RFC6539

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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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

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.

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.

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.

Abbreviations

EC Elliptic Curve

IBE Identity-Based Encryption

IBAKE Identity-Based Authenticated Key Exchange

IDi Initiator's Identity

IDr Responder's Identity

K_PUB Public Key

PKG Private-Key Generator

PKI Public Key Infrastructure

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.

Identity-Based Authenticated Key Exchange

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

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.

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)

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.

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

  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

  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.

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.

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

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.

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

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.

References

Normative References

RFC2119 Bradner, S., "Key words for use in RFCs to Indicate

           Requirement Levels", BCP 14, RFC 2119, March 1997.

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.

Authors' Addresses

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

Phone: +1 908 582 3207 EMail: [email protected]

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

Phone: +1 908 582 3209 EMail: [email protected]

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

Phone: +1 908 582 3744 EMail: [email protected]