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Network Working Group                                         D. Harkins
Internet-Draft                                            Aruba Networks
Intended status: Standards Track                           March 7, 2010
Expires: September 8, 2010


                   Secure PSK Authentication for IKE
                   draft-harkins-ipsecme-spsk-auth-01

Status of this Memo

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   This Internet-Draft will expire on September 8, 2010.

Copyright Notice

   Copyright (c) 2010 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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Abstract

   This memo describes a secure pre-shared key authentication method for
   IKE.  It is resistant to dictionary attack and retains security even
   when used with weak pre-shared keys.



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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Keyword Definitions  . . . . . . . . . . . . . . . . . . .  3
   2.  Scenarios  . . . . . . . . . . . . . . . . . . . . . . . . . .  3
   3.  Notation . . . . . . . . . . . . . . . . . . . . . . . . . . .  5
   4.  Discrete Logarithm Cryptography  . . . . . . . . . . . . . . .  5
     4.1.  Elliptic Curve Cryptography (ECP) Groups . . . . . . . . .  6
     4.2.  Finite Field Cryptography (MODP) Groups  . . . . . . . . .  7
   5.  Random Numbers . . . . . . . . . . . . . . . . . . . . . . . .  8
   6.  The Random Function  . . . . . . . . . . . . . . . . . . . . .  8
   7.  Assumptions  . . . . . . . . . . . . . . . . . . . . . . . . .  8
   8.  Secure Pre-Shared Key Authentication Message Exchange  . . . .  9
     8.1.  Fixing the Secret Element, SKE . . . . . . . . . . . . . .  9
       8.1.1.  ECP Operation to Select SKE  . . . . . . . . . . . . . 10
       8.1.2.  MODP Operation to Select SKE . . . . . . . . . . . . . 11
     8.2.  Encoding of Group Elements and Scalars . . . . . . . . . . 12
       8.2.1.  Encoding of ECP Elements . . . . . . . . . . . . . . . 12
       8.2.2.  Encoding of MODP Elements  . . . . . . . . . . . . . . 13
       8.2.3.  Scalars  . . . . . . . . . . . . . . . . . . . . . . . 13
     8.3.  Message Generation and Processing  . . . . . . . . . . . . 13
       8.3.1.  Generation of a Commit . . . . . . . . . . . . . . . . 13
       8.3.2.  Processing of a Commit . . . . . . . . . . . . . . . . 13
         8.3.2.1.  Validation of an ECP Element . . . . . . . . . . . 14
         8.3.2.2.  Validation of a MODP Element . . . . . . . . . . . 14
         8.3.2.3.  Commit Processing Steps  . . . . . . . . . . . . . 14
       8.3.3.  Generation of a Confirm  . . . . . . . . . . . . . . . 14
       8.3.4.  Processing of a Confirm  . . . . . . . . . . . . . . . 15
     8.4.  Payload Formats  . . . . . . . . . . . . . . . . . . . . . 15
       8.4.1.  Commit Payload . . . . . . . . . . . . . . . . . . . . 16
       8.4.2.  Confirm Payload  . . . . . . . . . . . . . . . . . . . 16
     8.5.  IKEv1 Messaging  . . . . . . . . . . . . . . . . . . . . . 17
     8.6.  IKEv2 Messaging  . . . . . . . . . . . . . . . . . . . . . 18
   9.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 18
   10. Security Considerations  . . . . . . . . . . . . . . . . . . . 19
   11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 20
   12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 21
     12.1. Normative References . . . . . . . . . . . . . . . . . . . 21
     12.2. Informative References . . . . . . . . . . . . . . . . . . 21
   Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 22











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1.  Introduction

   Both [RFC2409] and [RFC4306] allow for authentication of the IKE
   peers using a pre-shared key.  The exchanges, though, are susceptible
   to dictionary attack and are therefore insecure.

   To address this security issue, [RFC4306] recommends that the pre-
   shared key used for authentication "contain as much unpredictability
   as the strongest key being negotiated".  That means any non-
   hexidecimal key would require over 100 characters to provide enough
   strength to generate a 128-bit key for AES.  This is an unrealistic
   requirement because humans have a hard time entering a string over 20
   characters without error.  Consequently, pre-shared key
   authentication in [RFC2409] and [RFC4306] are used insecurely today.

   A pre-shared key authentication method built on top of a zero-
   knowledge proof will provide resistance to dictionary attack and
   still allow for security when used with weak pre-shared keys, such as
   user-chosen passwords.  Such an authentication method is described in
   this memo.

   Resistance to dictionary attack is achieved when an attacker gets
   one, and only one, guess at the secret per active attack (see for
   example, [BM92], [BMP00] and [BPR00]).  Another way of putting this
   is that any advantage the attacker can realize is through interaction
   and not through computation.  This is demonstrably different than the
   technique from [RFC4306] of using a large, random number as the pre-
   shared key.  That can only make a dictionary attack less likely to
   suceed, it does not prevent a dictionary attack.  And, as [RFC4306]
   notes, it is completely insecure when used with weak keys like user-
   generated passwords.

1.1.  Keyword Definitions

   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.  Scenarios

   [RFC4306] describes usage scenarios for IKEv2.  These are:

   1.  "Security Gateway to Security Gateway Tunnel": the endpoints of
       the IKE (and IPsec) communication are network nodes that protect
       traffic on behalf of connected networks.  Protected traffic is
       between devices on the respective protected networks.




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   2.  "Endpoint-to-Endpoint Transport": the endpoints of the IKE (and
       IPsec) communication are hosts according to [RFC4301].  Protected
       traffic is between the two endpoints.

   3.  "Endpoint to Securty Gateway Tunnel": one endpoint connects to a
       protected network through a network node.  The endpoints of the
       IKE (and IPsec) communication are the endpoint and network node,
       but the protected traffic is between the endpoint and another
       device on the protected network behind the node.

   [RFC4306] also defines an EAP authentication method which can use a
   pre-shared key or password in a manner that is resistant to
   dictionary attack.  But this requires the IKE Responder to have a
   certificate.  Also, EAP is strictly a client-server protocol used for
   network access where one side is, typically, has a human behind it
   and the other side is a network node.  And, for EAP to scale a server
   that terminates the EAP conversation is typically located on the
   protected network behind the network node.  Therefore EAP
   authentication is really only applicable to the "Endpoint to Security
   Gateway Tunnel" usage scenario.

   The authentication and key exchange described in this memo is
   therefore suitable for both the "Security Gateway to Security Gateway
   Tunnel" scenario and the "Endpoint-to-Endpoint Transport" scenario.
   In both of those, there is no defined roles.  Either party could
   initiate an IKE connection to the other and there isn't necessarily a
   human involved.  Also, both sides will have access to the pre-shared
   key (i.e. no external authentication server) and neither side is
   required to have a certificate.  While it is certainly possible to
   use EAP authentication in these cases with an EAP method such as
   [EAPPWD], it will be a pointless and problematic encapsulation-- it
   requires implementation of both the EAP client and EAP server state
   machines, requires support of at least one EAP method, requires
   support for EAP fragmentation, etc.

   [RFC2409] does not describe usage scenarios for IKEv1 but IKEv1 has,
   traditionally, been used in the same "Security Gateway to Security
   Gateway Tunnel" scenario and the "Endpoint-to-Endpoint Transport"
   scenario.  Its pre-shared key-based authentication method is
   constrained to only allow keys identified by IP address.  Also, it
   lacks a robust way to do user authentication using a password,
   prompting the definition of different insecure ways to do password
   authentication.  Therefore, a secure pre-shared key-based
   authentication method in IKEv1 will mitigate the need to do insecure
   password-based authentication and remove the requirement that a pre-
   shared key in IKEv1 needs to be based on IP address.

   There is a need to do secure pre-shared key-based authentication in



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   IKE and it makes sense to do it as part of IKE and not by requiring
   additional authentication protocols.


3.  Notation

   The following notation is used in this memo:

   psk
       A shared, secret and potentially low-entropy word, phrase, code
       or key used as a credential to mutually authenticate the peers.

   a = H(b)
       The binary string "b" is given to a function H which produces a
       fixed-length output "a".

   a | b
       denotes concatenation of string "a" with string "b".

   [a]b
       indicates a string consisting of the single bit "a" repeated "b"
       times.

   len(x)
       indicates the length in bits of the string x.

   LSB(x)
       returns the least-significant bit of the bitstring "x".

   The convention for this memo to represent an element in a finite
   cyclic group is to use an upper-case letter while a scalar is
   indicated with a lower-case letter.


4.  Discrete Logarithm Cryptography

   This protocol uses Discrete Logarithm Cryptography to achieve
   authentication.  Each party to the exchange derives ephemeral public
   and private keys with respect to a particular set of domain
   parameters (referred to here as a "group").  Groups can be either
   based on finite field cryptography (MODP groups) or elliptic curve
   cryptography (ECP groups).

   This protocol uses the same group as the IKE exchange in which it is
   being used for authentication, with the exception of characteristic-
   two elliptic curve groups (EC2N).  Use of such groups is undefined
   for this authentication method and an IKE exchange that negotiates
   one of these groups MUST NOT use this method of authentication.



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   The key exchange defined in this memo uses fundamental algorithms of
   ECP groups as described in [ECC-CRYPTO].

   For each group the following operations are defined:

   o   "scalar operation"-- taking a scalar and an element in the group
       producing another element-- Z = scalar-op(x, Y).

   o   "element operation"-- taking two elements in the group to produce
       a third-- Z = element-op(X, Y).

   o   "inverse operation"-- take an element an return another element
       such that the element operation on the two produces the identity
       element of the group-- Y = inverse(X).

4.1.  Elliptic Curve Cryptography (ECP) Groups

   Domain parameters for ECP elliptic curves used for secure pre-shared
   key-based authentication include:

   o  A prime, p, determining a prime field GF(p).  The cryptographic
      group will be a subgroup of the full elliptic curve group which
      consists points on an elliptic curve-- elements from GF(p) that
      satisfy the curve's equation-- together with the "point at
      infinity" (denoted here as "O") that serves as the identity
      element.  The group operation for ECP groups is addition of points
      on the elliptic curve.

   o  Elements a and b from GF(p) that define the curve's equation.  The
      point (x,y) is on the elliptic curve if and only if (y^2 - x^3 -
      a*x - b) mod p equals zero (0).

   o  A prime, r, which is the order of G, and thus is also the size of
      the cryptographic subgroup that is generated by G.

   The scalar operation is multiplication of a point on the curve by
   itself a number of times.  The point Y is multiplied x-times to
   produce another point Z:

       Z = scalar-op(x, Y) = x*Y

   The element operation is addition of two points on the curve.  Points
   X and Y are summed to produce another point Z:

       Z = element-op(X, Y) = X + Y

   The inverse function is defined such that the sum of an element and
   its inverse is "0":



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       Q + inverse(Q) = "O"

   Elliptic curve groups require a mapping function, q = F(Q), to
   convert a group element to an integer.  The mapping function used in
   this memo returns the x-coordinate of the point it is passed.

   Note: There is another ECP domain parameter, a co-factor, f, that is
   defined by the requirement that the size of the full elliptic curve
   group (including "O") is the product f and r.  ECP groups used for
   secure pre-shared key-based authentication MUST have a co-factor of
   one (1).  At the time of publication of this memo, all ECP groups in
   the IANA registry used by IKE had a co-factor of one (1).

4.2.  Finite Field Cryptography (MODP) Groups

   Domain parameters for MODP groups used for secure pre-shared key-
   based authentication include:

   o  A prime, p, determining a prime field GF(p), the integers modulo
      p.  The group operation for MODP groups is multiplication modulo
      p.

   o  A prime, r, which is the multiplicative order of G, and thus also
      the size of the cryptographic subgroup of GF(p)* that is generated
      by G.

   The scalar operation is exponentiation of a generator modulus a
   prime.  An element Y is taken to the x-th power modulo the prime
   returning another element, Z:

       Z = scalar-op(x, Y) = Y^x mod p

   The element operation is modular multiplication.  Two elementx, X and
   Y, are multiplied modulo the prime returning another element, Z:

       Z = element-op(X, Y) = (X * Y) mod p

   The inverse function for a MODP group is defined such that the
   product of an element and its inverse modulo the group prime equals
   one (1).  In other words,

       (Q * inverse(Q)) mod p = 1

   Unlike ECP groups, MODP groups do not require a mapping function to
   convert an element into a scalar.  But for the purposes of notation
   in protocol definition, the function F, when used below, shall just
   return the integer that was passed to it-- i.e.  F(i) = i.




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   Some MODP groups in the IANA registry for use by IKE (and the secure
   pre-shared key authentication method) are based on safe primes and
   the order is not included in the group's domain parameter set.  In
   this case only, the order, r, MUST be computed as the prime minus one
   divided by two-- (p-1)/2.  If an order is included in the group's
   domain parameter set that value MUST be used in this exchange when an
   order is called for.  If a MODP group does not include an order in
   its domain parameter set and is not based on a safe prime it MUST NOT
   be used with this exchange.


5.  Random Numbers

   As with IKE itself, the security of the secure pre-shared key
   authenticaiton method relies upon each participant in the protocol
   producing quality secret random numbers.  A poor random number chosen
   by either side in a single exchange can compromise the shared secret
   from that exchange and open up the possibility of dictionary attack.

   Producing quality random numbers without specialized hardware entails
   using a cryptographic mixing function (like a strong hash function)
   to distill entropy from multiple, uncorrelated sources of information
   and events.  A very good discussion of this can be found in
   [RFC4086].


6.  The Random Function

   The protocol described in this memo uses a random function, H. This
   is a "random oracle" as defined in [RANDOR].  At first glance one may
   view this as a hash function.  As noted in [RANDOR], though, hash
   functions are too structured to be used directly as a random oracle.
   But they can be used to instantiate a random oracle.

   The random function, H, in this memo is instantiated by HMAC-SHA256
   (see [RFC4634]) with a key whose length is 32 octets and whose value
   is zero.  In other words,

       H(x) = HMAC-SHA-256([0]32, x)


7.  Assumptions

   The security of the protocol relies on certain assumptions.  They
   are:

   1.  Function H maps a binary string of indeterminate length onto a
       fixed binary string that is x bits in length.



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           H: {0,1}^* --> {0,1}^x

   2.  Function H is a "random oracle" (see [RANDOR]).  Given knowledge
       of the input to H an adversary is unable to distinguish the
       output of H from a random data source.

   3.  The discrete logarithm problem for the chosen finite cyclic group
       is hard.  That is, given G, p and Y = G^x mod p it is
       computationally infeasible to determine x.  Similarly for an
       elliptic curve group given the curve definition, a generator G,
       and Y = x * G it is computationally infeasible to determine x.

   4.  The pre-shared key is drawn from a finite pool of potential keys.
       Each possible key in the pool has equal probability of being the
       shared key.  All potential attackers have access to this pool of
       keys.


8.  Secure Pre-Shared Key Authentication Message Exchange

   To perform secure pre-shared key authentication each side must
   generate a shared and secret element in the chosen group based on the
   pre-shared key.  This element, called the Secret Key Element, or SKE,
   is then used in an authentication and key exchange protocol.  The key
   exchange protocol consists of each side exchanging two data, a
   "Commit" and a "Confirm".

   The "Commit" contributes ephemeral information to the exchange and
   binds the sender to a single value of the pre-shared key from the
   pool of potential pre-shared keys.  The "Confirm" proves that the
   pre-shared key is known and completes the zero-knowledge proof.

8.1.  Fixing the Secret Element, SKE

   The method of fixing SKE depends on the type of group, either MODP or
   ECP.  For the sake of convenience, we will use a single notation of
   prf+() to denote the function prf+() from [RFC4306] as well as the
   function prf() from [RFC2409], depending on whether the exchange is
   being performed in IKEv2 or IKEv1, respectively.

   Fixing the SKE involves an iterative hunting-and-pecking technique
   using the prime from the negotiated group's domain parameter set and
   an ECP- or MODP-specific operation depending on the negotiated group.

   First, an 8-bit counter is set to the value one (1).  Then, the
   random function is used to generate a secret seed using the counter,
   the pre-shared key, and the two nonces exchanged by the Initiator and
   the Responder:



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      ske-seed = H(Ni | Nr | psk | counter)

   Then, the swe-seed is expanded using prf+ to create an ske-value:

      ske-value = prf+(ske-seed, "IKE SKE Hunting And Pecking")

   where len(ske-value) is the same as len(p), the length of the prime
   from the domain parameter set of the negotiated group.

   If the swe-seed is greater than or equal to the prime, p, the counter
   is incremented and a new ske-seed is generated and the hunting-and-
   pecking continues.  If swe-seed is less than the prime, p, it is
   passed to the group-specific operation to select the SKE or fail.  If
   the group-specific operation fails, the counter is incremented, a new
   ske-seed is generated and the hunting-and-pecking continues.

8.1.1.  ECP Operation to Select SKE

   The group-specific operation for ECP groups uses ske-value, ske-seed
   and the equation of the curve to produce SKE.  First ske-value is
   used directly as the x-coordinate, x, with the equation of the
   elliptic curve, with parameters a and b from the domain parameter set
   of the curve, to solve for a y-coordinate, y.

   If there is no solution to the equation the operation fails (and the
   hunting-and-pecking continues).  If a solution is found then an
   ambiguity exists as there are technically two solutions to the
   equation, and ske-seed is used to unambiguously select one of them.
   If the low-order bit of ske-seed is equal to the low-order bit of y
   then a candidate SKE is defined as the point (x,y); if the low-order
   bit of ske-seed differs from the low-order bit of y then a candidate
   SKE is defined as the point (x, p-y) where p is the prime from the
   negotiated group's domain parameter set.  The candidate SKE becomes
   the SKE and the ECP-specific operation completes successfully.

   Algorithmically, the process looks like this:















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         found = 0
         counter = 1
         do {
           ske-seed = H(Ni | Nr | psk | counter)
           ske-value = prf+(swd-seed, "IKE SKE Hunting And Pecking")
           if (ske-value < p)
           then
             x = ske-value
             if ( (y = sqrt(x^3 + ax + b)) != FAIL)
             then
               if (LSB(y) == LSB(ske-seed))
               then
                 SKE = (x,y)
               else
                 SKE = (x, p-y)
               fi
               found = 1
             fi
           fi
           counter = counter + 1
         } while (found == 0)

                    Figure 1: Fixing SKE for ECP Groups

8.1.2.  MODP Operation to Select SKE

   The group-specific operation for MODP groups takes ske-value, and the
   prime, p, and order, r, from the group's domain parameter set to
   directly produce a candidate SKE by exponentiating the ske-value to
   the value ((p-1)/r) modulo the prime.  If the candidate SKE is
   greater than one (1) the candidate SKE becomes the SKE and the MODP-
   specific operation completes successfully.  Otherwise, the MODP-
   specific operation fails (and the hunting-and-pecking continues).

   Algorithmically, the process looks like this:
















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         found = 0
         counter = 1
         do {
           ske-seed = H(Ni | Nr | psk | counter)
           ske-value = prf+(swd-seed, "IKE SKE Hunting And Pecking")
           if (ske-value < p)
           then
             SKE = ske-value ^ ((p-1)/r) mod p
             if (SKE > 1)
             then
               found = 1
             fi
           fi
           counter = counter + 1
         } while (found == 0)

                   Figure 2: Fixing SKE for MODP Groups

8.2.  Encoding of Group Elements and Scalars

   The payloads used in the secure pre-shared key authentication method
   contain elements from the negotiated group and scalar values.  To
   ensure interoperability, field elements and scalars MUST be
   represented in payloads in accordance with the requirements in this
   section.

8.2.1.  Encoding of ECP Elements

   Elements in ECP groups are points on the negotiated elliptic curve.
   Each such element MUST be rpresented by the concatenation of two
   components, an x-coordinate and a y-coordinate.

   Each of the two components, the x-coordinate and the y-coordinate,
   MUST be represented (in binary form) as an unsigned integer that is
   strictly less than the prime, p, from the group's domain parameter
   set.  The binary representation of each component MUST have a bit
   length equal to the bit length of the binary representation of p.
   This length requirement is enforced, if necessary, by prepending the
   binary representation of the integer with zeros until the required
   length is achieved.

   Since the field element is represented in a payload by the
   x-coordinate followed by the y-coordinate it follows, then, that the
   length of the element in the payload MUST be twice the bit length of
   p.






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8.2.2.  Encoding of MODP Elements

   Elements in MODP groups MUST be represented (in binary form) as
   unsigned integers that are strictly less than the prime, p, from the
   group's domain parameter set.  The binary representation of each
   group element MUST have a bit length equal to the bit length of the
   binary representation of p.  This length requirement is enforced, if
   necessary, by prepending the binary representation of the interger
   with zeros until the required length is achieved.

8.2.3.  Scalars

   Scalars MUST be represented (in binary form) as unsigned integers
   that are strictly less than r, the order of the generator of the
   agreed-upon cryptographic group.  The binary representation of each
   scalar MUST have a bit length equal to the bit length of the binary
   representation of r.  This requirement is enforced, if necessary, by
   prepending the binary representation of the integer with zeros until
   the required length is achieved.

8.3.  Message Generation and Processing

8.3.1.  Generation of a Commit

   A Commit has two components, a Scalar and an Element.  To generate a
   Commit, two random numbers, a "private" value and a "mask" value, are
   generated (see Section 5).  Their sum modulo the order of the group,
   r, becomes the Scalar component:

       Scalar = (private + mask) mod r

   If the Scalar is not greater than one (1), the private and mask
   values MUST be thrown away and new values randomly generated.  If the
   Scalar is greater than one (1), the inverse of the scalar operation
   with the mask and SWE becomes the Element component.

       Element = inverse(scalar-op(mask, SKE))

   The Commit payload consists of the Scalar followed by the Element.

8.3.2.  Processing of a Commit

   Upon receipt of a peer's Commit the scalar and element MUST be
   validated.  The processing of an element depends on the type, either
   an ECP element or a MODP element.






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8.3.2.1.  Validation of an ECP Element

   Validating a received ECP Element involves: 1) checking whether the
   two coordinates, x and y, are both greater than zero (0) and less
   than the prime defining the underlying field; and 2) checking whether
   the x- and y-coordinates satisfy the equation of the curve (that is,
   that they produce a valid point on the curve that is not "0").  If
   either of these conditions are not met the received Element is
   invalid, otherwise the received Element is valid.

8.3.2.2.  Validation of a MODP Element

   A received MODP Element is valid if: 1) it is between one (1) and the
   prime, p, exclusive; and 2) if modular exponentiation of the Element
   by the group order, r, equals one (1).  If either of these conditions
   are not true the received Element is invalid.

8.3.2.3.  Commit Processing Steps

   Commit validation is accomplished by the following steps:

   1.  The length of the Commit payload is checked against the
       anticipated size (the length of the scalar plus the length of the
       element for the negotiated group.  If it is incorrect, the Commit
       is invalidated, otherwise processing continues.

   2.  The scalar is extracted from the Commit payload and checked to
       ensure it is between one (1) and r, the order of the negotiated
       group, exclusive.  If it is not, the Commit is invalidated,
       otherwise processing continues.

   3.  The element is extracted from the Commit payload and checked in a
       manner that depends on the type of group negotiated.  If the
       group is ECP the element is validated according to
       Section 8.3.2.1, if the group is MODP the element is validated
       according to Section 8.3.2.2.  If the Element is not valid then
       the Commit is invalidated, otherwise the Commit is validated.

   If the Commit is invalidated the payload MUST be discarded and the
   IKE exchange aborted.

8.3.3.  Generation of a Confirm

   A Confirm message is generated after a Commit has been generated and
   a pper's Commit has been processed.  First, a candidate shared secret
   to authenticate the peer is derived.  Using SKE, the "private" value
   generated as part of Commit generation, and the peer's Scalar and
   Element from its Commit, peer-scalar and peer-element, respectively,



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   the shared secret, ss, is generated as:

         ss = F(scalar-op(private,
                          element-op(peer-element,
                                     scalar-op(peer-scalar, SKE))))

   For the purposes of subsequent computation, the bit length of ss
   SHALL be equal to the bit length of the prime, p, used in either a
   MODP or ECP group.  This bit length SHALL be enforced, if necessary,
   by prepending zeros to the value until the required length is
   achieved.

   Then, using the shared secret, ss, and the generated Scalar and
   Element, self-scalar and self-element, respectively, and the received
   Scalar and Element, peer-scalar and peer-element, respectively, an
   authenticating Tag is generated as:

              Tag = H(self-scalar | peer-scalar |
                      F(self-element) | F(peer-element) | ss)

   The Commit payload consists of the authenticating Tag.

8.3.4.  Processing of a Confirm

   Upon receipt of a peer's Confirm message an expected Tag value is
   computed and compared against the Tag value in the Confirm payload.
   If the two differ the exchange MUST be aborted.  If they equal the
   peer has been successfully authenticated.

8.4.  Payload Formats





















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8.4.1.  Commit Payload


    The Commit Payload is defined as follows:

                              1                   2                   3
        0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
       ! Next Payload  !C!  RESERVED   !         Payload Length        !
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
       |                                                               |
       ~                            Scalar                             ~
       |                                                               |
       ~                               +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
       |                               |                               |
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+                               ~
       |                                                               |
       ~                           Element                             ~
       |                                                               |
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The Commit Payload SHALL be indicated in both IKEv1 and IKEv2 with
   TBD1 from the [IKEV2-IANA] registry maintained by IANA.

   The Scalar SHALL be encoded as an unsigned integer with a bit length
   equal to the bit length of the order of the group used in the
   exchange.  This length is enforced, if necessary, by prepending the
   integer with zeros until the required length is achieved.  The
   Element is encoded according to Section 8.2.

8.4.2.  Confirm Payload


    The Confirm Payload is defined as follows:

                              1                   2                   3
        0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
       ! Next Payload  !C!  RESERVED   !         Payload Length        !
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
       !                                                               !
       ~                              Tag                              ~
       !                                                               !
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The Confirm Payload SHALL be indicated in both IKEv1 and IKEv2 with
   TBD2 from the [IKEV2-IANA] registry maintained by IANA.




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8.5.  IKEv1 Messaging

   Secure pre-shared key authentication can be used in either Main Mode
   (see Figure 3) or Aggressive Mode (see Figure 4) with IKEv1 and SHALL
   be indicated by negotiation of the TBD3 Authentication Method from
   the [IKEV1-IANA] registry maintained by IANA, in the SA payload.
   When using IKEv1 the "C" (critical) bit from Section 8.4.1 and
   Section 8.4.2 MUST be clear (i.e. a value of zero).


         Initiator                          Responder
        -----------                        -----------
         HDR, SAi                 -->
                                  <--    HDR, SAr
         HDR, KEi, Ni             -->
                                  <--    HDR, KEr, Nr
         HDR*, IDii, Commit       -->
                                  <--    HDR*, IDir, Commit, Confirm
         HDR*, Confirm, HASH_I    -->
                                  <--    HDR*, HASH_R

                     Figure 3: Secure PSK in Main Mode



          Initiator                          Responder
         -----------                        -----------
          HDR, SAi, KEi, Ni, IDii,
               Commit               -->
                                   <--    HDR, SAr, KEr, Nr, IDir,
                                          Commit, Confirm
          HDR, Confirm, HASH_I     -->
                                   <--    HDR, HASH_R

                  Figure 4: Secure PSK in Aggressive Mode

   For secure pre-shared key authentication with IKEv1 the SKEYID value
   is computed as follows:

       SKEYID = prf(Ni_b | Nr_b, g^xy)

   And HASH_I and HASH_R are computed as follows:

          HASH_I = prf(SKEYID, ss | g^xi | g^xr | CKY-I | CKY-R |
                       SA_ib | IDii_b)

          HASH_R = prf(SKEYID, ss | g^xr | g^xi | CKY-R | CKY-I |
                       SA_ib | IDir_b)



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   Where "ss" is the shared secret derived in Section 8.3.3.

8.6.  IKEv2 Messaging

   The specific authentication method being employed in IKEv2 is not
   negotiated, like in IKEv1.  It is inferred from the components of the
   message.  The presence of a Commit payload in second message sent by
   the Initiator indicates an intention to perform secure pre-shared key
   authentication (see Figure 5).  The critical bit is used in both the
   Commit and Confirm payloads to allow for backwards compatibility and
   MUST be set (i.e. a value of one).


       Initiator                          Responder
      -----------                        -----------
       HDR, SAi1, KEi, Ni       -->
                                <--    HDR, SAr1, KEr, Nr, [CERTREQ]
       HDR, SK {IDi, Commit, [IDr,]
                SAi2, TSi, TSr} -->
                                <--    HDR, SK {IDr, Commit, Confirm}
       HDR, SK {Confirm, AUTH}  -->
                                <--    HDR, SK {AUTH, SAr2, TSi, TSr}

                       Figure 5: Secure PSK in IKEv2

   In the case of secure pre-shared key authentication the AUTH value is
   computed as:

       AUTH = prf(ss, <msg octets>)

   Where "ss" is the shared secret derived in Section 8.3.3.  The
   Authentication Method indicated in the AUTH payload SHALL be TBD4
   from the [IKEV2-IANA] registry maintained by IANA.


9.  IANA Considerations

   IANA SHALL assign values for the Commit payload (Section 8.4.1) and
   the Confirm payload (Section 8.4.2), and replace TBD1 and TBD2,
   respectively, above, from the [IKEV2-IANA] of "IKEv2 Payload Types".

   IANA SHALL assign a value for "Secure Shared Key Authentication",
   replacing TBD3 above, from the IPSEC Authentication Method registry
   in [IKEV1-IANA].

   IANA SHALL assign a value for "Secure Shared Key Authentication",
   replacing TBD4 above, from the IKEv2 Authentication Method registry
   in [IKEV2-IANA].



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10.  Security Considerations

   Both the Initiator and Responder obtain a shared secret, "ss" (see
   Section 8.3.3) based on a secret group element and their own private
   values contributed to the exchange.  If they do not share the same
   pre-shared key they will be unable to derive the same secret group
   element and if they do not share the same secret group element they
   will be unable to derive the same shared secret.

   Resistance to dictionary attack means that the attacker must launch
   an active attack to make a single guess at the pre-shared key.  If
   the size of the pool from which the key was extracted was D, and each
   key in the pool has an equal probability of being chosen, then the
   probability of success after a single guess is 1/D. After X guesses,
   and removal of failed guesses from the pool of possible keys, the
   probability becomes 1/(D-X).  As X grows so does the probability of
   success.  Therefore it is possible for an attacker to determine the
   pre-shared key through repeated brute-force, active, guessing
   attacks.  This authentication method does not presume to be secure
   against this and implementations SHOULD ensure the size of D is
   sufficiently large to prevent this attack.  Implementations SHOULD
   also take countermeasures, for instance refusing authentication
   attempts for a certain amount of time, after the number of failed
   authentication attempts reaches a certain threshold.  No such
   threshold or amount of time is recommended in this memo.

   An active attacker can impersonate the Initiator of the exchange and
   send a forged Commit payload.  The attacker then waits until it
   receives a Commit and a Confirm from the Responder.  Now the attacker
   can attempt to run through all possible values of the pre-shared key,
   computing SKE (see Section 8.1), computing "ss" (see Section 8.3.3),
   and attempting to recreate the Confirm payload from the Responder.

   But the attacker committed to a single guess of the pre-shared key
   with her forged Commit.  That value was used by the Responder in his
   computation of "ss" which was used to construct his Confirm.  Any
   guess of the pre-shared key which differs from the one used in the
   forged Commit would result in each side using a different secret
   element in the computation of "ss" and therefore the Confirm could
   not be verified as correct, even if a subsequent guess, while running
   through all possible values, was correct.  The attacker gets one
   guess, and one guess only, per active attack.

   An attacker, acting as either the Initiator or Responder, can take
   the Element from the Commit message received from the other party,
   reconstruct the random "mask" value used in its construction and then
   recover the other party's "private" value from the Scalar in the
   Commit message.  But this requires the attacker to solve the discrete



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   logarithm problem which we assumed was intractable above (Section 7).

   Instead of attempting to guess at pre-shared keys an attacker can
   attempt to determine SKE and then launch an attack.  But SKE is
   determined by the output of the random function, H, which is assumed
   to be indistinguishable from a random source (Section 7).  Therefore,
   each element of the finite cyclic group will have an equal
   probability of being the SKE.  The probability of guessing SKE will
   be 1/r, where r is the order of the group.  This is the same
   probability of guessing the solution to the discrete logarithm which
   is assumed to be intractable (Section 7).  The attacker would have a
   better chance of success at guessing the input to H, i.e. the pre-
   shared key, since the order of the group will be many orders of
   magnitude greater than the size of the pool of pre-shared keys.

   The implications of resistance to dictionary attack are significant.
   An implementation can provision a pre-shared key in a practical and
   realistic manner-- i.e. it MAY be a character string and it MAY be
   relatively short-- and still maintain security.  The nature of the
   pre-share key determines the size of the pool, D, and countermeasures
   can prevent an attacker from determining the secret in the only
   possible way: repeated, active, guessing attacks.  For example, a
   simple four character string using lower-case English characters, and
   assuming random selection of those characters, will result in D of
   over four hundred thousand.  An attacker would need to mount over one
   hundred thousand active, guessing attacks (which will easily be
   detected) before gaining any significant advantage in determining the
   pre-shared key.

   For a more detailed discussion of the security of the key exchange
   underlying this authentication method see [SAE] and [EAPPWD].


11.  Acknowledgements

   The author would like to thank Scott Fluhrer and Hideyuki Suzuki for
   their insight in discovering flaws in earlier versions of the key
   exchange that underlies this authentication method and for their
   helpful suggestions in improving it.  Thanks to Lily Chen for useful
   advice on the hunting-and-pecking technique to "hash into" an element
   in a group and to Jin-Meng Ho for a discussion on countering a small
   sub-group attack.  Rich Davis suggested several checks on received
   messages that greatly increase the security of the underlying key
   exchange.  Hugo Krawczyk suggested the particular instantiation of
   the random function, H.


12.  References



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12.1.  Normative References

   [ECC-CRYPTO]
              McGrew, D., "Fundamental Elliptic Curve Cryptography
              Algorithms", draft-mcgrew-fundamental-ecc-01 (work in
              progress), October 2009.

   [IKEV1-IANA]
              "Internet Assigned Numbers Authority, Internet Key
              Exchange (IKE) Attributes",
              <http://www.iana.org/assignments/ipsec-registry>.

   [IKEV2-IANA]
              "Internet Assigned Numbers Authority, IKEv2 Parameters",
              <http://www.iana.org/assignments/ikev2_parameters>.

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

   [RFC2409]  Harkins, D. and D. Carrel, "The Internet Key Exchange
              (IKE)", RFC 2409, November 1998.

   [RFC4301]  Kent, S. and K. Seo, "Security Architecture for the
              Internet Protocol", RFC 4301, December 2005.

   [RFC4306]  Kaufman, C., "Internet Key Exchange (IKEv2) Protocol",
              RFC 4306, December 2005.

   [RFC4634]  Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and HMAC-SHA)", RFC 4634, July 2006.

12.2.  Informative References

   [BM92]     Bellovin, S. and M. Merritt, "Encrypted Key Exchange:
              Password-Based Protocols Secure Against Dictionary
              Attack", Proceedings of the IEEE Symposium on Security and
              Privacy, Oakland, 1992.

   [BMP00]    Boyko, V., MacKenzie, P., and S. Patel, "Provably Secure
              Password Authenticated Key Exchange Using Diffie-Hellman",
              Proceedings of Eurocrypt 2000, LNCS 1807 Springer-Verlag,
              2000.

   [BPR00]    Bellare, M., Pointcheval, D., and P. Rogaway,
              "Authenticated Key Exchange Secure Against Dictionary
              Attacks", Advances in Cryptology -- Eurocrypt '00, Lecture
              Notes in Computer Science Springer-Verlag, 2000.




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   [EAPPWD]   Harkins, D. and G. Zorn, "EAP Authentication Using Only A
              Password", draft-harkins-emu-eap-pwd-12 (work in
              progress), October 2009.

   [RANDOR]   Bellare, M. and P. Rogaway, "Random Oracles are Practical:
              A Paradigm for Designing Efficient Protocols", Proceedings
              of the 1st ACM Conference on Computer and Communication
              Security, ACM Press, 1993,
              <http://www.cs.ucsd.edu/~mihir/papers/ro.pdf>.

   [RFC4086]  Eastlake, D., Schiller, J., and S. Crocker, "Randomness
              Requirements for Security", BCP 106, RFC 4086, June 2005.

   [SAE]      Harkins, D., "Simultaneous Authentication of Equals: A
              Secure, Password-Based Key Exchange for Mesh Networks",
              Proceedings of the 2008 Second International Conference on
              Sensor Technologies and Applications Volume 00, 2008.


Author's Address

   Dan Harkins
   Aruba Networks
   1322 Crossman Avenue
   Sunnyvale, CA  94089-1113
   United States of America

   Email: dharkins@arubanetworks.com























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