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Requirements for Password-Authenticated Key Agreement (PAKE) Schemes

The information below is for an old version of the document that is already published as an RFC.
Document Type
This is an older version of an Internet-Draft that was ultimately published as RFC 8125.
Author Joern-Marc Schmidt
Last updated 2017-04-19 (Latest revision 2017-02-08)
RFC stream Internet Research Task Force (IRTF)
Intended RFC status Informational
IETF conflict review conflict-review-irtf-cfrg-pake-reqs
Additional resources Mailing list discussion
Stream IRTF state Published RFC
Consensus boilerplate Yes
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IESG IESG state Became RFC 8125 (Informational)
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IANA IANA review state Version Changed - Review Needed
IANA action state No IANA Actions
Internet Research Task Force                                  J. Schmidt
Internet-Draft                                 secunet Security Networks
Intended status: Informational                          February 8, 2017
Expires: August 12, 2017

                     Requirements for PAKE schemes


   Password-Authenticated Key Agreement (PAKE) schemes are interactive
   protocols that allow the participants to authenticate each other and
   derive shared cryptographic keys using a (weaker) shared password.
   This document reviews different types of PAKE schemes.  Furthermore,
   it presents requirements and gives recommendations to designers of
   new schemes.  It is a product of the Crypto Forum Research Group

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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   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on August 12, 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
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   ( 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.  Requirements notation . . . . . . . . . . . . . . . . . . . .   2
   2.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   3.  PAKE Taxonomy . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.1.  Storage of the Password . . . . . . . . . . . . . . . . .   3
     3.2.  Transmission of Public Keys . . . . . . . . . . . . . . .   4
     3.3.  Two Party versus Multiparty . . . . . . . . . . . . . . .   4
   4.  Security of PAKEs . . . . . . . . . . . . . . . . . . . . . .   5
     4.1.  Implementation Aspects  . . . . . . . . . . . . . . . . .   6
     4.2.  Special case: Elliptic Curves . . . . . . . . . . . . . .   6
   5.  Protocol Considerations and Applications  . . . . . . . . . .   6
   6.  Privacy . . . . . . . . . . . . . . . . . . . . . . . . . . .   7
   7.  Performance . . . . . . . . . . . . . . . . . . . . . . . . .   8
   8.  Requirements  . . . . . . . . . . . . . . . . . . . . . . . .   8
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   9
   10. Security Considerations . . . . . . . . . . . . . . . . . . .   9
   11. References  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     11.1.  Normative References . . . . . . . . . . . . . . . . . .   9
     11.2.  Informative References . . . . . . . . . . . . . . . . .   9
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  10

1.  Requirements notation

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in [RFC2119].

2.  Introduction

   Passwords are the predominant method of accessing the Internet today
   due, in large part, to their intuitiveness and ease of use.  Since a
   user needs to enter passwords repeatedly in many connections and
   applications, these passwords tend to be easy to remember and be able
   to be entered repeatedly with a low probability of error.  They tend
   to be low-grade and not-so-random secrets that are susceptible to
   brute-force guessing attacks.

   A Password-Authenticated Key Exchange (PAKE) attempts to address this
   issue by constructing a cryptographic key exchange that does not
   result in the password, or password-derived data, being transmitted
   across an unsecured channel.  Two parties in the exchange prove
   possession of the shared password without revealing it.  Such
   exchanges are therefore resistant to off-line, brute-force dictionary
   attacks.  The idea was initially described by Bellovin and Merritt in

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   [BM92] and has received considerable cryptographic attention since
   then.  PAKEs are especially interesting due to the fact that they can
   achieve mutual authentication without requiring any Public Key
   Infrastructure (PKI).

   Different types of PAKE schemes are reviewed in this document.  It
   defines requirements for new schemes and gives additional
   recommendations for designers of PAKE schemes.  The specific
   recommendations are discussed throughout Section 3 till Section 7.
   Section 8 summarizes the requirements.

   This document represents the consensus of the Crypto Forum Research
   Group (CFRG).

3.  PAKE Taxonomy

   Broadly speaking, different PAKEs satisfy their goals in a number of
   common ways.  This leads to various design choices: how public keys
   are transmitted (encrypted or not), whether both parties possess the
   same representation of the password (balanced versus augmented) and
   the number of parties (two party versus multiparty).

3.1.  Storage of the Password

   When both sides of a PAKE store the same representation of the
   password, the PAKE is said to be "balanced".  In a balanced PAKE the
   password can be stored directly, in a salted state by hashing it with
   a random salt, or by representing the credential as an element in a
   finite field (by, for instance, multiplying a generator from a finite
   field and the password represented as a number to produce a "password
   element").  The benefits of such PAKEs are that they are applicable
   to situations where either party can initiate the exchange or both
   parties can initiate simultaneously, i.e. where they both believe
   themselves to be the "initiator".  This sort of PAKE can be useful
   for mesh networking (see, for example, [DOT11]) or Internet-of-Things

   When one side maintains a transform of the password and the other
   maintains the raw password, the PAKE is said to be "augmented".
   Typically, a client will maintain the raw password (or some
   representation of it as in the balanced case), and a server will
   maintain a transformed element generated with a one-way function.
   The benefit of an augmented PAKE is that it provides some protection
   for the server's password in a way that is not possible with a
   balanced PAKE.  In particular, an adversary that has successfully
   obtained the server's PAKE credentials cannot directly use them to
   impersonate the users to other servers.  The adversary has to learn
   the individual passwords first, e.g. by performing an (offline)

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   dictionary attack.  This sort of PAKE is useful for strict client-
   server protocols such as the one discussed in [RFC5246].

3.2.  Transmission of Public Keys

   All known PAKEs use public key cryptography.  A fundamental
   difference in PAKEs is how the public key is communicated in the

   One class of PAKEs uses symmetric key cryptography, with a key
   derived from the password, to encrypt an ephemeral public key.  The
   ability of the peer to demonstrate it has successfully decrypted the
   public key proves knowledge of the shared password.  Examples of this
   exchange include the first PAKE called the Encrypted Key Exchange
   (EKE) which was introduced in [BM92].

   Another class of PAKEs transmits unencrypted public keys, like the
   J-PAKE protocol [JPAKE].  During key agreement, ephemeral public keys
   and values derived using the shared password are exchanged.  In the
   case that the passwords match both parties can compute a common
   secret by combining password, public keys and private keys.  The
   SPEKE [SPEKE] scheme also exchanges public keys, namely Diffie-
   Hellman values.  Here, the generator for the public keys is derived
   from the shared secret.  Afterwards, only the public Diffie-Hellman
   values are exchanged, the generator is kept secret.  In both cases,
   the values that are transmitted across the unsecured medium is an
   element in a finite field and not a random blob.

   A combination of the EKE and SPEKE is used in PACE as described in
   [BFK09], which is e.g. used in international travel documents.  In
   this method a nonce is encrypted rather than a key.  This nonce is
   used to generate a common base for the key agreement.  Without
   knowing the password, the nonce cannot be determined and hence, the
   subsequent key agreement will fail.

3.3.  Two Party versus Multiparty

   The majority of PAKE protocols allow two parties to agree on a shared
   key based on a shared password.  Nevertheless, there exist proposals
   that allow key agreement for more than two parties.  Those protocols
   allow key establishment for a group of parties and are hence called
   Group PAKEs or GPAKEs.  Examples of such protocols can be found in
   [ABCP06], while [ACGP11] and [HYCS15] propose a generic construction
   that allows the transformation of any two-party PAKE into a GPAKE
   protocol.  Another possibility of defining a multi-party PAKE
   protocol is to assume the existence of a trusted server with which
   each party shares a password.  This server enables different parties
   to agree on a common secret key without the need to share a password

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   among each other.  Each party has only a shared secret with the
   trusted server.  For example, Abdalla et al. designed such a protocol
   as discussed in [AFP05].

4.  Security of PAKEs

   PAKE schemes are modelled on the scenario of two parties, typically
   Alice and Bob, who share a password (or perhaps Bob shares a function
   of the password) and would like to use it to establish a secure
   session key over an untrusted link.  There is a powerful adversary,
   typically Eve, who would like to subvert the exchange.  Eve has
   access to a dictionary that is likely to contain Alice and Bob's
   password, and Eve is capable of enumerating through the dictionary in
   a brute-force manner to try and discover Alice and Bob's password.

   All PAKEs have a limitation.  If Eve guesses the password, she can
   subvert the exchange.  It is therefore necessary to model likelihood
   that Eve will guess the password to access the security of a PAKE.
   If the probability of her discovering the password is a function of
   interaction with the protocol participants and not a function of
   computation, then the PAKE is secure.  That is, if Eve is unable to
   take information from a passive attack or from a single active
   attack.  Thus, she cannot enumerate through her dictionary without
   interacting with Alice or Bob for each password guess, i.e. the only
   attack left is repeated guessing.  Eve learns one thing from a single
   active attack: whether her single guess is correct or not.

   In other words, the security of a PAKE scheme is based on the idea
   that Eve, who is trying to impersonate Alice, cannot efficiently
   verify a password guess without interacting with Bob (or Alice).  If
   she were to interact with either, she would thereby be detected.
   Thus, it is to balance restricting the number of allowed
   authentication attempts with the potential of a denial-of-service
   vulnerability.  In order to judge and compare the security of PAKE
   schemes, security proofs in commonly accepted models SHOULD be used.
   Each proof and model, however, is based on assumptions.  Often
   security proofs show that if an adversary is able to break the
   scheme, the adversary is also able to solve a problem that is assumed
   to be hard such as computing a discrete logarithm.  By conversion,
   breaking the scheme is considered to be a hard problem as well.

   A PAKE scheme SHOULD be accompanied with a security proof with
   clearly stated assumptions and models used.  In particular, the proof
   MUST show that the probability is negligible that an active adversary
   would be able to pass authentication, learn additional information
   about the password or learn anything about the established key.
   Moreover, the authors MAY specify which underlying primitives are to
   be used with the scheme or MAY consider specific use cases or

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   assumptions like resistance to quantum computers.  A clear and
   comprehensive proof is the foundation for users to trust in the
   security of the scheme.

4.1.  Implementation Aspects

   Aside from the theoretical security of a scheme, practical
   implementation pitfalls have to be considered as well.  If not
   carefully implemented, even a scheme that is secure in a well-defined
   mathematical model can leak information via side-channels.  The
   design of the scheme might allow or prevent easy protection against
   information leakage.  In a network scenario, an adversary can measure
   the time the computation of an answer takes and derive information
   about secret parameters of the scheme.  If a device operates in a
   potentially hostile environment, such as a smart card, other side-
   channels like power consumption and electromagnetic emanations or
   even active implementation attacks have to be taken into account as

   The developers of a scheme SHOULD keep the implementation aspects in
   mind and show how to implement the protocol in constant time.
   Furthermore, adding a discussion about how to protect implementations
   of the scheme in potential hostile environments is encouraged.

4.2.  Special case: Elliptic Curves

   Since Elliptic Curve Cryptography (ECC) allows for a smaller key-
   length compared to traditional schemes based on the discrete
   logarithm problem in finite fields at similar security levels, using
   ECC for PAKE schemes is also of interest.  In contrast to schemes
   that can use the finite field element directly, an additional
   challenge has to be considered for some schemes based on ECC, namely
   the mapping of a random string to an element that can be computed
   with, i.e. a point on the curve.  In some cases, also the opposite is
   needed, i.e. the mapping of a curve point to a string that is not
   distinguishable from a random one.  When choosing a mapping, it is
   crucial to consider the implementation aspects as well.

   In the case that the PAKE scheme is intended to be used with ECC, the
   authors SHOULD state whether there is a mapping function needed, and
   if so, discuss its requirements.  Alternatively, the authors MAY
   define a mapping to be used with the scheme.

5.  Protocol Considerations and Applications

   In most cases, the PAKE scheme is a building block in a more complex
   protocol like IPsec or TLS.  This can influence the choice of a
   suitable PAKE scheme.  For example, an augmented scheme can be

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   beneficial for protocols that have a strict server-client
   relationship.  In the case that both parties can initiate a
   connection of a protocol, a balanced PAKE might be more appropriate.

   A special variation of the network password problem, called Password
   Authenticated Key Distribution, is defined in [P1363] as password
   authenticated key retrieval: "The retrieval of a key from a secure
   key repository or escrow requiring authentication derived in part
   from a password."

   In addition to key retrieval from escrow, there is also the variant
   of two parties exchanging public keys using a PAKE in lieu of
   certificates.  In this variant, public keys can be encrypted using a
   password.  Authentication key distribution can be performed because
   each side knows the private key associated with its unencrypted
   public key and can also decrypt the peer's public key.  This
   technique can be used to transform a short, one-time code into a
   long-term public key.

   Another possible variant of a PAKE scheme allows combining
   authentication with certificates and the use of passwords.  In this
   variant, the private key of the certificate is used to blind the
   password key agreement.  For verification, the message is unblinded
   with the public key.  A correct key establishment therefore implies
   the possession of the private key belonging to the certificate.  This
   method enables one-sided authentication as well as mutual
   authentication when the password is used.

   The authors of a PAKE scheme MAY discuss variations of their scheme
   and explain application scenarios where these variations are
   beneficial.  In particular, techniques that allow long-term (public)
   key agreement are encouraged.

6.  Privacy

   In order to establish a connection, each party of the PAKE protocol
   needs to know the identity of its communication partner to identify
   the right password for the agreement.  In cases where a user wants to
   establish a secure channel with a server, the user first has to let
   the server know which password to use by sending some kind of
   identifier to the server.  If this identifier is not protected,
   everyone who is able to eavesdrop on the connection can identify the
   user.  In order to prevent this and protect the privacy of the user,
   the scheme might provide a way to protect the transmission of the
   user's identity.  A simple way to achieve privacy of a user that
   communicates with a server is to use a public key provided by the
   server to encrypt the user's identity.

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   The PAKE scheme MAY discuss special ideas and solutions how to
   protect the privacy of the users of the scheme.

7.  Performance

   The performance of a scheme can be judged along different lines
   depending on the optimization goals of the target application.
   Potential metrics include latency, code-size/area, power consumption,
   or exchanged messages.  In addition, there might be application
   scenarios in which a constrained client communicates with a powerful
   server.  In such a case, the scheme has to require minimal efforts on
   the client side.  Note that for some clients the computations might
   even be carried out in a hardware implementation, which require
   different optimizations compared to software.

   Furthermore, the design of the scheme can influence the cost of
   protecting the implementation from adversaries exploiting its
   physical properties (see Section 4.1).

   The authors of a PAKE scheme MAY discuss their design choices and the
   influence of these choices on the performance.  In particular, the
   optimization goals could be stated.

8.  Requirements

   This section summarizes the requirements for PAKE schemes to be
   compliant with this document based on the previous discussed

      R1: A PAKE scheme MUST clearly state its features regarding
      balanced/augmented versions.

      R2: A PAKE scheme SHOULD come with a security proof and clearly
      state its assumptions and models.

      R3: The authors SHOULD show how to protect their PAKE scheme
      implementation in hostile environments, particularly, how to
      implement their scheme in constant time to prevent timing attacks.

      R4: In the case that the PAKE scheme is intended to be used with
      ECC, the authors SHOULD discuss their requirements for a potential
      mapping or define a mapping to be used with the scheme.

      R5: The authors of a PAKE scheme MAY discuss its design choice
      with regard to performance, i.e., its optimization goals.

      R6: The authors of a scheme MAY discuss variations of their scheme
      that allows the use in special application scenarios.  In

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      particular, techniques that facilitate long-term (public) key
      agreement are encouraged.

      R7: Authors of a scheme MAY discuss special ideas and solutions on
      privacy protection of its users.

      R8: The authors MUST follow the IRTF IPR policy <

9.  IANA Considerations

   This document makes no request of IANA.

10.  Security Considerations

   This document analyses requirements for a cryptographic scheme.
   Security considerations are discussed throughout the document.

11.  References

11.1.  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,

11.2.  Informative References

   [ABCP06]   Abdalla, M., Bresson, E., Chevassut, O., and D.
              Pointcheval, "Password-Based Group Key Exchange in a
              Constant Number of Rounds", PKC 2006, LNCS 3958, 2006.

   [ACGP11]   Abdalla, M., Chevalier, C., Granboulan, L., and D.
              Pointcheval, "Contributory Password-Authenticated Group
              Key Exchange with Join Capability", CT-RSA 2011,
              LNCS 6558, 2011.

   [AFP05]    Abdalla, M., Fouque, P., and D. Pointcheval, "Password-
              based authenticated key exchange in the three-party
              setting", PKC 2005, LNCS 3386, 2005.

   [BFK09]    Bender, J., Fischlin, M., and D. Kuegler, "Security
              Analysis of the PACE Key-Agreement Protocol", ISC 2009,
              LNCS 5735, 2009.

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

   [DOT11]    IEEE Computer Society, "Telecommunications and information
              exchange between systems Local and metropolitan area
              networks", Part 11: Wireless LAN Medium Access Control
              (MAC) and Physical Layer (PHY) Specifications IEEE Std
              802.11-2012, 2012.

   [HYCS15]   Hao, F., Yi, X., Chen, L., and S. Shahandashti, "The
              Fairy-Ring Dance: Password Authenticated Key Exchange in a
              Group", IoTPTS 2015, ACM , 2015.

   [JPAKE]    Hao, F. and P. Ryan, "Password Authenticated Key Exchange
              by Juggling", SP 2008, LNCS 6615, 2008.

   [P1363]    IEEE Microprocessor Standards Committee, "Draft Standard
              for Specifications for Password-based Public Key
              Cryptographic Techniques", IEEE P1363.2, 2006.

   [RFC5246]  Dierks, T. and E. Rescorla, "The Transport Layer Security
              (TLS) Protocol Version 1.2", RFC 5246,
              DOI 10.17487/RFC5246, August 2008,

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

Author's Address

   Joern-Marc Schmidt
   secunet Security Networks
   Mergenthaler Allee 77
   65760 Eschborn


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