nothing
   2  user             user       no transformation
   3  USER             USER       case preserved, will not match #2
   4  <U+00AA>         a          output is NFKC, input in ISO 8859-1
   5  <U+2168>         IX         output is NFKC, will match #1
   6  <U+0007>                    Error - prohibited character
   7  <U+0627><U+0031>            Error - bidirectional check

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.







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2.3.1.  Initialization

   U -> S: (U, W)
           The user U computes W = g^w mod p (instead of w, the
           effective password w' may be used), 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.

   If resistance to server compromise is not necessary, the server can
   store w' instead of W. In either case, server S SHOULD NOT store any
   plaintext passwords.

   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).

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

              Figure 1: Actual Protocol Execution of AugPAKE

   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



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           chooses a random element y from Z_q^* and computes Y = (X *
           (W^r))^y mod p where r = H'(0x01 | U | S | bn2bin(X)).  Note
           that X^y * g^(w * r * y) mod p can be computed from y and (w
           * r * y) efficiently using Shamir's trick [MOV97].  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 mod p 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.

   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].  After generating SK, the user
   and the server MUST delete all the internal states (e.g., Diffie-
   Hellman exponents x and y) from memory.

   For the formal proof [SKI10] of the AugPAKE protocol, we need to
   change slightly the computation of Y (in the above S -> U: (S, Y))
   and K (in the above S -> U: V_S) as follows: Y = (X * (W^r))^y' and K
   = g^y' where y' = H'(0x05 | bn2bin(y)).




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3.  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.

3.1.  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.

3.2.  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
   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.

3.3.  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



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   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.

3.3.1.  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.

3.3.2.  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.





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3.3.3.  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.

3.4.  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
   honest party).

   As discussed in Section 3.2, 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 3.3, 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.







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3.5.  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,

           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.

4.  Implementation Consideration

   As discussed in Section 3, 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



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   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]).

5.  IANA Considerations

   This document has no request to IANA.

6.  References

6.1.  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>.

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

   [RFC3454]  Hoffman, P. and M. Blanchet, "Preparation of
              Internationalized Strings ("stringprep")", RFC 3454,
              December 2002.

   [RFC4013]  Zeilenga, K., "SASLprep: Stringprep Profile for User Names
              and Passwords", RFC 4013, February 2005.

   [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>.

6.2.  Informative References








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   [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.

   [IEEE1363.2]
              IEEE 1363.2, , "IEEE Standard Specifications for Password-
              Based Public-Key Cryptographic Techniques", IEEE Std
              1363.2, IEEE Computer Society , January 2009.

   [IEEEP1363.2]
              IEEE P1363.2, , "Password-Based Public-Key Cryptography",
              Submissions to IEEE P1363.2 , <http://grouper.ieee.org/
              groups/1363/passwdPK/submissions.html>.

   [ISOIEC11770-4]
              ISO/IEC 11770-4, , "Information technology -- Security
              techniques -- Key management -- Part 4: Mechanisms based
              on weak secrets", International Standard ISO/IEC
              11770-4:2006, May 2006, <http://www.iso.org/iso/
              iso_catalogue/catalogue_tc/
              catalogue_detail.htm?csnumber=39723>.

   [MOV97]    Menezes, A., Oorschot, P., and S. Vanstone, "Simultaneous
              Multiple Exponentiation", in Handbook of Applied
              Cryptography , CRC Press , 1997.

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



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   [RFC5114]  Lepinski, M. and S. Kent, "Additional Diffie-Hellman
              Groups for Use with IETF Standards", RFC 5114, January
              2008.

   [SKI10]    Shin, S., Kobara, K., and H. Imai, "Security Proof of
              AugPAKE", Cryptology ePrint Archive: Report 2010/334, June
              2010, <http://eprint.iacr.org/2010/334>.

   [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>.

   [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>.

Appendix A.  Features of AugPAKE

   Below are some features of the AugPAKE protocol.

   Security:

   o  AugPAKE is zero knowledge (password) proof.  It is secure against
      passive/active/off-line dictionary attacks.  It is also resistant
      to server-compromise impersonation attacks.

   o  AugPAKE provides Perfect Forward Secrecy (PFS) and is secure
      against Denning-Sacco attack.

   o  Any cryptographically secure Diffie-Hellman groups can be used.

   o  The formal security proof of AugPAKE can be found at [SKI10].

   o  AugPAKE can be easily used with strong credentials.

   o  In the case of server compromise, an attacker has to perform off-
      line dictionary attacks while computing modular exponentiation
      with a password candidate.

   Intellectual Property:

   o  AugPAKE was publicly disclosed on Oct. 2008.



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   o  AIST applied for a patent in Japan on July 10, 2008.  AIST would
      provide royal-free license of AugPAKE.

   o  IPR disclosure (see https://datatracker.ietf.org/ipr/2037/)

   Miscellaneous:

   o  The user needs to compute only 2 modular exponentiation
      computations while the server needs to compute 2.17 modular
      exponentiation computations.  AugPAKE needs to exchange 2 group
      elements and 2 hash values.  This is almost the same computation/
      communication costs as the plain Diffie-Hellman key exchange.  If
      we use a large (e.g., 2048/3072-bits) parent group, the hash size
      would be relatively small.

   o  AugPAKE can be easily converted to 'balanced' PAKE.

   o  AugPAKE has the same performance for any type of secret.

   o  Internationalization of character-based passwords can be
      supported.

   o  AugPAKE can be implemented over any ECP (Elliptic Curve Group over
      GF[P]), EC2N (Elliptic Curve Group over GF[2^N]), and MODP
      (Modular Exponentiation Group) groups.

   o  AugPAKE has request/response nature.

   o  No Trusted Third Party (TTP) and clock synchronization

   o  No additional primitive (e.g., Full Domain Hash (FDH) and/or ideal
      cipher) is needed.

   o  Easy implementation.  We already implemented AugPAKE and have been
      testing in AIST.

Appendix B.  Test Vector of AugPAKE

   Here is a test vector of the AugPAKE protocol.

   p = 0x FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
          43000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000



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          00000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000
          00000000000000000000000000000000000000000000000000000000000000
          0000000000000000330A0DFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
          FFFFFFFFFFFFFFFFDA5193AB

   q = 0x FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
          43

   g = 0x F1AC99884ABBBBCC9BAA19BF375607FD14570B3019A03871147032445ADA7F
          A5B8BDC399C1889BBDA197ADB1E3939D55361241F5CD5ED529B0ADD921B274
          44BD2EB698DC962A9F7D202EAB98BC0C8CC950CA13BC6B1E632D0876A4E796
          26FDE85F06A46C9991EB02A6D6096E0DF6BCA2CAA12E838BEC47A7CB4AF2B0
          D94107B9CDBD67327238ECAF84DF292E776AF0F76288B39F9D9E4DDF3A9731
          CC832D70F150A0F29E7A1E193D1D21CBE8A84B56B0A4692CB39D3048086782
          85A23F08F9DB402487746F7E2A19CAF2171E55C76337E359217516213FF3BF
          616F8B20586A8B3168DA444AEA862BB76B9EA2BF8CB84773D29D4EFE511C53
          95F89CB547EFBBAE333E0BDB22DA40CE0B942A59841A12790910CC1332699D
          64BBF667E0DF3791C4E29CEB48E8397D50C72F7765C5A18809E3497F6BD374
          F5D185BBC8F57E36051E11E8DD0C5DD385A9DA442F22598111960CC2B83CBA
          0A1D980745562F6C62DD6D81B7BAEA7650B1E6E57AB9CC4C95EF17256A79B1
          31859E1BAC81FF1E

   U =    augpakeuser@aist.go.jp

   S =    augpakeserver@aist.go.jp

   X = 0x AF261CB6FD99E2E3B4FCDE8A9C538A872EBB54CC82845E8038EA34804DD739
          90689F2191BF6436BFFD13459DC5FF1FBD56734CA6347ADF52AFAB85EC98A0
          4D27C122EBAF1840229C2F74E9AEEB79C27ECAF6C8B88FCD5FB3F9C8F20F8F
          88D45CEBB56D6CAB251DC34D3656DB73E4DF77B71420565D4696DBF8D27023
          36E909F4C33B2F14605BDEB535423F02B779D7AF0CCB4F3705E177C4334F14
          707140218197845C708E6ABC025BCA954AA2FDAA352D284DE41D33F7CCFCFD
          99CAB3CFD34361B6D0551C6D8AEE604316F99758A9C58A96C39AA811E8BA10
          2E4D21D8F5EFC26920B3F95E6C800D8EBE9914B53144B038BE0E0B43D86479
          E3CBE623FD148CC90784548C1C7C522C6C71FD4A095B15CBF3EB74C7759493
          38AC7691A3763C0A3AB97E9E2B439192C49470BF90F292C4A8D336D86780FD
          DC7DC3C2CC04A6E3AB632788D97D4FDDEE5B117DCF76D91CEA1794FAD91CA1
          7C9715D83589A00CBB72DD513F6A30E4DB31ACA8DA5D6ECD0E20307D70D6DD
          0C2D6D3D7962694B5E1B0848

   Y = 0x 39033C00E1C30FF1A945DD699C516D3BB194FABBB46ADF54A2ED0820FEE0A4
          DE52128E2126A4393E3040E07D90432B8C19433EC920274E5A7C165DC89AA2
          C6D77E801A0C7676BC71955A52E74775C57C63B97304C73211C2035BD7B6D1
          8844A28AC50DD2DA96B257236A6090CCB08D2006BF57AC69EA14ABC5D71BA0
          6A6BD4093A2EF27C74D5D9189BB2EC865E6321D0DFECDE2D9AC537E8254E98
          C38AE00BE2554F71FE6EFBBDBE8D7038128957E98C99206998B0B4E578EC47
          957205C228FAC57B9A1589B8FF2B134980504F56B8A84809B8FF70EFF67520



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          2B255F0724DC0F76F3802D8A42ACC33D349A7FAF249BFBFEB324C3966D2B30
          6093C32A928A8BEB99AC301D20372E95BB8A3E500778B4651EB8A19B162666
          8DDFB77D0DF4C1932F1FE63389F3B1F29AE99F34BC39EF0AD04BC3A6A129DE
          E66E50B6768EDECC529F06FE5F7AD3825E8ECFCB12DB579C40F19D12BF6F60
          4621F60413DAEB77FE48C136518C57D02A2C6BB596EDFA0DACC127C2FD5FE1
          9B72580A722307C3F86C0EB1

   V_U = 0x  490C7CE33DCC3EBE8D0406EEB97CA154882DCBBA0A728F3B870263BCA36
          9DB6

   V_S = 0x  D70D2CAA821B9D84E29D75EB5E9B2DB038BA1256ECFC35C553832743A6E
          36F

Authors' Addresses

   SeongHan Shin
   AIST
   Central 2, 1-1-1, Umezono
   Tsukuba, Ibaraki  305-8568
   JP

   Phone: +81 29-861-5284
   Email: seonghan.shin@aist.go.jp


   Kazukuni Kobara
   AIST

   Email: kobara_conf-ml@aist.go.jp






















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