IBAKE: Identity-Based Authenticated Key Exchange
RFC 6539

Independent Submission                                        V. Cakulev
Request for Comments: 6539                                   G. Sundaram
Category: Informational                                      I. Broustis
ISSN: 2070-1721                                           Alcatel Lucent
                                                              March 2012

            IBAKE: Identity-Based Authenticated Key Exchange

Abstract

   Cryptographic protocols based on public-key methods have been
   traditionally based on certificates and Public Key Infrastructure
   (PKI) to support certificate management.  The emerging field of
   Identity-Based Encryption (IBE) protocols allows simplification of
   infrastructure requirements via a Private-Key Generator (PKG) while
   providing the same flexibility.  However, one significant limitation
   of IBE methods is that the PKG can end up being a de facto key escrow
   server, with undesirable consequences.  Another observed deficiency
   is a lack of mutual authentication of communicating parties.  This
   document specifies the Identity-Based Authenticated Key Exchange
   (IBAKE) protocol.  IBAKE does not suffer from the key escrow problem
   and in addition provides mutual authentication as well as perfect
   forward and backward secrecy.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This is a contribution to the RFC Series, independently of any other
   RFC stream.  The RFC Editor has chosen to publish this document at
   its discretion and makes no statement about its value for
   implementation or deployment.  Documents approved for publication by
   the RFC Editor are not a candidate for any level of Internet
   Standard; see Section 2 of RFC 5741.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc6539.

Independent Submissions Editor Note

   This document specifies the Identity-Based Authenticated Key Exchange
   (IBAKE) protocol.  Due to its specialized nature, this document
   experienced limited review within the Internet Community.  Readers of
   this RFC should carefully evaluate its value for implementation and
   deployment.

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Copyright Notice

   Copyright (c) 2012 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.

Table of Contents

   1. Introduction ....................................................2
   2. Requirements Notation ...........................................3
      2.1. IBE: Definition ............................................3
      2.2. Abbreviations ..............................................3
      2.3. Conventions ................................................4
   3. Identity-Based Authenticated Key Exchange .......................5
      3.1. Overview ...................................................5
      3.2. IBAKE Message Exchange .....................................6
      3.3. Discussion .................................................7
   4. Security Considerations .........................................9
      4.1. General ....................................................9
      4.2. IBAKE Protocol ............................................10
   5. References .....................................................12
      5.1. Normative References ......................................12
      5.2. Informative References ....................................12

1.  Introduction

   Authenticated key agreements are cryptographic protocols where two or
   more participants authenticate each other and agree on key material
   used for securing future communication.  These protocols could be
   symmetric key or asymmetric public-key protocols.  Symmetric-key
   protocols require an out-of-band security mechanism to bootstrap a
   secret key.  On the other hand, public-key protocols traditionally
   require certificates and a large-scale Public Key Infrastructure
   (PKI).  Clearly, public-key methods are more flexible; however, the
   requirement for certificates and a large-scale PKI have proved to be
   challenging.  In particular, efficient methods to support large-scale
   certificate revocation and management have proved to be elusive.

   Recently, Identity-Based Encryption (IBE) protocols have been
   proposed as a viable alternative to public-key methods by replacing
   the PKI with a Private-Key Generator (PKG).  However, one significant
   limitation of IBE methods is that the PKG can end up being a de facto

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   key escrow entity (i.e., an entity that has sufficient information to
   decrypt communicated data), with undesirable consequences.  Another
   limitation is a lack of mutual authentication between communicating
   parties.  This document specifies an Identity-Based Authenticated Key
   Encryption (IBAKE) protocol that does not suffer from the key escrow
   problem and that provides mutual authentication.  In addition, the
   scheme described in this document allows the use of time-bound public
   identities and corresponding public and private keys, resulting in
   automatic expiration of private keys at the end of a time span
   indicated in the identity itself.  With the self-expiration of the
   public identities, the traditional real-time validity verification
   and revocation procedures used with certificates are not required.
   For example, if the public identity is bound to one day, then, at the
   end of the day, the public/private key pair issued to this peer will
   simply not be valid anymore.  Nevertheless, just as with public-key-
   based certificate systems, if there is a need to revoke keys before
   the designated expiry time, communication with a third party will be
   needed.  Finally, the protocol also provides forward and backward
   secrecy of session keys; i.e., a session key produced using IBAKE is
   always fresh and unrelated to any past or future sessions between the
   protocol participants.

2.  Requirements Notation

   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 [RFC2119].

2.1.  IBE: Definition

   Identity-Based Encryption (IBE) is a public-key encryption technology
   that allows a public key to be calculated from an identity and a set
   of public parameters, and the corresponding private key to be
   calculated from the public key.  The public key can then be used by
   an Initiator to encrypt messages that the recipient can decrypt using
   the corresponding private key.  The IBE framework is defined in
   [RFC5091], [RFC5408], and [RFC5409].

2.2.  Abbreviations

   EC          Elliptic Curve

   IBE         Identity-Based Encryption

   IBAKE       Identity-Based Authenticated Key Exchange

   IDi         Initiator's Identity

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   IDr         Responder's Identity

   K_PUB       Public Key

   PKG         Private-Key Generator

   PKI         Public Key Infrastructure

2.3.  Conventions

   o  E is an elliptic curve over a finite field F.

   o  P is a point on E of large prime order.

   o  s is a non-zero positive integer.  s is a secret stored in a PKG.
      This is a system-wide secret and not revealed outside the PKG.

   o  sP is the public key of the system that is known to all
      participants.  sP denotes a point on E, and denotes the point P
      added to itself s times where addition refers to the group
      operation on E.

   o  H1 is a known hash function that takes a string and assigns it to
      a point on the elliptic curve, i.e., H1(A) = QA on E, where A is
      usually based on the identity.

   o  E(k, A) denotes that A is IBE-encrypted with the key k.

   o  s||t denotes concatenation of the strings s and t.

   o  K_PUBx denotes a public key of x.

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3.  Identity-Based Authenticated Key Exchange

3.1.  Overview

   IBAKE consists of a three-way exchange between an Initiator and a
   Responder.  In the figure below, a conceptual signaling diagram of
   IBAKE is depicted.

                 +---+                             +---+
                 | I |                             | R |
                 +---+                             +---+

                                MESSAGE_1
                   ---------------------------------->
                                MESSAGE_2
                   <----------------------------------
                                MESSAGE_3
                   ---------------------------------->

                 Figure 1: Example IBAKE Message Exchange

   The Initiator (I) and Responder (R) are attempting to mutually
   authenticate each other and agree on a key using IBAKE.  This
   specification assumes that the Initiator and the Responder trust a
   third party -- the PKG.  Rather than a single PKG, different PKGs may
   be involved, e.g., one for the Initiator and one for the Responder.
   The Initiator and the Responder do not share any credentials;
   however, they know or can obtain each other's public identity (key)
   as well as the public parameters of each other's PKG.  This
   specification does not make any assumption on when and how the
   private keys are obtained.  However, to complete the protocol
   described (i.e., to decrypt encrypted messages in the IBAKE protocol
   exchange), the Initiator and the Responder need to have their
   respective private keys.  The procedures needed to obtain the private
   keys and public parameters are outside the scope of this
   specification.  The details of these procedures can be found in
   [RFC5091] and [RFC5408].  Finally, the protocol described in this
   document relies on the use of elliptic curves.  Section 3.3 discusses
   the choice of elliptic curves.  However, how the Initiator and the
   Responder agree on a specific elliptic curve is left to the
   application that is leveraging the IBAKE protocol (see [EAP-IBAKE],
   for example).

   The Initiator chooses a random x.  In the first step, the Initiator
   computes xP (i.e., P, as a point on E, added to itself x times using
   the addition law on E); encrypts xP, the IDi, and the IDr using the
   Responder's public key (e.g., K_PUBr=H1(IDr||date)); and includes

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   this encrypted information in MESSAGE_1 sent to the Responder.  In
   this step, encryption refers to IBE as described in [RFC5091] and
   [RFC5408].

   The Responder, upon receiving the message, IBE-decrypts it using its
   private key (e.g., a private key for that date), and obtains xP.  The
   Responder further chooses a random y and computes yP.  The Responder
   then IBE-encrypts the Initiator's identity (IDi), its own identity
   (IDr), xP, and yP using the Initiator's public key (e.g.,
   K_PUBi=H1(IDi||date)).  The Responder includes this encrypted
   information in MESSAGE_2 sent to the Initiator.

   The Initiator, upon receiving and IBE-decrypting MESSAGE_2, obtains
   yP.  Subsequently, the Initiator sends MESSAGE_3, which includes the
   IBE-encrypted IDi, IDr, and yP, to the Responder.  At this point,
   both the Initiator and the Responder are able to compute the same
   session key as xyP.

3.2.  IBAKE Message Exchange

   Initially, the Initiator selects a random x and computes xP; the
   Initiator MUST use a fresh, random value for x on each run of the
   protocol.  The Initiator then encrypts xP, the IDi, and the IDr using
   the Responder's public key (e.g., K_PUBr=H1(IDr||date)).  The
   Initiator includes this encrypted information in MESSAGE_1 and sends
   it to the Responder, as shown below.

   Initiator   ---->   Responder

      MESSAGE_1 = E(K_PUBr, IDi || IDr || xP)

   Upon receiving MESSAGE_1, the Responder SHALL perform the following:

   o  Decrypt the message as specified in [RFC5091] and [RFC5408].

   o  Obtain xP.

   o  Select a random y and compute yP.  The Responder MUST use a fresh,
      random value for x on each run of the protocol.

   o  Encrypt the Initiator's identity (IDi), its own identity (IDr),
      xP, and yP using the Initiator's public key (K_PUBi).

   Responder   ---->   Initiator

      MESSAGE_2 = E(K_PUBi, IDi || IDr || xP || yP)

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   Upon receiving MESSAGE_2, the Initiator SHALL perform the following:

   o  Decrypt the message as specified in [RFC5091] and [RFC5408].

   o  Verify that the received xP is the same as that sent in MESSAGE_1.

   o  Obtain yP.

   o  Encrypt its own identity (IDi), the Responder's identity (IDr),
      and yP using the Responder's public key (K_PUBi).

   Initiator   ---->   Responder

      MESSAGE_3 = E(K_PUBr, IDi || IDr || yP)

   Upon receiving MESSAGE_3, the Responder SHALL perform the following:

   o  Decrypt the message as specified in [RFC5091] and [RFC5408].

   o  Verify that the received yP is the same as that sent in MESSAGE_2.

   If any of the above verifications fail, the protocol halts;
   otherwise, following this exchange, both the Initiator and the
   Responder have authenticated each other and are able to compute xyP
   as the session key.  At this point, both protocol participants MUST
   discard all intermediate cryptographic values, including x and y.
   Similarly, both parties MUST immediately discard these values
   whenever the protocol terminates as a result of a verification
   failure or timeout.

3.3.  Discussion

   Properties of the protocol are as follows:

   o  Immunity from key escrow: Observe that all of the steps in the
      protocol exchange are encrypted using IBE.  So, clearly, the PKG
      can decrypt all of the exchanges.  However, given the assumption
      that PKGs are trusted and well behaved (e.g., PKGs will not mount
      an active man-in-the-middle (MitM) attack), they cannot compute
      the session key.  This is because of the hardness of the Elliptic
      Curve Diffie-Hellman problem.  In other words, given xP and yP, it
      is computationally hard to compute xyP.

   o  Mutually authenticated key agreement: Observe that all of the
      steps in the protocol exchange are encrypted using IBE.  In
      particular, only the Responder and its corresponding PKG can
      decrypt the contents of MESSAGE_1 and MESSAGE_3 sent by the
      Initiator, and similarly only the Initiator and its corresponding

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      PKG can decrypt the contents of MESSAGE_2 sent by the Responder.
      Again, given the assumption made above -- that PKGs are trusted
      and well behaved (e.g., a PKG will not impersonate a user to which
      it issued a private key) -- upon receiving MESSAGE_2, the
      Initiator can verify the Responder's authenticity, since xP could
      have been sent in MESSAGE_2 only after decryption of the contents
      of MESSAGE_1 by the Responder.  Similarly, upon receiving
      MESSAGE_3, the Responder can verify the Initiator's authenticity,
      since yP could have been sent back in MESSAGE_3 only after correct
      decryption of the contents of MESSAGE_2 by the Initiator.
      Finally, both the Initiator and the Responder can agree on the
      same session key.  In other words, IBAKE is a mutually
      authenticated key agreement protocol based on IBE.  The hardness
      of the key agreement protocol relies on the hardness of the
      Elliptic Curve Diffie-Hellman problem.  Thus, in any practical
      implementation, care should be devoted to the choice of elliptic
      curve.

   o  Perfect forward and backward secrecy: Since x and y are random,
      xyP is always fresh and unrelated to any past or future sessions
      between the Initiator and the Responder.

   o  No passwords: Clearly, the IBAKE protocol does not require any
      offline exchange of passwords or secret keys between the Initiator
      and the Responder.  In fact, the method is applicable to any two
      parties communicating for the first time through any communication
      network.  The only requirement is to ensure that both the
      Initiator and the Responder are aware of each other's public keys
      and the public parameters of the PKG that generated the
      corresponding private keys.

   o  PKG availability: Observe that PKGs need not be contacted during
      an IBAKE protocol exchange, which dramatically reduces the
      availability requirements on PKGs.

   o  Choice of elliptic curves: This specification relies on the use of
      elliptic curves for both IBE and Elliptic Curve Diffie-Hellman
      exchange.  When making a decision on the choice of elliptic
      curves, it is beneficial to choose two different elliptic curves
      -- a non-supersingular curve for the internal calculations of
      Elliptic Curve Diffie-Hellman values xP and yP, and a
      supersingular curve for the IBE encryption/decryption.  For the
      calculations of Elliptic Curve Diffie-Hellman values, it is
      beneficial to use the curves recommended by NIST [FIPS-186].
      These curves make the calculations simpler while keeping the
      security high.  On the other hand, IBE systems are based on
      bilinear pairings.  Therefore, the choice of an elliptic curve for

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      IBE is restricted to a family of supersingular elliptic curves
      over finite fields of large prime characteristic.  The appropriate
      elliptic curves for IBE are described in [RFC5091].

   o  Implementation considerations: An implementation of IBAKE would
      consist of two primary modules, i.e., point addition operations
      over a NIST curve, and IBE operations over a supersingular curve.
      The implementation of both modules only needs to be aware of the
      following parameters: (a) the full description of the curves that
      are in use (fixed or negotiated), (b) the public parameters of the
      PKG used for the derivation of IBE private keys, and (c) the exact
      public identity of each IBAKE participant.  The knowledge of these
      parameters is sufficient to perform Elliptic Curve Cryptography
      (ECC) operations in different terminals and produce the same
      results, independently of the implementation.

4.  Security Considerations

   This document is based on the basic IBE protocol, as specified in
   [BF], [RFC5091]), [RFC5408], and [RFC5409], and as such inherits some
   properties of that protocol.  For instance, by concatenating the
   "date" with the identity (to derive the public key), the need for any
   key revocation mechanisms is virtually eliminated.  Moreover, by
   allowing the participants to acquire multiple private keys (e.g., for
   duration of contract) the availability requirements on the PKG are
   also reduced without any reduction in security.  The granularity
   associated with the date is a matter of security policy and as such
   is a decision made by the PKG administrator.  However, the
   granularity applicable to any given participant should be publicly
   available and known to other participants.  For example, this
   information can be made available in the same venue that provides
   "public information" on a PKG server (i.e., P, sP) needed to
   execute IBE.

4.1.  General

   Attacks on the cryptographic algorithms used in IBE are outside the
   scope of this document.  It is assumed that any administrator will
   pay attention to the desired strengths of the relevant cryptographic
   algorithms based on an up-to-date understanding of the strength of
   these algorithms from published literature, as well as to known
   attacks.

   It is assumed that the PKGs are secure, not compromised, trusted, and
   will not engage in launching active attacks independently or in a
   collaborative environment.  Nevertheless, if an active adversary can
   fool the parties into believing that it is a legitimate PKG, then it
   can mount a successful MitM attack.  Therefore, care should be taken

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   when choosing a PKG.  In addition, any malicious insider could
   potentially launch passive attacks (by decryption of one or more
   message exchanges offline).  While it is in the best interest of
   administrators to prevent such an issue, it is hard to eliminate this
   problem.  Hence, it is assumed that such problems will persist, and
   hence the session key agreement protocols are designed to protect
   participants from passive adversaries.

   It is also assumed that the communication between participants and
   their respective PKGs is secure.  Therefore, in any implementation of
   the protocols described in this document, administrators of any PKG
   have to ensure that communication with participants is secure and not
   compromised.

   Finally, concatenating the date to the identity ensures that the
   corresponding private key is applicable only to that date.  This
   serves to limit the damage related to a leakage or compromise of
   private keys to just that date.  This, in particular, eliminates the
   revocation mechanisms that are typical to various certificate-based
   public key protocols.

4.2.  IBAKE Protocol

   For the basic IBAKE protocol, from a cryptographic perspective, the
   following security considerations apply.

   In every step, IBE is used, with the recipient's public key.  This
   guarantees that only the intended recipient of the message and its
   corresponding PKG can decrypt the message [BF].

   Next, the use of identities within the encrypted payload is intended
   to eliminate some basic reflection attacks.  For instance, suppose we
   did not use identities as part of the encrypted payload, in the first
   step of the IBAKE protocol exchange (i.e., MESSAGE_1 of Figure 1 in
   Section 3.1).  Furthermore, assume that an adversary has access to
   the conversation between the Initiator and the Responder and can
   actively snoop packets and drop/modify them before routing them to
   the destination.  For instance, assume that the IP source address and
   destination address can be modified by the adversary.  After the
   first message is sent by the Initiator (to the Responder), the
   adversary can take over and trap the packet.  Next, the adversary can
   modify the IP source address to include the adversary's IP address,
   before routing it on to the Responder.  The Responder will assume
   that the request for an IBAKE session came from the adversary, and
   will execute step 2 of the IBAKE protocol exchange (i.e., MESSAGE_2
   of Figure 1 in Section 3.1) but encrypt it using the adversary's
   public key.  The above message can be decrypted by the adversary (and
   only by the adversary).  In particular, since the second message

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   includes the challenge sent by the Initiator to the Responder, the
   adversary will now learn the challenge sent by the Initiator.
   Following this, the adversary can carry on a conversation with the
   Initiator, "pretending" to be the Responder.  This attack will be
   eliminated if identities are used as part of the encrypted payload.
   In summary, at the end of the exchange, both the Initiator and the
   Responder can mutually authenticate each other and agree on a
   session key.

   Recall that IBE guarantees that only the recipient of the message can
   decrypt the message using the private key, with the caveat that the
   PKG that generated the private key of the recipient of the message
   can decrypt the message as well.  However, the PKG cannot learn the
   public key xyP given xP and yP, based on the hardness of the Elliptic
   Curve Diffie-Hellman problem.  This property of resistance to passive
   key escrow from the PKG is not applicable to the basic IBE protocols
   proposed in [RFC5091]), [RFC5408], and [RFC5409].

   Observe that the protocol works even if the Initiator and Responder
   belong to two different PKGs.  In particular, the parameters used for
   encryption to the Responder and parameters used for encryption to the
   Initiator can be completely different and independent of each other.
   Moreover, the elliptic curve used to generate the session key xyP can
   be completely different and can be chosen during the key exchange.
   If such flexibility is desired, then it would be required to add
   optional extra data to the protocol to exchange the algebraic
   primitives used in deriving the session key.

   In addition to mutual authentication and resistance to passive
   escrow, the Diffie-Hellman property of the session key exchange
   guarantees perfect secrecy of keys.  In other words, accidental
   leakage of one session key does not compromise past or future session
   keys between the same Initiator and Responder.

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5.  References

5.1.  Normative References

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

5.2.  Informative References

   [BF]        Boneh, D. and M. Franklin, "Identity-Based Encryption
               from the Weil Pairing", in SIAM Journal on Computing,
               Vol. 32, No. 3, pp. 586-615, 2003.

   [EAP-IBAKE] Cakulev, V. and I. Broustis, "An EAP Authentication
               Method Based on Identity-Based Authenticated Key
               Exchange", Work in Progress, February 2012.

   [FIPS-186]  National Institute of Standards and Technology, "Digital
               Signature Standard (DSS)", FIPS Pub 186-3, June 2009.

   [RFC5091]   Boyen, X. and L. Martin, "Identity-Based Cryptography
               Standard (IBCS) #1: Supersingular Curve Implementations
               of the BF and BB1 Cryptosystems", RFC 5091,
               December 2007.

   [RFC5408]   Appenzeller, G., Martin, L., and M. Schertler, "Identity-
               Based Encryption Architecture and Supporting Data
               Structures", RFC 5408, January 2009.

   [RFC5409]   Martin, L. and M. Schertler, "Using the Boneh-Franklin
               and Boneh-Boyen Identity-Based Encryption Algorithms with
               the Cryptographic Message Syntax (CMS)", RFC 5409,
               January 2009.

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Authors' Addresses

   Violeta Cakulev
   Alcatel Lucent
   600 Mountain Ave.
   3D-517
   Murray Hill, NJ  07974
   US

   Phone: +1 908 582 3207
   EMail: violeta.cakulev@alcatel-lucent.com

   Ganapathy S. Sundaram
   Alcatel Lucent
   600 Mountain Ave.
   3D-517
   Murray Hill, NJ  07974
   US

   Phone: +1 908 582 3209
   EMail: ganesh.sundaram@alcatel-lucent.com

   Ioannis Broustis
   Alcatel Lucent
   600 Mountain Ave.
   3D-526
   Murray Hill, NJ  07974
   US

   Phone: +1 908 582 3744
   EMail: ioannis.broustis@alcatel-lucent.com

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