HMAC-based Extract-and-Expand Key Derivation Function (HKDF)
RFC 5869

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.

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   described in the Simplified BSD License.

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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 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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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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   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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   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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   [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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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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Authors' Addresses

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

   EMail: hugokraw@us.ibm.com

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

   EMail: pasi.eronen@nokia.com

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