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:
[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]
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