Internet Engineering Task Force (IETF) H. Krawczyk

Internet Engineering Task Force (IETF) H. Krawczyk
Request for Comments: 5869 IBM Research
Category: Informational P. Eronen
ISSN: 2070-1721 Nokia
May 2010

HMAC-based Extract-and-Expand Key Derivation Function (HKDF)

Abstract

This document specifies a simple Hashed Message Authentication Code
(HMAC)-based key derivation function (HKDF), which can be used as a
building block in various protocols and applications. The key
derivation function (KDF) is intended to support a wide range of
applications and requirements, and is conservative in its use of
cryptographic hash functions.

Status of This Memo

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

This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Not all documents
approved by the IESG are 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/rfc5869.

Copyright Notice

Copyright (c) 2010 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
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include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.

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RFC 5869 Extract-and-Expand HKDF May 2010

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 and does not change or update existing specifications using
this KDF.

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
[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).

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RFC 5869 Extract-and-Expand HKDF May 2010

2. HMAC-based Key Derivation Function (HKDF)

2.1. Notation

HMAC-Hash denotes the HMAC function [HMAC] instantiated with hash
function 'Hash'. HMAC always has two arguments: the first is a key
and the second an input (or message). (Note that in the extract
step, 'IKM' is used as the HMAC input, not as the HMAC key.)

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

HKDF-Extract(salt, IKM) -> PRK

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 pseudorandom key (of HashLen octets)

The output PRK is calculated as follows:

PRK = HMAC-Hash(salt, IKM)

2.3. Step 2: Expand

HKDF-Expand(PRK, info, L) -> OKM

Options:
Hash a hash function; HashLen denotes the length of the
hash function output in octets

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RFC 5869 Extract-and-Expand HKDF May 2010

Inputs:
PRK a pseudorandom 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.

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 pseudorandom
number generator (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

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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", where the "salt" to the extractor is computed from nonces that
are secret; similarly, the pre-shared mode of IKEv1 uses a secret
salt derived from the pre-shared 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 (IKM) 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, the premaster
secret in TLS RSA cipher suites would be a pseudorandom string,
except for the first two octets). In this case, one can skip the
extract part and use IKM directly to key HMAC in the expand 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

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RFC 5869 Extract-and-Expand HKDF May 2010

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 Diffie-
Hellman, 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 extract 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 where 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 because 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 independently 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 in 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 authentication is
an integral part of the authenticated Diffie-Hellman exchange).

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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 random number generator
(RNG)); the generation of pseudorandomness 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 into account in the design and
analysis of this construction. An exposition of all of 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 [HKDF-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 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.

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6. 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.

7. References

7.1. 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", BCP 14, RFC 2119, March 1997.

[SHS] National Institute of Standards and Technology, "Secure
Hash Standard", FIPS PUB 180-3, October 2008.

7.2. 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
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., "Cryptographic Extraction and Key
Derivation: The HKDF Scheme", Proceedings of CRYPTO 2010
(to appear), 2010, <http://eprint.iacr.org/2010/264>.

[IKEv2] Kaufman, C., Ed., "Internet Key Exchange (IKEv2)
Protocol", RFC 4306, December 2005.

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RFC 5869 Extract-and-Expand HKDF May 2010

[PANA] Forsberg, D., Ohba, Y., Ed., Patil, B., Tschofenig, H.,
and A. Yegin, "Protocol for Carrying Authentication for
Network Access (PANA)", RFC 5191, May 2008.

[PKCS5] Kaliski, B., "PKCS #5: Password-Based Cryptography
Specification Version 2.0", RFC 2898, September 2000.

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RFC 5869 Extract-and-Expand HKDF May 2010

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 zero-length 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 zero-length 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)

A.7. Test Case 7

Test with SHA-1, salt not provided (defaults to HashLen zero octets),
zero-length info

Hash = SHA-1
IKM = 0x0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c (22 octets)
salt = not provided (defaults to HashLen zero octets)
info = (0 octets)
L = 42

PRK = 0x2adccada18779e7c2077ad2eb19d3f3e731385dd (20 octets)
OKM = 0x2c91117204d745f3500d636a62f64f0a
b3bae548aa53d423b0d1f27ebba6f5e5
673a081d70cce7acfc48 (42 octets)

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RFC 5869 Extract-and-Expand HKDF May 2010

Authors' Addresses

Hugo Krawczyk
IBM Research
19 Skyline Drive
Hawthorne, NY 10532
USA

EMail: [email protected]

Pasi Eronen
Nokia Research Center
P.O. Box 407
FI-00045 Nokia Group
Finland

EMail: [email protected]

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