Internet Research Task Force Harkins
Internet-Draft HP Enterprise
Intended status: Informational September 12, 2016
Expires: March 16, 2017
PKEX
draft-harkins-pkex-00
Abstract
This memo describes a password-authenticated protocol to allow two
devices to exchange "raw" (uncertified) public keys and establish
trust that the keys belong to their respective identities.
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 2
1.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Properties . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 4
4. Protocol Definition . . . . . . . . . . . . . . . . . . . . . 4
4.1. Exchange Phase . . . . . . . . . . . . . . . . . . . . . 5
4.2. Commit Phase . . . . . . . . . . . . . . . . . . . . . . 5
4.3. Reveal Phase . . . . . . . . . . . . . . . . . . . . . . 6
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 7
6. Security Considerations . . . . . . . . . . . . . . . . . . . 7
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 8
7.1. Normative References . . . . . . . . . . . . . . . . . . 8
7.2. Informative References . . . . . . . . . . . . . . . . . 8
Appendix A. Appendix . . . . . . . . . . . . . . . . . . . . . . 9
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 9
1. Introduction
Many authenticated key exchange protocols allow for authentication
using uncertified, or "raw", public keys, for example TLS
([RFC7250]), or IKEv2 ([RFC7670]) Usually these specifications state
that "establishing trust in raw public keys is outside the scope of
this standard." The Public Key Exchange (PKEX) is designed to fill
that gap and enable the establishment of trust in public keys that
can subsequently be used to faccilitate authentication in other
authentication and key exchange protocols.
1.1. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
1.2. Notation
This memo describes a cryptographic exchange using sets of elements
called groups. Groups can be either traditional finite field or can
be based on elliptic curves. The public keys exchanged by PKEX are
elements in a group. Elements in groups are denoted in upper-case
and scalar values are denoted with lower-case. The generator of the
group is G.
When both the initator and responder use a similar, but unique, datum
it is denoted by appending an "i" for initiator or "r" for responder,
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e.g. if each side needs an element C then the initiator's is Ci and
the responder's is Cr.
During the exchange, one side will generate data and the other side
will attempt to reconstruct it. The reconstructed data is "primed".
That is, if the initiator generates C then when responder tries to
reconstruct it, the responder will refer to it as C'. Data that is
directly sent and received is not primed.
The following notation is used in this memo:
C = A + B
The "group operation" on two elements, A and B, that produces a
third element, C. For finite field cryptography this is the
modular multiplication, for elliptic curve cryptography this is
point addition.
C = a * B
This denotes repeated application of the group operation to B--
i.e. B + B-- (a - 1) times.
a = H(b)
A cryptographic hash function that takes data b of indeterminate
length and returns a fixed sized digest a.
a = F(B)
A mapping function that takes an element and returns a scalar.
For elliptic curve cryptography, F() returns the x-coordinate of
the point B. For finite field cryptography, F() is the identity
function.
a = KDF(b, c)
A key derivation function that derives an output key a from an
input key b and context c.
c = a | b
Concatentation of data a with data b producing c.
2. Properties
Subversion of PKEX involves an adversary being able to insert its own
public key into the exchange resulting in one of the parties to the
exchange believing the adversary's public key actually belongs to the
protocol peer.
PKEX has the following properties:
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o An adversary is unable to subvert the exchange without knowing the
password.
o An adversary is unable to discover the password through passive
attack.
o The only information exposed by an active attack is whether a
single guess of the password is correct or not.
o Proof-of-possession of the private key is provided.
o At the end of the protocol, either trust is established in the
peer's public key or the exchange fails.
3. Assumptions
Due to the nature of the exchange, only DSA ([DSS]) and ECDSA
([X9.62]) keys can be exchanged with PKEX.
PKEX requires fixed elements that are unique to the particular role
in the protocol, an initiator-specific element and a responder-
specific element. They need not be secret. It is assumed that both
parties know the role-specific elements for the particular group in
which their key pairs were derived. This memo does not proscribe any
way to generate these role-specific elements but the "Hunting and
Pecking" technique of [RFC7664] could be used with a slight
variation. Instead of inputting a password and generating a secret
element, a common string such as "PKEX Initiator Element" can be used
to generate a public element. For elliptic curve cryptography, the
technique of "hashing into an elliptic curve" from [hash2ec] could be
used, again with a common string, to produce role-specific elements.
The following assumptions are made on PKEX:
o Only the peers involved in the exchange know the password.
o The peers' public keys are from the same group.
o The discrete logarithms of the public role-specific elements are
unknown, and determining them is computationally infeasible.
4. Protocol Definition
PKEX is a balanced PAKE. The identical version of the password is
used by both parties.
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PKEX consists of three phases: exchange, commit, and reveal. It is
described using the popular protocol participants, Alice (an
initiator of PKEX), and Bob (a responder of PKEX).
We denote Alice's role-specific element a Pi and Bob's as Pr. The
password is pw. For simplicity, Alice's identity is "Alice" and
Bob's identity is "Bob". Alice's public key she wants to share with
Bob is A and her private key is a, while Bob's public key he wants to
share with Alice is B and his private key is b.
4.1. Exchange Phase
The Exchange phase is essentially the SPAKE key exchange. The peers
derive ephemeral public keys, encrypt, and exchange them. Each party
hashes a concatentation of his or her identity and the password and
operates on the role-specific element to obtain a secret encrypting
element. The group operation is then performed with the ephemeral
key and the secret encrypting element to produce an encrypted
ephmeral key.
Alice: Bob:
------ ----
x, X = x*G y, Y = y*G
Qi = H(Alice|pw)*Pi Qr = H(Bob|pw)*Pr
M = X + Qa
M ------>
Qi = H(Alice|pw)*Pi
X' = M - Qi
N = Y + Qr
<------ N
Qr = H(Bob|pw)*Pr
Y' = N - Qr
At this point in time the peers have exchanged ephemeral elements
that will be unknown except by someone with knowledge of the
password. Given our assumptions that means only Alice and Bob can
know the elements X and Y.
The secret encrypting elements are irretrievably deleted at this
point.
4.2. Commit Phase
In the Commit phase the peers commit to the particular public key
they wish to exchange.
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Alice: Bob:
------ ----
sa = F(a*Y')
ka = KDF(sa, F(M) | F(N) |
F(A) | F(Y') | pw)
u = HMAC(ka, F(X) | F(Y') |
F(A) | Alice | 0)
u ------>
sb = F(b*X')
kb = KDF(sb, F(N) | F(M) |
F(B) | F(X') | pw)
v = HMAC(kb, F(Y) | F(X') |
F(B) | Bob | 1)
<------ v
where 0 and 1 are single octets of the value zero and one,
respectively.
At this point the parties have committed to their public/private key
pairs but have net yet exchanged their public keys. There is no
proof that either side possesses the private key or whether the
public key is really the analog to the private key but they have made
irrevocable committments to those statements.
4.3. Reveal Phase
In the Reveal phase the peers encrypt their public keys using a
secret element derived from the exchange in the Commit phase. This
allows each side to determine the other's public key and verify that
the peer holds the private key.
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Alice: Bob:
------ ----
Z = x*Y'
R = A + Z
R ------>
Z = y*X'
A' = R - Z
sa' = F(y*A')
ka' = KDF(sa', F(M) | F(N) |
F(A') | F(Y) | pw)
u' = HMAC(ka', F(X') | F(Y) |
F(A') | Alice | 0)
if (u' != u) fail
T = B + Z
<------ T
B' = T - Z
sb' = F(x*B')
kb' = KDF(sb', F(N) | F(M) |
F(B') | F(X) | pw)
v' = HMAC(kb', F(Y') | F(X) |
F(B') | Bob | 1)
if (v'!= v) fail
where 0 and 1 are single octets of the value zero and one,
respectively.
At this point, if the parties didn't fail they have each other's
public key and trust that it belongs to the peer's stated identlty.
They can use the public key in another protocol to authenticate that
identity. They provided proof of possession by binding their private
key to the peer's ephemeral share made during the Exchange phase,
they signed their public key with the resulting secret. The ability
of the peer to compute this secret and verify the data exchanged
during the Commit phase demonstrates the public key is the analog to
the private key.
5. IANA Considerations
This memo could create a registry of the fixed public elements for a
nice cross section of popular groups. Or not. If it ends up doing
so there will be IANA Considerations here, otherwise there won't be.
6. Security Considerations
The encrypted shares exchanged in the Exchange phase MUST be
ephemeral. Reuse of these keys, even with a different password,
voids the security of the exchange.
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The discrete logaritm of the fixed public elements MUST not be known.
Knowledge of either of these values voids the security of the
exchange.
For PKEX to be useful, a public key is going to be exchanged with a
multitude of people and once exchanged the public key is, well,
public. This means that an adversary will know the public key that a
particular peer wants to exchange in a future run of PKEX. With this
knowledge an adversary can attack the Reveal exchange and, knowing A
(or B), determine Z for the PKEX exchange and insert her public key.
This will fail, though, because A (or B) was committed to in the
Commit phase. The adversary is unable to subvert the Commit phase
because, while knowing A (or B) she does not know the corresponding
private key and does not know the ephemeral share that the peer
provided since she does not know the password.
There is no proof of security of PKEX at this time.
7. References
7.1. Normative References
[DSS] U.S. Department of Commerce/National Institute of
Standards and Technology, "Digital Signature Standard
(DSS)", Federal Information Processing Standards FIPS PUB
186-4, July 2013.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[X9.62] American National Standards Institute, "X9.62-2005",
Public Key Cryptography for the Financial Services
Industry (ECDSA), 2005.
7.2. Informative References
[RFC7250] Wouters, P., Ed., Tschofenig, H., Ed., Gilmore, J.,
Weiler, S., and T. Kivinen, "Using Raw Public Keys in
Transport Layer Security (TLS) and Datagram Transport
Layer Security (DTLS)", RFC 7250, DOI 10.17487/RFC7250,
June 2014, <http://www.rfc-editor.org/info/rfc7250>.
[RFC7664] Harkins, D., Ed., "Dragonfly Key Exchange", RFC 7664, DOI
10.17487/RFC7664, November 2015,
<http://www.rfc-editor.org/info/rfc7664>.
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[RFC7670] Kivinen, T., Wouters, P., and H. Tschofenig, "Generic Raw
Public-Key Support for IKEv2", RFC 7670, DOI 10.17487/
RFC7670, January 2016,
<http://www.rfc-editor.org/info/rfc7670>.
[hash2ec] Coron, J-S. and T. Icart, "An indifferentiable hash
function into elliptic curves", Cryptology ePrint Archive
Report 2009/340, 2009.
Appendix A. Appendix
Maybe show a sample PKEX exchange
Author's Address
Dan Harkins
HP Enterprise
1322 Crossman avenue
Sunnyvale, California 94089
USA
Phone: +1 415 997 9834
Email: dharkins@lounge.org
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