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EMU                                                           D. Harkins
Internet-Draft                                                       HPE
Intended status: Informational                             July 24, 2019
Expires: January 25, 2020


   Improved Extensible Authentication Protocol Using Only a Password
                   draft-harkins-eap-pwd-prime-00.txt

Abstract

   Passwords are a popular form of credential for user authentication.
   EAP-pwd (RFC 5931) is a popular method of performing secure password
   authenticaiton.  EAP-pwd requires a secret element in a finite cyclic
   group, unfortunately the technique it uses to derive this secret is
   open to timing and cache attacks.  This improved version, EAP-pwd',
   uses a different technique to derive the secret element which is
   resistant to timing and cache attacks.

Requirements Language

   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 [1].

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
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on January 25, 2020.

Copyright Notice

   Copyright (c) 2019 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
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   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
   2.  EAP-pwd'  . . . . . . . . . . . . . . . . . . . . . . . . . .   2
     2.1.  Secret Element Derivation for ECC . . . . . . . . . . . .   3
     2.2.  Secret Element Derivation for FFC . . . . . . . . . . . .   6
     2.3.  Fixing the Password Element . . . . . . . . . . . . . . .   7
   3.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   8
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   5.  Implementation Considerations . . . . . . . . . . . . . . . .   8
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .   9
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  10
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  10

1.  Introduction

   EAP-pwd is a popular EAP method due to the fact that it authenticates
   without requiring certificates.  Large federated networks sometimes
   have latency issues with numerous fragmented packets going between
   the EAP client and EAP server, a problem exacerbated by using EAP
   methods that require certificate-based authentication.  EAP-pwd
   obviates this.

   The technique used by EAP-pwd to obtain its secret element is
   susceptible to timing attacks and cache attacks that can partition
   the dictionary enough to successfully determine the password.  Recent
   work in the Crypto Forum Research Group on constant time techniques
   to hash a string into a point on an elliptic curve in constant time
   [2] provides an opportunity to address this.

2.  EAP-pwd'

   EAP-pwd' is an EAP method that follows the EAP-pwd specification
   ([3]) in all respects except for the following:

   o  It uses the Type code TBD-1, not 52 which is used by EAP-pwd.



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   o  It derives PWE/pwe as defined in Section 2.1 and Section 2.2 for
      ECC and FFC groups, respectively, using a different technique than
      the "hunting and pecking" loop defined in [3].

   o  it defines three new random functions using HKDF instantiated with
      SHA-256, SHA-384, and SHA-512.

   EAP-pwd' MUST be used with one of the random functions defined in
   this document.

   The technique used by EAP-pwd' for deriving PWE/pwe can be
   implemented in constant time and is resistant to the side channel and
   timing attacks that the hunting-and-pecking loop of [3] is
   susceptible to.  Computing the password element in EAP-pwd' is a two-
   step process.  First, a secret element based on the password is
   generated using one of the two new techniques, one for ECC and one
   for FFC.  Next the identities of the EAP server and EAP peer are
   combined with the secret element to create the password element used
   by the key exchange of [3].

   The secret element can be generated at provisioning time or a run-
   time.  Either way, the EAP server will generate the password element
   prior to generation of an EAP-pwd-Commit/Request and the EAP peer
   will generate the password element prior to generation of an EAP-pwd-
   Commit/Response.

2.1.  Secret Element Derivation for ECC

   The new technique to hash into an elliptic curve is the "Simplified
   Shallue-van de Woestijne-Ulas Method" from [2].  The operations to
   derive the secret element can be implemented in constant time.

   The Simplified SWU method takes a password as input and generates 2
   values-- x1 and x2-- at least one of which will be the abscissa of a
   point on the curve.  Since this method does not map its input to the
   entire curve it is necessary to use a construct from [5] that uses
   Simplified SWU with two functions that operate as random oracles to
   produce two different points whose sum is the secret point S:

      S := SSWU( h1(m) ) + SSWU( h2(m) )

   Where m is the message to hash, h1() and h2() are random oracles
   based on hash functions, '+' is point addition, and SSWU() is the
   "Simplified SWU" hash-to-curve method.

   EAP-pwd' uses HKDF ([4]) to instantiate the random oracles.  The
   password and a label is passed to HKDF() to produce a password-seed.
   The password seed is then reduced modulo the prime to produce the



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   input variable, u, for "Simplified SWU" which generates the first
   intermediate point.  This process is repeated with a different label
   to produce the second intermediate point.  Their sum is S.

   The particular flavor of HKDF is the random function negotiated by
   EAP-pwd'.

   Algorithmically, the process looks like this:











































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   simplified_swu(password) {
       pwd-seed = HKDF(0^n, password,
                       "EAP-pwd' Hash to Element P1", olen(p))
       u = (pwd-seed modulo (p - 2)) + 2

       t = inverse(z^2 * u^4 + z * u^2)
       x1 = (-b/a) * (1 + t)
       gx1 = x1^3 + a * x1 + b
       x2 = z * u^2 * x1
       gx2 = x2^3 + a * x2 + b

       l = gx1 is a quadratic residue modulo p
       v = CSEL(l, gx1, gx2)
       x = CSEL(l, x1, x2)
       y = sqrt(v)

       l = CEQ(LSB(u), LSB(y))
       P1 = CSEL(l, (x,y), (x, p-y))


       pwd-seed = HKDF(0^n, password,
                       "EAP-pwd' Hash to Element P2", olen(p))
       u = (pwd-seed modulo (p - 2)) + 2

       t = inverse(z^2 * u^4 + z * u^2)
       x1 = (-b/a) * (1 + t)
       gx1 = x1^3 + a * x1 + b
       x2 = z * u^2 * x1
       gx2 = x2^3 + a * x2 + b

       l = gx1 is a quadratic residue modulo p
       v = CSEL(l, gx1, gx2)
       x = CSEL(l, x1, x2)
       y = sqrt(v)

       l = CEQ(LSB(u), LSB(y))
       P2 = CSEL(l, (x,y), (x, p-y))

       S = P1 + P2

       output S
   }

               Figure 1: Generation of the ECC Secret Point

   Where:





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   o  0^n is a salt of all zeros whose length equals the length of the
      digest of the hash function that instantiates HKDF

   o  p is the prime, q is the order, a and b are part of the equation
      of the curve, and all of these are defined in the domain parameter
      set of the chosen curve

   o  z is a curve-specific parameter derived according to [2] for the
      chosen curve

   o  LSB(x) returns the least significant bit of x

   o  CSEL(x,y,z) operates in constant time and returns y if x is true
      and z otherwise

   o  CEQ(x,y) operates in constant time and returns true if x equals y
      and false otherwise

2.2.  Secret Element Derivation for FFC

   The new technique to hash into an FFC group is similar to the
   technique used in [3] but it does so without looping thereby
   obviating a timing attack that can partition the dictionary.

   EAP-pwd' uses HKDF ([4]) to produce a password value which is
   exponentiated to produce a new element of the same order as the
   generator of the group.  This new element is output.

   Algorithmically, the process looks like this:

   hash_to_ffc(password) {
       pwd-value = HKDF(0^n, password,
                        "EAP-pwd' Hash To Element",
                        olen(p))
       pwd-value = (pwd-value modulo (p - 2)) + 2

       s = pwd-value^((p-1)/q) modulo p

       output s
   }

               Figure 2: Generation of the FFC Secret Point

   Where:

   o  0^n is a salt of all zeros whose length equals the length of the
      digest of the hash function that instantiates HKDF




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   o  p is the prime, and q is the order and are defined in the domain
      parameter set of the chosen group

   The secret element, s, is guaranteed to have an order of either 1 or
   q and the probability that it is 1 is remote enough to ignore.

2.3.  Fixing the Password Element

   The secret element derived in Section 2.1 or Section 2.2 is used to
   fix EAP-pwd's Password Element prior to the generation of the EAP-
   pwd-Commit/Request by the EAP server and prior to generation of the
   EAP-pwd-Commit/Response by the EAP peer.  To do this, they use the
   negotiated random function to hash the anti-clogging token from [3]
   and their identities to the length of the order of the negotiated
   group.  This is interpreted as an integer and reduced such that it is
   between 1 and the order of the group, exclusive.  The secret element
   is then operated on by this value, point multiplication for ECC and
   exponentiation for FFC, to produce the Password Element.

   For ECC groups, this process looks like:

   fix_PWE(S) {
       val = HKDF(peer-ID | server-ID, token, "Fixing PWE", olen(p))
       val = val modulo (q - 1) + 1

       PWE = val * S
   }

                        Figure 3: Generation of PWE

   Where: p is the prime, and q is the order and are defined in the
   domain parameter set of the chosen group.

   For FFC groups, this process looks like:

   fix_pwe(S) {
       val = HKDF(peer-ID | server-ID, token, "Fixing pwe", olen(p))
       val = val modulo (q - 1) + 1

       pwe = s^val modulo p
   }

                        Figure 4: Generation of pwe

   Where: p is the prime, and q is the order and are defined in the
   domain parameter set of the chosen group.





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3.  Acknowledgements

   The author thanks Hugo Krawczyk and Riad Wahby.

4.  IANA Considerations

   IANA is insructed to assign a new EAP method type to EAP-pwd' and
   replace TBD-1 in this document with that value.

   IANA is instructed to assign values from the Random Function registry
   of [3] for the following:

   o  TBD-2: HKDF with SHA256 as defined in [4]

   o  TBD-3: HKDF with SHA384 as defined in [4]

   o  TBD-4: HKDF with SHA512 as defined in [4]

   Replacing TBD-[2-4] with the assigned values.

5.  Implementation Considerations

   Implementations SHOULD generate the secret element from Section 2.1
   and Section 2.2 when the password is provisioned and wait to generate
   a session-specific password element when the EAP-pwd' protocol
   begins.

   Implementations SHOULD offer use a random function that provides
   commensurate strength for the curve being negotiated.  Guidance is as
   follows based on the length of the curve's prime, len(p):

   o  HKDF-SHA256 when len(p) <= 256

   o  HKDF-SHA384 when 256 < len(p) <= 384

   o  HKDF-SHA512 when 384 < len(p)

   The technique to generate the secret element on an elliptic curve
   from Section 2.1 only works on Weierstrass curves with an equation of
   y^2 = x^3 + a*x + b, with a != 0 and b != 0.  A different hash-to-
   curve technique implementable in constant time will have to be used
   for other curves. [2] defines curve-specific techniques to obtain a
   secret element for other curves.  In the event that such a technique
   is used, the random function negotiated SHALL be HKDF based on the
   hash function defined in the ciphersuite of the particular hash to
   curve technique.





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   [2] describes useful utility functions that can be used to perform
   the operations in Figure 1 in constant time.  In addition, [7]
   describes a useful blinding technique that can be used to determine
   whether number is a quadratic residue modulo a prime in constant
   time.

6.  Security Considerations

   The "hunting and pecking" loop done in [3] leaked information on how
   many loops it took to determine the password element.  This allows an
   attacker to partition the dictionary by excluding possible passwords
   which would take a different number of loops.  After a frighteningly
   few such partitionings it becomes possible for the attacker to
   eliminate enough passwords to feasibly launch active attacks to learn
   the password.  [6] describes cache based attacks and timing attacks
   that are possible against [3].

   The Simplified SWU hash-to-curve method with the Brier construct
   allows for the password element to be derived in constant time which
   obviates these attacks.

   For implementations that cannot become completely constant time (due
   to, for instance, limitations in a crypto library) it is possible to
   limit timing attacks by generating the secret element from
   Section 2.1 and Section 2.2 when the password is provisioned and then
   generating the password element at run time.

7.  References

7.1.  Normative References

   [1]        Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997,
              <http://xml.resource.org/public/rfc/html/rfc2119.html>.

   [2]        Fax-Hernandez, A., Scott, S., Sullivan, N., Wahby, R., and
              C. Wood, "Hashing to Elliptic Curves", draft-irtf-cfrg-
              hash-to-curve A work in progress, July 2019.

   [3]        Harkins, D. and G. Zorn, "Extensible Authentication
              Protocol (EAP) Authentication Using Only a Password", RFC
              5931, August 2010.

   [4]        Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869, DOI 10.17487/
              RFC5869, May 2010,
              <http://www.rfc-editor.org/info/rfc5869>.




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7.2.  Informative References

   [5]        Brier, E., "Efficient Indifferentiable Hashing into
              Ordinary Elliptic Curves", Advances in Cryptology-- Crypto
              2010 Springer-Verlag, 2010.

   [6]        Vanhoef, M. and E. Ronen, "Dragonblood: A Security
              Analysis of WPA3's SAE Handshake", Cryptology ePrint
              Archive Report 2019, 2019.

   [7]        Harkins, D., Ed., "Dragonfly Key Exchange", RFC 7664, DOI
              10.17487/RFC7664, November 2015,
              <http://www.rfc-editor.org/info/rfc7664>.

Author's Address

   Dan Harkins
   Hewlett Packard Enterprise
   3333 Scott boulevard
   Santa Clara
   United States of America

   Email: dharkins@lounge.org




























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