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Versions: 00 01 02 03 04 05 06 rfc8236                     Informational
Network Working Group                                        F. Hao, Ed.
Internet-Draft                                 Newcastle University (UK)
Intended status: Informational                            April 26, 2017
Expires: October 28, 2017


        J-PAKE: Password Authenticated Key Exchange by Juggling
                           draft-hao-jpake-06

Abstract

   This document specifies a Password Authenticated Key Exchange by
   Juggling (J-PAKE) protocol.  This protocol allows the establishment
   of a secure end-to-end communication channel between two remote
   parties over an insecure network solely based on a shared password,
   without requiring a Public Key Infrastructure (PKI) or any trusted
   third party.

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
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   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 October 28, 2017.

Copyright Notice

   Copyright (c) 2017 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
   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




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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   3
     1.2.  Notations . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  J-PAKE over Finite Field  . . . . . . . . . . . . . . . . . .   4
     2.1.  Protocol Setup  . . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Two-Round Key Exchange  . . . . . . . . . . . . . . . . .   5
     2.3.  Computational Cost  . . . . . . . . . . . . . . . . . . .   6
   3.  J-PAKE over Elliptic Curve  . . . . . . . . . . . . . . . . .   7
     3.1.  Protocol Setup  . . . . . . . . . . . . . . . . . . . . .   7
     3.2.  Two-Round Key Exchange  . . . . . . . . . . . . . . . . .   7
     3.3.  Computational Cost  . . . . . . . . . . . . . . . . . . .   8
   4.  Three-Pass Variant  . . . . . . . . . . . . . . . . . . . . .   8
   5.  Key Confirmation  . . . . . . . . . . . . . . . . . . . . . .   9
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  11
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
   8.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  12
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  12
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  13
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  14
     9.3.  URIs  . . . . . . . . . . . . . . . . . . . . . . . . . .  15
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  15

1.  Introduction

   Password-Authenticated Key Exchange (PAKE) is a technique that aims
   to establish secure communication between two remote parties solely
   based on their shared password, without relying on a Public Key
   Infrastructure or any trusted third party [BM92].  The first PAKE
   protocol, called EKE, was proposed by Steven Bellovin and Michael
   Merrit in 1992 [BM92].  Other well-known PAKE protocols include SPEKE
   (by David Jablon in 1996) [Jab96] and SRP (by Tom Wu in 1998) [Wu98].
   SRP has been revised several times to address reported security and
   efficiency issues.  In particular, the version 6 of SRP, commonly
   known as SRP-6, is specified in [RFC5054].

   This document specifies a PAKE protocol called Password Authenticated
   Key Exchange by Juggling (J-PAKE), which was designed by Feng Hao and
   Peter Ryan in 2008 [HR08].

   There are a few factors that may be considered in favor of J-PAKE.
   First, J-PAKE has security proofs, while equivalent proofs are
   lacking in EKE, SPEKE and SRP-6.  Second, J-PAKE follows a completely
   different design approach from all other PAKE protocols, and is built



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   upon a well-established Zero Knowledge Proof (ZKP) primitive: Schnorr
   NIZK proof [SchnorrNIZK].  Third, J-PAKE adopts novel engineering
   techniques to optimize the use of ZKP so that overall the protocol is
   sufficiently efficient for practical use.  Fourth, J-PAKE is designed
   to work generically in both the finite field and elliptic curve
   settings (i.e., DSA and ECDSA-like groups respectively).  Unlike
   SPEKE, it does not require any extra primitive to hash passwords onto
   a designated elliptic curve.  Unlike SPAKE2 [AP05] and SESPAKE
   [SOAA15], it does not require a trusted setup (i.e., the so-called
   common reference model) to define a pair of generators whose discrete
   logarithm must be unknown.  Finally, J-PAKE has been used in real-
   world applications at a relatively large scale, e.g., Firefox sync
   [1], Pale moon sync [2] and Google Nest products [ABM15]; it has been
   included into widely distributed open source libraries such as
   OpenSSL [3], Network Security Services (NSS) [4] and the Bouncy
   Castle [5]; since 2015, it has been included into Thread [6] as a
   standard key agreement mechanism for IoT (Internet of Things)
   applications, and also included into ISO/IEC 11770-4 [7].

1.1.  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 [RFC2119].

1.2.  Notations

   The following notations are used in this document:

   o  Alice: the assumed identity of the prover in the protocol

   o  Bob: the assumed identity of the verifier in the protocol

   o  s: a low-entropy secret shared between Alice and Bob

   o  a | b: a divides b

   o  a || b: concatenation of a and b

   o  [a, b]: the interval of integers between and including a and b

   o  H: a secure cryptographic hash function

   o  p: a large prime

   o  q: a large prime divisor of p-1, i.e., q | p-1

   o  Zp*: a multiplicative group of integers modulo p



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   o  Gq: a subgroup of Zp* with prime order q

   o  g: a generator of Gq

   o  g^x: g raised to the power of x

   o  a mod b: a modulo b

   o  Fp: a finite field of p elements where p is a prime

   o  E(Fp): an elliptic curve defined over Fp

   o  G: a generator of the subgroup over E(Fp) with prime order n

   o  n: the order of G

   o  h: the cofactor of the subgroup generated by G, which is equal to
      the order of the elliptic curve divided by n

   o  P x [b]: multiplication of a point P with a scalar b over E(Fp)

   o  KDF(a): Key Derivation Function with input a

   o  MAC(MacKey, MacData): MAC function with MacKey as the key and
      MacData as the input data

2.  J-PAKE over Finite Field

2.1.  Protocol Setup

   When implemented over a finite field, J-PAKE may use the same group
   parameters as DSA [FIPS186-4].  Let p and q be two large primes such
   that q | p-1.  Let Gq denote a subgroup of Zp* with prime order q.
   Let g be a generator for Gq.  Any non-identity element in Gq can be a
   generator.  The two communicating parties, Alice and Bob, both agree
   on (p, q, g), which can be hard-wired in the software code.  They can
   also use the method in NIST FIPS 186-4, Appendix A [FIPS186-4] to
   generate (p, q, g).  Here DSA group parameters are used only as an
   example.  Other multiplicative groups suitable for cryptography can
   also be used for the implementation, e.g., groups defined in
   [RFC4419].  A group setting that provides 128-bit security or above
   is recommended.  The security proof of J-PAKE depends on the
   Decisional Diffie-Hellman (DDH) problem being intractable in the
   considered group.

   Let s be a secret value derived from a low-entropy password shared
   between Alice and Bob.  The value of s is required to fall within the
   range of [1, q-1].  (Note that s must not be 0 for any non-empty



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   secret.)  This range is defined as a necessary condition in [HR08]
   for proving the "on-line dictionary attack resistance", since s, s+q,
   s+2q, ..., are all considered equivalent values as far as the
   protocol specification is concerned.  In a practical implementation,
   one may obtain s by taking a cryptographic hash of the password and
   wrapping the result with respect to modulo q.  Alternatively, one may
   simply treat the password as an octet string and convert the string
   to an integer modulo q by following the method defined in
   Section 2.3.8 of [SEC1].  In either case, one must ensure s is not
   equal to 0 modulo q.

2.2.  Two-Round Key Exchange

   Round 1: Alice selects an ephemeral private key x1 uniformly at
   random from [0, q-1] and another ephemeral private key x2 uniformly
   at random from [1, q-1].  Similarly, Bob selects an ephemeral private
   key x3 uniformly at random from [0, q-1] and another ephemeral
   private key x4 uniformly at random from [1, q-1].

   o  Alice -> Bob: g1 = g^x1 mod p, g2 = g^x2 mod p and ZKPs for x1 and
      x2

   o  Bob -> Alice: g3 = g^x3 mod p, g4 = g^x4 mod p and ZKPs for x3 and
      x4

   In this round, the sender must send zero knowledge proofs to
   demonstrate the knowledge of the ephemeral private keys.  A suitable
   technique is to use the Schnorr NIZK proof [SchnorrNIZK].  As an
   example, suppose one wishes to prove the knowledge of the exponent
   for X = g^x mod p.  The generated Schnorr NIZK proof will contain:
   {UserID, V = g^v mod p, r = v - x * c mod q} where UserID is the
   unique identifier for the prover, v is a number chosen uniformly at
   random from [0, q-1] and c = H(g || V || X || UserID).  The
   "uniqueness" of UserID is defined from the user's perspective -- for
   example, if Alice communicates with several parties, she shall
   associate a unique identity with each party.  Upon receiving a
   Schnorr NIZK proof, Alice shall check the prover's UserID is a valid
   identity and is different from her own identity.  During the key
   exchange process using J-PAKE, each party shall ensure that the other
   party has been consistently using the same identity throughout the
   protocol execution.  Details about the Schnorr NIZK proof, including
   the generation and the verification procedures, can be found in
   [SchnorrNIZK].

   When this round finishes, Alice verifies the received ZKPs as
   specified in [SchnorrNIZK] and also checks that g4 != 1 mod p.
   Similarly, Bob verifies the received ZKPs and also checks that g2 !=




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   1 mod p.  If any of these checks fails, this session should be
   aborted.

   Round 2:

   o  Alice -> Bob: A = (g1*g3*g4)^(x2*s) mod p and a ZKP for x2*s

   o  Bob -> Alice: B = (g1*g2*g3)^(x4*s) mod p and a ZKP for x4*s

   In this round, the Schnorr NIZK proof is computed in the same way as
   in the previous round except that the generator is different.  For
   Alice, the generator used is (g1*g3*g4) instead of g; for Bob, the
   generator is (g1*g2*g3) instead of g.  Since any non-identity element
   in Gq can be used as a generator, Alice and Bob just need to ensure
   g1*g3*g4 != 1 mod p and g1*g2*g3 != 1 mod p.  With overwhelming
   probability, these inequalities are statistically guaranteed even
   when the user is communicating with an adversary (i.e., in an active
   attack).  Nonetheless, for absolute guarantee, the receiving party
   shall explicitly check if these inequalities hold, and abort the
   session in case such a check fails.

   When the second round finishes, Alice and Bob verify the received
   ZKPs.  If the verification fails, the session is aborted.  Otherwise,
   the two parties compute the common key material as follows:

   o  Alice computes Ka = (B/g4^(x2*s))^x2 mod p

   o  Bob computes Kb = (A/g2^(x4*s))^x4 mod p

   Here Ka = Kb = g^((x1+x3)*x2*x4*s) mod p.  Let K denote the same key
   material held by both parties.  Using K as input, Alice and Bob then
   apply a Key Derivation Function (KDF) to derive a common session key
   k.  If the subsequent secure communication uses a symmetric cipher in
   an authenticated mode (say AES-GCM), then one key is sufficient,
   i.e., k = KDF(K).  Otherwise, the session key should comprise an
   encryption key (for confidentiality) and a MAC key (for integrity),
   i.e., k = k_enc || k_mac, where k_enc = KDF(K || "JPAKE_ENC") and
   k_mac = KDF(K || "JPAKE_MAC").  The exact choice of the KDF is left
   to specific applications to define.

2.3.  Computational Cost

   The computational cost is estimated based on counting the number of
   modular exponentiations since they are the predominant cost factors.
   Note that it takes one exponentiation to generate a Schnorr NIZK
   proof and two to verify it [SchnorrNIZK].  For Alice, she needs to
   perform 8 exponentiations in the first round, 4 in the second round,
   and 2 in the final computation of the session key.  Hence, that is 14



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   modular exponentiations in total.  Based on the symmetry, the
   computational cost for Bob is exactly the same.

3.  J-PAKE over Elliptic Curve

3.1.  Protocol Setup

   The J-PAKE protocol works basically the same in the elliptic curve
   (EC) setting, except that the underlying multiplicative group over a
   finite field is replaced by an additive group over an elliptic curve.
   Nonetheless, the EC version of J-PAKE is specified here for
   completeness.

   When implemented over an elliptic curve, J-PAKE may use the same EC
   parameters as ECDSA [FIPS186-4].  The FIPS 186-4 standard [FIPS186-4]
   defines three types of curves suitable for ECDSA: pseudo-random
   curves over prime fields, pseudo-random curves over binary fields and
   special curves over binary fields called Koblitz curves or anomalous
   binary curves.  All these curves that are suitable for ECDSAA can
   also be used to implement J-PAKE.  However, for the illustration
   purpose, only curves over prime fields are described in this
   document.  Typically, such curves include NIST P-256, P-384 and
   P-521.  When choosing a curve, a level of 128-bit security or above
   is recommended.  Let E(Fp) be an elliptic curve defined over a finite
   field Fp where p is a large prime.  Let G be a generator for the
   subgroup over E(Fp) of prime order n.  Here the NIST curves are used
   only as an example.  Other secure curves such as Curve25519 are also
   suitable for the implementation.  The security proof of J-PAKE relies
   on the assumption that the DDH problem is intractable in the
   considered group.

   As before, let s denote the shared secret between Alice and Bob. The
   value of s falls within [1, n-1].  In particular, note that s must
   not be equal to 0 mod n.

3.2.  Two-Round Key Exchange

   Round 1: Alice selects ephemeral private keys x1 and x2 uniformly at
   random from [1, n-1].  Similarly, Bob selects ephemeral private keys
   x3 and x4 uniformly at random from [1, n-1].

   o  Alice -> Bob: G1 = G x [x1], G2 = G x [x2] and ZKPs for x1 and x2

   o  Bob -> Alice: G3 = G x [x3], G4 = G x [x4] and ZKPs for x3 and x4

   When this round finishes, Alice and Bob verify the received ZKPs as
   specified in [SchnorrNIZK].  As an example, to prove the knowledge of
   the discrete logarithm of X = G x [x] with respect to the base point



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   G, the ZKP contains: {UserID, V = G x [v], r = v - x * c mod n} where
   UserID is the unique identifier for the prover, v is a number chosen
   uniformly at random from [1, n-1] and c = H(G || V || X || UserID).
   The verifier shall check the prover's UserID is a valid identity and
   is different from its own identity.  If the verification of the ZKP
   fails, the session is aborted.

   Round 2:

   o  Alice -> Bob: A = (G1 + G3 + G4) x [x2*s] and a ZKP for x2*s

   o  Bob -> Alice: B = (G1 + G2 + G3) x [x4*s] and a ZKP for x4*s

   When the second round finishes, Alice and Bob verify the received
   ZKPs.  The ZKPs are computed in the same way as in the previous round
   except that the generator is different.  For Alice, the new generator
   is G1 + G3 + G4; for Bob, it is G1 + G2 + G3.  Alice and Bob shall
   check that these new generators are not points at infinity.  If any
   of these checks fails, the session is aborted.  Otherwise, the two
   parties compute the common key material as follows:

   o  Alice computes Ka = (B - (G4 x [x2*s])) x [x2]

   o  Bob computes Kb = (A - (G2 x [x4*s])) x [x4]

   Here Ka = Kb = G x [(x1+x3)*(x2*x4*s)].  Let K denote the same key
   material held by both parties.  Using K as input, Alice and Bob then
   apply a Key Derivation Function (KDF) to derive a common session key
   k.

3.3.  Computational Cost

   In the EC setting, the computational cost of J-PAKE is estimated
   based on counting the number of scalar multiplications over the
   elliptic curve.  Note that it takes one multiplication to generate a
   Schnorr NIZK proof and one to verify it [SchnorrNIZK].  For Alice,
   she has to perform 6 multiplications in the first round, 3 in the
   second round, and 2 in the final computation of the session key.
   Hence, that is 11 multiplications in total.  Based on the symmetry,
   the computational cost for Bob is exactly the same.

4.  Three-Pass Variant

   The two-round J-PAKE protocol is completely symmetric, which
   significantly simplifies the security analysis.  In practice, one
   party normally initiates the communication and the other party
   responds.  In that case, the protocol will be completed in three
   passes instead of two rounds.  The two-round J-PAKE protocol can be



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   trivially changed to three passes without losing security.  Take the
   finite field setting as an example and assume Alice initiates the key
   exchange.  The three-pass variant works as follows:

   1.  Alice -> Bob: g1 = g^x1 mod p, g2 = g^x2 mod p, ZKPs for x1 and
       x2.

   2.  Bob -> Alice: g3 = g^x3 mod p, g4 = g^x4 mod p, B =
       (g1*g2*g3)^(x4*s) mod p, ZKPs for x3, x4, and x4*s.

   3.  Alice -> Bob: A = (g1*g3*g4)^(x2*s) mod p and a ZKP for x2*s.

   Both parties compute the session keys in exactly the same way as
   before.

5.  Key Confirmation

   The two-round J-PAKE protocol (or the three-pass variant) provides
   cryptographic guarantee that only the authenticated party who used
   the same password at the other end is able to compute the same
   session key.  So far the authentication is only implicit.  The key
   confirmation is also implicit [Stinson06].  The two parties may use
   the derived key straight-away to start secure communication by
   encrypting messages in an authenticated mode.  Only the party with
   the same derived session key will be able to decrypt and read those
   messages.

   For achieving explicit authentication, an additional key confirmation
   procedure should be performed.  This provides explicit assurance that
   the other party has actually derived the same key.  In this case, the
   key confirmation is explicit [Stinson06].

   In J-PAKE, explicit key confirmation is recommended whenever the
   network bandwidth allows it.  It has the benefit of providing
   explicit and immediate confirmation if the two parties have derived
   the same key and hence are authenticated to each other.  This allows
   a practical implementation of J-PAKE to effectively detect online
   dictionary attacks (if any), and stop them accordingly by setting a
   threshold for the consecutively failed connection attempts.

   To achieve explicit key confirmation, there are several methods
   available.  They are generically applicable to all key exchange
   protocols, not just J-PAKE.  In general, it is recommended to use a
   different key from the session key for key confirmation, say using k'
   = KDF(K || "JPAKE_KC").  The advantage of using a different key for
   key confirmation is that the session key remains indistinguishable
   from random after the key confirmation process (although this




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   perceived advantage is actually subtle and only theoretical).  Two
   explicit key confirmation methods are presented here.

   The first method is based on the one used in the SPEKE protocol
   [Jab96].  Suppose Alice initiates the key confirmation.  Alice sends
   to Bob H(H(k')), which Bob will verify.  If the verification is
   successful, Bob sends back to Alice H(k'), which Alice will verify.
   This key confirmation procedure needs to be completed in two rounds,
   as shown below.

   1.  Alice -> Bob: H(H(k'))

   2.  Bob -> Alice: H(k')

   The above procedure requires two rounds instead of one, because the
   second message depends on the first.  If both parties attempt to send
   the first message at the same time without an agreed order, they
   cannot tell if the message that they receive is a genuine challenge
   or a replayed message, and consequently may enter a deadlock.

   The second method is based on the unilateral key confirmation scheme
   specified in NIST SP 800-56A Revision 1 [BJS07].  Alice and Bob send
   to each other a MAC tag, which they will verify accordingly.  This
   key confirmation procedure can be completed in one round.

   In the finite field setting it works as follows.

   o  Alice -> Bob: MacTagAlice = MAC(k', "KC_1_U" || Alice || Bob ||
      g1 || g2 || g3 || g4)

   o  Bob -> Alice: MacTagBob = MAC(k', "KC_1_U" || Bob || Alice ||
      g3 || g4 || g1 || g2)

   In the EC setting, the key confirmation works basically the same.

   o  Alice -> Bob: MacTagAlice = MAC(k', "KC_1_U" || Alice || Bob ||
      G1 || G2 || G3 || G4)

   o  Bob -> Alice: MacTagBob = MAC(k', "KC_1_U" || Bob || Alice ||
      G3 || G4 || G1 || G2)

   The second method assumes an additional secure MAC function (e.g.,
   one may use HMAC) and is slightly more complex than the first method.
   However, it can be completed within one round and it preserves the
   overall symmetry of the protocol implementation.  For this reason,
   the second method is recommended.





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6.  Security Considerations

   A PAKE protocol is designed to provide two functions in one protocol
   execution.  The first one is to provide zero-knowledge authentication
   of a password.  It is called "zero knowledge" because at the end of
   the protocol, the two communicating parties will learn nothing more
   than one bit information: whether the passwords supplied at two ends
   are equal.  Therefore, a PAKE protocol is naturally resistant against
   phishing attacks.  The second function is to provide session key
   establishment if the two passwords are equal.  The session key will
   be used to protect the confidentiality and integrity of the
   subsequent communication.

   More concretely, a secure PAKE protocol shall satisfy the following
   security requirements [HR10].

   1.  Off-line dictionary attack resistance: It does not leak any
       information that allows a passive/active attacker to perform off-
       line exhaustive search of the password.

   2.  Forward secrecy: It produces session keys that remain secure even
       when the password is later disclosed.

   3.  Known-key security: It prevents a disclosed session key from
       affecting the security of other sessions.

   4.  On-line dictionary attack resistance: It limits an active
       attacker to test only one password per protocol execution.

   First, a PAKE protocol must resist off-line dictionary attacks.  A
   password is inherently weak.  Typically, it has only about 20-30 bits
   entropy.  This level of security is subject to exhaustive search.
   Therefore, in the PAKE protocol, the communication must not reveal
   any data that allows an attacker to learn the password through off-
   line exhaustive search.

   Second, a PAKE protocol must provide forward secrecy.  The key
   exchange is authenticated based on a shared password.  However, there
   is no guarantee on the long-term secrecy of the password.  A secure
   PAKE scheme shall protect past session keys even when the password is
   later disclosed.  This property also implies that if an attacker
   knows the password but only passively observes the key exchange, he
   cannot learn the session key.

   Third, a PAKE protocol must provide known key security.  A session
   key lasts throughout the session.  An exposed session key must not
   cause any global impact on the system, affecting the security of
   other sessions.



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   Finally, a PAKE protocol must resist on-line dictionary attacks.  If
   the attacker is directly engaging in the key exchange, there is no
   way to prevent such an attacker trying a random guess of the
   password.  However, a secure PAKE scheme should mitigate the effect
   of the on-line attack to the minimum.  In the best case, the attacker
   can only guess exactly one password per impersonation attempt.
   Consecutively failed attempts can be easily detected and the
   subsequent attempts shall be thwarted accordingly.  It is recommended
   that the false authentication counter should be handled in such a way
   that any error (which causes the session to fail during the key
   exchange or key confirmation) would lead to incrementing the false
   authentication counter.

   It has been proven in [HR10] that J-PAKE satisfies all of the four
   requirements based on the assumptions that the Decisional Diffie-
   Hellman problem is intractable and the underlying Schnorr NIZK proof
   is secure.  An independent study that proves security of J-PAKE in a
   model with algebraic adversaries and random oracles can be found in
   [ABM15].  By comparison, it has been known that EKE has the problem
   of leaking partial information about the password to a passive
   attacker, hence not satisfying the first requirement [Jas96].  For
   SPEKE and SRP-6, an attacker may be able to test more than one
   password in one on-line dictionary attack (see [Zha04] and [Hao10]),
   hence they do not satisfy the fourth requirement in the strict
   theoretical sense.  Furthermore, SPEKE is found vulnerable to an
   impersonation attack and a key-malleability attack [HS14].  These two
   attacks affect the SPEKE protocol specified in Jablon's original 1996
   paper [Jab96] as well in the D26 draft of IEEE P1363.2 and the latest
   published ISO/IEC 11770-4:2006 standard.  As a result, the
   specification of SPEKE in ISO/IEC 11770-4:2006 has been revised to
   address the identified problems.

7.  IANA Considerations

   This document has no actions for IANA.

8.  Acknowledgements

   The editor would like to thank Dylan Clarke, Siamak Shahandashti,
   Robert Cragie, Stanislav Smyshlyaev and Russ Housley for many useful
   comments.  This work is supported by EPSRC First Grant (EP/J011541/1)
   and ERC Starting Grant (No. 306994).

9.  References







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9.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

   [RFC5054]  Taylor, D., Wu, T., Mavrogiannopoulos, N., and T. Perrin,
              "Using the Secure Remote Password (SRP) Protocol for TLS
              Authentication", RFC 5054, DOI 10.17487/RFC5054, November
              2007, <http://www.rfc-editor.org/info/rfc5054>.

   [SEC1]     "Standards for Efficient Cryptography. SEC 1: Elliptic
              Curve Cryptography",  SECG SEC1-v2, May 2004,
              <http://www.secg.org/sec1-v2.pdf>.

   [ABM15]    Abdalla, M., Benhamouda, F., and P. MacKenzie, "Security
              of the J-PAKE Password-Authenticated Key Exchange
              Protocol",  IEEE Symposium on Security and Privacy, May
              2015.

   [BM92]     Bellovin, S. and M. Merrit, "Encrypted Key Exchange:
              Password-based Protocols Secure against Dictionary
              Attacks",  IEEE Symposium on Security and Privacy, May
              1992.

   [HR08]     Hao, F. and P. Ryan, "Password Authenticated Key Exchange
              by Juggling",  16th Workshop on Security Protocols
              (SPW'08), May 2008.

   [HR10]     Hao, F. and P. Ryan, "J-PAKE: Authenticated Key Exchange
              Without PKI",  Springer Transactions on Computational
              Science XI, 2010.

   [HS14]     Hao, F. and S. Shahandashti, "The SPEKE Protocol
              Revisited",  Security Standardisation Research, December
              2014.

   [Jab96]    Jablon, D., "Strong Password-Only Authenticated Key
              Exchange",  ACM Computer Communications Review, October
              1996.

   [Stinson06]
              Stinson, D., "Cryptography: Theory and Practice (3rd
              Edition)",  CRC, 2006.

   [Wu98]     Wu, T., "The Secure Remote Password protocol",  Symposimum
              on Network and Distributed System Security, March 1998.



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   [SchnorrNIZK]
              Hao, F., "Schnorr NIZK proof: Non-interactive Zero
              Knowledge Proof for Discrete Logarithm",  IETF Internet
              Draft-06 (work in progress), 2017,
              <https://datatracker.ietf.org/doc/draft-hao-schnorr/>.

9.2.  Informative References

   [RFC4419]  Friedl, M., Provos, N., and W. Simpson, "Diffie-Hellman
              Group Exchange for the Secure Shell (SSH) Transport Layer
              Protocol", RFC 4419, DOI 10.17487/RFC4419, March 2006,
              <http://www.rfc-editor.org/info/rfc4419>.

   [BJS07]    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>.

   [Jas96]    Jaspan, B., "Dual-Workfactor Encrypted Key Exchange:
              Efficiently Preventing Password Chaining and Dictionary
              Attacks",  USENIX Symphosium on Security, July 1996.

   [Zha04]    Zhang, M., "Analysis of The SPEKE Password-Authenticated
              Key Exchange Protocol",  IEEE Communications Letters,
              January 2004.

   [Hao10]    Hao, F., "On Small Subgroup Non-Confinement Attacks",
               IEEE conference on Computer and Information Technology,
              2010.

   [AP05]     Abdalla, M. and D. Pointcheval, "Simple Password-Based
              Encrypted Key Exchange Protocols",  Topics in Cryptology -
              CT-RSA, 2005.

   [FIPS186-4]
              "Federal Information Processing Standards Publication
              186-4: Specifications for the Digital Signature Standard
              (DSS)", July 2013, <http://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.186-4.pdf>.

   [SOAA15]   Smyshlyaev, S., Oshkin, I., Alekseev, E., and L.
              Ahmetzyanova, "On the Security of One Password
              Authenticated Key Exchange Protocol", 2015,
              <http://eprint.iacr.org/2015/1237.pdf>.





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9.3.  URIs

   [1] https://wiki.mozilla.org/Services/Sync/SyncKey/J-PAKE

   [2] https://www.palemoon.org/sync/

   [3] http://boinc.berkeley.edu/android-boinc/libssl/crypto/jpake/

   [4] https://dxr.mozilla.org/mozilla-
       central/source/security/nss/lib/freebl/jpake.c

   [5] https://www.bouncycastle.org/docs/docs1.5on/org/bouncycastle/cryp
       to/agreement/jpake/package-summary.html

   [6] http://threadgroup.org/Portals/0/documents/whitepapers/
       Thread%20Commissioning%20white%20paper_v2_public.pdf

   [7] https://www.iso.org/standard/67933.html

Author's Address

   Feng Hao (editor)
   Newcastle University (UK)
   Claremont Tower, School of Computing Science, Newcastle University
   Newcastle Upon Tyne
   United Kingdom

   Phone: +44 (0)191-208-6384
   EMail: feng.hao@ncl.ac.uk






















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