Network Working Group H. Krawczyk
Internet-Draft IBM Research
Intended status: Informational P. Eronen
Expires: July 29, 2010 Nokia
January 25, 2010
HMAC-based Extract-and-Expand Key Derivation Function (HKDF)
draft-krawczyk-hkdf-01.txt
Abstract
This document specifies a simple HMAC-based key derivation function
(HKDF) which can be used as a building block in various protocols and
applications. The KDF is intended to support a wide range of
applications and requirements, and is conservative in its use of
cryptographic hash functions.
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1. Introduction
A key derivation function (KDF) is a basic and essential component of
cryptographic systems. Its goal is to take some source of initial
keying material and derive from it one or more cryptographically
strong secret keys.
This document specifies a simple HMAC-based [HMAC] KDF, named HKDF,
which can be used as a building block in various protocols and
applications, and is already used in several IETF protocols,
including [IKEv2], [PANA], and [EAP-AKA]. The purpose is to document
this KDF in a general way to facilitate adoption in future protocols
and applications, and to discourage the proliferation of multiple KDF
mechanisms. It is not intended as a call to change existing
protocols.
HKDF follows the "extract-then-expand" paradigm where the KDF
logically consists of two modules. The first stage takes the input
keying material and "extracts" from it a fixed-length pseudorandom
key K. The second stage "expands" the key K into several additional
pseudorandom keys (the output of the KDF).
In many applications, the input keying material is not necessarily
distributed uniformly, and the attacker may have some partial
knowledge about it (for example, a Diffie-Hellman value computed by a
key exchange protocol) or even partial control of it (as in some
entropy-gathering applications). Thus, the goal of the "extract"
stage is to "concentrate" the possibly dispersed entropy of the input
keying material into a short, but cryptographically strong,
pseudorandom key. In some applications, the input may already be a
good pseudorandom key; in these cases, the "extract" stage is not
necessary, and the "expand" part can be used alone.
The second stage "expands" the pseudorandom key to the desired
length; the number and lengths of the output keys depend on the
specific cryptographic algorithms for which the keys are needed.
Note that some existing KDF specifications, such as NIST Special
Publication 800-56A [800-56A], NIST Special Publication 800-108
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[800-108] and IEEE Standard 1363a-2004 [1363a], either only consider
the second stage (expanding a pseudorandom key), or do not explicitly
differentiate between the "extract" and "expand" stages, often
resulting in design shortcomings. The goal of this specification is
to accommodate a wide range of KDF requirements while minimizing the
assumptions about the underlying hash function. The "extract-then-
expand" paradigm supports well this goal (see [HKDF-paper] for more
information about the design rationale).
2. HMAC-based Key Derivation Function (HKDF)
2.1. Notation
HMAC-Hash denotes the HMAC function [HMAC] instantiated with hash
function 'Hash'. HMAC has always two arguments: the first is a key
and the second an input (or message). When the message is composed
of several elements we use concatenation (denoted |) in the second
argument; for example, HMAC(K, elem1 | elem2 | elem3).
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 [KEYWORDS].
2.2. Step 1: Extract
PRK = HKDF-Extract(salt, IKM)
Options:
Hash a hash function; HashLen denotes the length of the
hash function output in octets
Inputs:
salt optional salt value (a non-secret random value);
if not provided, it is set to a string of HashLen zeros.
IKM input keying material
Output:
PRK a pseudo-random key (of HashLen octets)
The output PRK is calculated as follows:
PRK = HMAC-Hash(salt, IKM)
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2.3. Step 2: Expand
OKM = HKDF-Expand(PRK, info, L)
Options:
Hash a hash function; HashLen denotes the length of the
hash function output in octets
Inputs:
PRK a pseudo-random key of at least HashLen octets
(usually, the output from the Extract step)
info optional context and application specific information
(can be a zero-length string)
L length of output keying material in octets
(<= 255*HashLen)
Output:
OKM output keying material (of L octets)
The output OKM is calculated as follows:
N = ceil(L/HashLen)
T = T(1) | T(2) | T(3) | ... | T(N)
OKM = first L octets of T
where:
T(0) = empty string (zero length)
T(1) = HMAC-Hash(PRK, T(0) | info | 0x01)
T(2) = HMAC-Hash(PRK, T(1) | info | 0x02)
T(3) = HMAC-Hash(PRK, T(2) | info | 0x03)
...
(where the constant concatenated to the end of each T(n) is a
single octet.)
3. Notes to HKDF Users
This section contains a set of guiding principles regarding the use
of HKDF. A much more extensive account of such principles and design
rationale can be found in [HKDF-paper].
3.1. To Salt or not to Salt
HKDF is defined to operate with and without random salt. This is
done to accommodate applications where a salt value is not available.
We stress, however, that the use of salt adds significantly to the
strength of HKDF, ensuring independence between different uses of the
hash function, supporting "source-independent" extraction, and
strengthening the analytical results that back the HKDF design.
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Random salt differs fundamentally from the initial keying material in
two ways: it is non-secret and can be re-used. As such, salt values
are available to many applications. For example, a PRNG that
continuously produces outputs by applying HKDF to renewable pools of
entropy (e.g., sampled system events) can fix a salt value and use it
for multiple applications of HKDF without having to protect the
secrecy of the salt. In a different application domain, a key
agreement protocol deriving cryptographic keys from a Diffie-Hellman
exchange can derive a salt value from public nonces exchanged and
authenticated between communicating parties as part of the key
agreement (this is the approach taken in [IKEv2]).
Ideally, the salt value is a random (or pseudorandom) string of the
length HashLen. Yet, even a salt value of less quality (shorter in
size or with limited entropy) may still make a significant
contribution to the security of the output keying material; designers
of applications are therefore encouraged to provide salt values to
HKDF if such values can be obtained by the application.
It is worth noting that, while not the typical case, some
applications may even have a secret salt value available for use; in
such a case, HKDF provides an even stronger security guarantee. An
example of such application is IKEv1 in its "public-key encryption
mode" or with a pre-shared secret where the "salt" to the extractor
is a secret key.
3.2. The 'info' Input to HKDF
While the 'info' value is optional in the definition of HKDF, it is
often of great importance in applications. Its main objective is to
bind the derived key material to application- and context-specific
information. For example, info may contain a protocol number,
algorithm identifiers, user identities, etc. In particular, it may
prevent the derivation of the same keying material for different
contexts (when the same input key material is used in such different
contexts). It may also accommodate additional inputs to the key
expansion part if so desired (e.g., an application may want to bind
the key material to its length L, thus making L part of the 'info'
field). There is one technical requirement from 'info': it should be
independent of the input key material value IKM.
3.3. To Skip or not to Skip
In some applications, the input key material IKM may already be
present as a cryptographically strong key (for example, this is the
case in TLS, with RSA, where keys are derived from the master secret
which in itself is a pseudorandom string). In this case, one can
skip the extract part and use IKM directly to key HMAC in the expand
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step. On the other hand, applications may still use the extract part
for the sake of compatibility with the general case. In particular,
if IKM is random (or pseudorandom) but longer than an HMAC key, the
extract step can serve to output a suitable HMAC key (in the case of
HMAC this shortening via the extractor is not strictly necessary
since HMAC is defined to work with long keys too). Note, however,
that if the IKM is a Diffie-Hellman value, as in the case of TLS with
DH, then the extract part SHOULD NOT be skipped. Doing so would
result in using the Diffie-Hellman value g^{xy} itself (which is NOT
a uniformly random or pseudorandom string) as the key PRK for HMAC.
Instead, HKDF should apply the extractor step to g^{xy} (preferably
with a salt value) and use the resultant PRK as a key to HMAC in the
expansion part.
In the case that the amount of required key bits, L, is no more than
HashLen, one could use PRK directly as the OKM. This, however, is
NOT RECOMMENDED, especially that it would omit the use of 'info' as
part of the derivation process (and adding 'info' as an input to the
extract step is not advisable -- see [HKDF-paper]).
3.4. The Role of Independence
The analysis of key derivation functions assumes that the input
keying material (IKM) comes from some source modeled as a probability
distribution over bit streams of a certain length (e.g., streams
produced by an entropy pool, values derived from Diffie-Hellman
exponents chosen at random, etc.); each instance of IKM is a sample
from that distribution. A major goal of key derivation functions is
to ensure that when applying the KDF to any two values IKM and IKM'
sampled from the (same) source distribution, the resultant keys OKM
and OKM' are essentially independent of each other (in a statistical
or computational sense). To achieve this goal it is important that
inputs to KDF are selected from appropriate input distributions and
also that inputs are chosen independent of each other (technically,
it is necessary that each sample will have sufficient entropy even
when conditioned on other inputs to KDF).
Independence is also an important aspect of the salt value provided
to a KDF. While there is no need to keep the salt secret, and the
same salt value can be used with multiple IKM values, it is assumed
that salt values are independent of the input keying material. In
particular, an application needs to make sure that salt values are
not chosen or manipulated by an attacker. As an example, consider
the case (as in IKE) where the salt is derived from nonces supplied
by the parties during a key exchange protocol. Before the protocol
can use such salt to derive keys, it needs to make sure that these
nonces are authenticated as coming from the legitimate parties rather
than selected by the attacker (in IKE, for example this
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authentication is an integral part of the authenticated Diffie-
Hellman exchange).
4. Applications of HKDF
HKDF is intended for use in a wide variety of KDF applications.
These include the building of pseudorandom generators from imperfect
sources of randomness (such as a physical RNG); the generation of
pseudo-randomness out of weak sources of randomness such as entropy
collected from system events, user's keystrokes, etc.; the derivation
of cryptographic keys from a shared Diffie-Hellman value in a key
agreement protocol; derivation of symmetric keys from a hybrid
public-key encryption scheme; key derivation for key-wrapping
mechanisms; and more. All of these applications can benefit from the
simplicity and multi-purpose nature of HKDF, as well as from its
analytical foundation.
On the other hand, it is anticipated that some applications will not
be able to use HKDF "as-is" due to specific operational requirements,
or will be able to use it but without the full benefits of the
scheme. One significant example is the derivation of cryptographic
keys from a source of low entropy, such as a user's password. The
extract step in HKDF can concentrate existing entropy but cannot
amplify entropy. In the case of password-based KDFs, a main goal is
to slow down dictionary attacks using two ingredients: a salt value
and the intentional slowing of the key derivation computation. HKDF
naturally accommodates the use of salt; however, a slowing down
mechanism is not part of this specification. Applications interested
in a password-based KDF should consider whether, for example, [PKCS5]
meets their needs better than HKDF.
5. Security Considerations
In spite of the simplicity of HKDF there are many security
considerations that have been taken in the design and analysis of
this construction. An exposition of all these aspects is beyond the
scope of this document. Please refer to [HKDF-paper] for detailed
information, including rationale for the design and for the
guidelines presented in Section 3.
A major effort has been made in the above paper to provide a
cryptographic analysis of HKDF as a multi-purpose KDF that exercises
much care in the way it utilizes cryptographic hash functions. This
is particularly important due to the limited confidence we have in
the strength of current hash functions. This analysis, however, does
not imply the absolute security of any scheme and it depends heavily
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on the strength of the underlying hash function and on modeling
choices. Yet, it serves as a strong indication of the correct
structure of the HKDF design and its advantages over other common KDF
schemes.
6. IANA Considerations
This document has no IANA actions.
7. Acknowledgments
The authors would like to thank members of the CFRG (Crypto Forum
Research Group) list for their useful comments, and to Dan Harkins
for providing test vectors.
8. References
8.1. Normative References
[HMAC] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
February 1997.
[KEYWORDS]
Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", RFC 2119, March 1997.
[SHS] National Institute of Standards and Technology, "Secure
Hash Standard", FIPS PUB 180-3, October 2008.
8.2. Informative References
[1363a] Institute of Electrical and Electronics Engineers, "IEEE
Standard Specifications for Public-Key Cryptography-
Amendment 1: Additional Techniques", IEEE Std 1363a-2004,
2004.
[800-108] National Institute of Standards and Technology,
"Recommendation for Key Derivation Using Pseudorandom
Functions", NIST Special Publication 800-108,
November 2008.
[800-56A] National Institute of Standards and Technology,
"Recommendation for Pair-Wise Key Establishment Schemes
Using Discrete Logarithm Cryptography (Revised)", NIST
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Special Publication 800-56A, March 2007.
[EAP-AKA] Arkko, J., Lehtovirta, V., and P. Eronen, "Improved
Extensible Authentication Protocol Method for 3rd
Generation Authentication and Key Agreement (EAP-AKA')",
RFC 5448, May 2009.
[HKDF-paper]
Krawczyk, H., "On Extract-then-Expand Key Derivation
Functions and an HMAC-based KDF",
URL http://www.ee.technion.ac.il/~hugo/kdf/kdf.pdf,
March 2008.
[IKEv2] Kaufman, C., "Internet Key Exchange (IKEv2) Protocol",
RFC 4306, December 2005.
[PANA] Forsberg, D., Ohba, Y., Ed., Patil, B., Tschofenig, H.,
and A. Yegin, "Protocol for Carrying Authentication for
Network Access (PANA)", RFC 5191, December 2008.
[PKCS5] Kaliski, B., "PKCS #5: Password-Based Cryptography
Specification Version 2.0", RFC 2898, September 2000.
Appendix A. Test Vectors
This appendix provides test vectors for SHA-256 and SHA-1 hash
functions [SHS].
A.1. Test Case 1
Basic test case with SHA-256
Hash = SHA-256
IKM = 0x0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b (22 octets)
salt = 0x000102030405060708090a0b0c (13 octets)
info = 0xf0f1f2f3f4f5f6f7f8f9 (10 octets)
L = 42
PRK = 0x077709362c2e32df0ddc3f0dc47bba63
90b6c73bb50f9c3122ec844ad7c2b3e5 (32 octets)
OKM = 0x3cb25f25faacd57a90434f64d0362f2a
2d2d0a90cf1a5a4c5db02d56ecc4c5bf
34007208d5b887185865 (42 octets)
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A.2. Test Case 2
Test with SHA-256 and longer inputs/outputs
Hash = SHA-256
IKM = 0x000102030405060708090a0b0c0d0e0f
101112131415161718191a1b1c1d1e1f
202122232425262728292a2b2c2d2e2f
303132333435363738393a3b3c3d3e3f
404142434445464748494a4b4c4d4e4f (80 octets)
salt = 0x606162636465666768696a6b6c6d6e6f
707172737475767778797a7b7c7d7e7f
808182838485868788898a8b8c8d8e8f
909192939495969798999a9b9c9d9e9f
a0a1a2a3a4a5a6a7a8a9aaabacadaeaf (80 octets)
info = 0xb0b1b2b3b4b5b6b7b8b9babbbcbdbebf
c0c1c2c3c4c5c6c7c8c9cacbcccdcecf
d0d1d2d3d4d5d6d7d8d9dadbdcdddedf
e0e1e2e3e4e5e6e7e8e9eaebecedeeef
f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff (80 octets)
L = 82
PRK = 0x06a6b88c5853361a06104c9ceb35b45c
ef760014904671014a193f40c15fc244 (32 octets)
OKM = 0xb11e398dc80327a1c8e7f78c596a4934
4f012eda2d4efad8a050cc4c19afa97c
59045a99cac7827271cb41c65e590e09
da3275600c2f09b8367793a9aca3db71
cc30c58179ec3e87c14c01d5c1f3434f
1d87 (82 octets)
A.3. Test Case 3
Test with SHA-256 and empty salt/info
Hash = SHA-256
IKM = 0x0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b (22 octets)
salt = (0 octets)
info = (0 octets)
L = 42
PRK = 0x19ef24a32c717b167f33a91d6f648bdf
96596776afdb6377ac434c1c293ccb04 (32 octets)
OKM = 0x8da4e775a563c18f715f802a063c5a31
b8a11f5c5ee1879ec3454e5f3c738d2d
9d201395faa4b61a96c8 (42 octets)
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A.4. Test Case 4
Basic test case with SHA-1
Hash = SHA-1
IKM = 0x0b0b0b0b0b0b0b0b0b0b0b (11 octets)
salt = 0x000102030405060708090a0b0c (13 octets)
info = 0xf0f1f2f3f4f5f6f7f8f9 (10 octets)
L = 42
PRK = 0x9b6c18c432a7bf8f0e71c8eb88f4b30baa2ba243 (20 octets)
OKM = 0x085a01ea1b10f36933068b56efa5ad81
a4f14b822f5b091568a9cdd4f155fda2
c22e422478d305f3f896 (42 octets)
A.5. Test Case 5
Test with SHA-1 and longer inputs/outputs
Hash = SHA-1
IKM = 0x000102030405060708090a0b0c0d0e0f
101112131415161718191a1b1c1d1e1f
202122232425262728292a2b2c2d2e2f
303132333435363738393a3b3c3d3e3f
404142434445464748494a4b4c4d4e4f (80 octets)
salt = 0x606162636465666768696a6b6c6d6e6f
707172737475767778797a7b7c7d7e7f
808182838485868788898a8b8c8d8e8f
909192939495969798999a9b9c9d9e9f
a0a1a2a3a4a5a6a7a8a9aaabacadaeaf (80 octets)
info = 0xb0b1b2b3b4b5b6b7b8b9babbbcbdbebf
c0c1c2c3c4c5c6c7c8c9cacbcccdcecf
d0d1d2d3d4d5d6d7d8d9dadbdcdddedf
e0e1e2e3e4e5e6e7e8e9eaebecedeeef
f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff (80 octets)
L = 82
PRK = 0x8adae09a2a307059478d309b26c4115a224cfaf6 (20 octets)
OKM = 0x0bd770a74d1160f7c9f12cd5912a06eb
ff6adcae899d92191fe4305673ba2ffe
8fa3f1a4e5ad79f3f334b3b202b2173c
486ea37ce3d397ed034c7f9dfeb15c5e
927336d0441f4c4300e2cff0d0900b52
d3b4 (82 octets)
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A.6. Test Case 6
Test with SHA-1 and empty salt/info
Hash = SHA-1
IKM = 0x0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b (22 octets)
salt = (0 octets)
info = (0 octets)
L = 42
PRK = 0xda8c8a73c7fa77288ec6f5e7c297786aa0d32d01 (20 octets)
OKM = 0x0ac1af7002b3d761d1e55298da9d0506
b9ae52057220a306e07b6b87e8df21d0
ea00033de03984d34918 (42 octets)
Authors' Addresses
Hugo Krawczyk
IBM Research
19 Skyline Drive
Hawthorne, NY 10532
USA
Email: hugo@ee.technion.ac.il
Pasi Eronen
Nokia Research Center
P.O. Box 407
FI-00045 Nokia Group
Finland
Email: pasi.eronen@nokia.com
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