AES-SHA2 for Kerberos: AES Encryption with HMAC-SHA2 for Kerberos 5

Internet Engineering Task Force (IETF)                        M. Jenkins
Request for Comments: 8009                      National Security Agency
Category: Informational                                          M. Peck
ISSN: 2070-1721                                    The MITRE Corporation
                                                               K. Burgin
                                                            October 2016


              AES Encryption with HMAC-SHA2 for Kerberos 5

Abstract

   This document specifies two encryption types and two corresponding
   checksum types for Kerberos 5.  The new types use AES in CTS mode
   (CBC mode with ciphertext stealing) for confidentiality and HMAC with
   a SHA-2 hash for integrity.

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 7841.

   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/rfc8009.

Copyright Notice

   Copyright (c) 2016 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  2
   2.  Protocol Key Representation  . . . . . . . . . . . . . . . . .  3
   3.  Key Derivation Function  . . . . . . . . . . . . . . . . . . .  3
   4.  Key Generation from Pass Phrases . . . . . . . . . . . . . . .  4
   5.  Kerberos Algorithm Protocol Parameters . . . . . . . . . . . .  5
   6.  Checksum Parameters  . . . . . . . . . . . . . . . . . . . . .  7
   7.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . .  8
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . .  8
     8.1.  Random Values in Salt Strings  . . . . . . . . . . . . . .  9
     8.2.  Algorithm Rationale  . . . . . . . . . . . . . . . . . . .  9
   9.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     9.1.  Normative References . . . . . . . . . . . . . . . . . . . 10
     9.2.  Informative References . . . . . . . . . . . . . . . . . . 11
   Appendix A.  Test Vectors  . . . . . . . . . . . . . . . . . . . . 12
   Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . 19
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 19

1.  Introduction

   This document defines two encryption types and two corresponding
   checksum types for Kerberos 5 using AES with 128-bit or 256-bit keys.

   To avoid ciphertext expansion, we use a variation of the CBC-CS3 mode
   defined in [SP800-38A+], also referred to as ciphertext stealing or
   CTS mode.  The new types conform to the framework specified in
   [RFC3961], but do not use the simplified profile, as the simplified
   profile is not compliant with modern cryptographic best practices
   such as calculating Message Authentication Codes (MACs) over
   ciphertext rather than plaintext.

   The encryption and checksum types defined in this document are
   intended to support environments that desire to use SHA-256 or
   SHA-384 (defined in [FIPS180]) as the hash algorithm.  Differences
   between the encryption and checksum types defined in this document
   and the pre-existing Kerberos AES encryption and checksum types
   specified in [RFC3962] are:

   *  The pseudorandom function (PRF) used by PBKDF2 is HMAC-SHA-256 or
      HMAC-SHA-384.  (HMAC is defined in [RFC2104].)

   *  A key derivation function from [SP800-108] using the SHA-256 or
      SHA-384 hash algorithm is used to produce keys for encryption,
      integrity protection, and checksum operations.

   *  The HMAC is calculated over the cipher state concatenated with the
      AES output, instead of being calculated over the confounder and
      plaintext.  This allows the message receiver to verify the
      integrity of the message before decrypting the message.

   *  The HMAC algorithm uses the SHA-256 or SHA-384 hash algorithm for
      integrity protection and checksum operations.

2.  Protocol Key Representation

   The AES key space is dense, so we can use random or pseudorandom
   octet strings directly as keys.  The byte representation for the key
   is described in [FIPS197], where the first bit of the bit string is
   the high bit of the first byte of the byte string (octet string).

3.  Key Derivation Function

   We use a key derivation function from Section 5.1 of [SP800-108],
   which uses the HMAC algorithm as the PRF.

      function KDF-HMAC-SHA2(key, label, [context,] k):
         k-truncate(K1)

   where the value of K1 is computed as below.

   key: The source of entropy from which subsequent keys are derived.
   (This is known as "Ki" in [SP800-108].)

   label: An octet string describing the intended usage of the derived
   key.

   context: This parameter is optional.  An octet string containing the
   information related to the derived keying material.  This
   specification does not dictate a specific format for the context
   field.  The context field is only used by the pseudorandom function
   defined in Section 5, where it is set to the pseudorandom function's
   octet-string input parameter.  The content of the octet-string input
   parameter is defined by the application that uses it.

   k: Length in bits of the key to be outputted, expressed in big-endian
   binary representation in 4 bytes.  (This is called "L" in
   [SP800-108].)  Specifically, k=128 is represented as 0x00000080, 192
   as 0x000000C0, 256 as 0x00000100, and 384 as 0x00000180.

   When the encryption type is aes128-cts-hmac-sha256-128, k must be no
   greater than 256 bits.  When the encryption type is
   aes256-cts-hmac-sha384-192, k must be no greater than 384 bits.

   The k-truncate function is defined in Section 5.1 of [RFC3961].  It
   returns the 'k' leftmost bits of the bit-string input.

   In all computations in this document, "|" indicates concatenation.

   When the encryption type is aes128-cts-hmac-sha256-128, then K1 is
   computed as follows:

     If the context parameter is not present:
     K1 = HMAC-SHA-256(key, 0x00000001 | label | 0x00 | k)

     If the context parameter is present:
     K1 = HMAC-SHA-256(key, 0x00000001 | label | 0x00 | context | k)

   When the encryption type is aes256-cts-hmac-sha384-192, then K1 is
   computed as follows:

     If the context parameter is not present:
     K1 = HMAC-SHA-384(key, 0x00000001 | label | 0x00 | k)

     If the context parameter is present:
     K1 = HMAC-SHA-384(key, 0x00000001 | label | 0x00 | context | k)

   In the definitions of K1 above, '0x00000001' is the i parameter (the
   iteration counter) from Section 5.1 of [SP800-108].

4.  Key Generation from Pass Phrases

   As defined below, the string-to-key function uses PBKDF2 [RFC2898]
   and KDF-HMAC-SHA2 to derive the base-key from a passphrase and salt.
   The string-to-key parameter string is 4 octets indicating an unsigned
   number in big-endian order, consistent with [RFC3962], except that
   the default is decimal 32768 if the parameter is not specified.

   To ensure that different long-term base-keys are used with different
   enctypes, we prepend the enctype name to the salt, separated by a
   null byte.  The enctype-name is "aes128-cts-hmac-sha256-128" or
   "aes256-cts-hmac-sha384-192" (without the quotes).

   The user's long-term base-key is derived as follows:

      iter_count = string-to-key parameter, default is decimal 32768
      saltp = enctype-name | 0x00 | salt
      tkey = random-to-key(PBKDF2(passphrase, saltp,
                                  iter_count, keylength))
      base-key = random-to-key(KDF-HMAC-SHA2(tkey, "kerberos",
                                             keylength))

      where "kerberos" is the octet-string 0x6B65726265726F73.

   where PBKDF2 is the function of that name from RFC 2898, the
   pseudorandom function used by PBKDF2 is HMAC-SHA-256 when the enctype
   is "aes128-cts-hmac-sha256-128" and HMAC-SHA-384 when the enctype is
   "aes256-cts-hmac-sha384-192", the value for keylength is the AES key
   length (128 or 256 bits), and the algorithm KDF-HMAC-SHA2 is defined
   in Section 3.

5.  Kerberos Algorithm Protocol Parameters

   The cipher state defined in RFC 3961 that maintains cryptographic
   state across different encryption operations using the same key is
   used as the formal initialization vector (IV) input into CBC-CS3.
   The plaintext is prepended with a 16-octet random value generated by
   the message originator, known as a confounder.

   The ciphertext is a concatenation of the output of AES in CBC-CS3
   mode and the HMAC of the cipher state concatenated with the AES
   output.  The HMAC is computed using either SHA-256 or SHA-384
   depending on the encryption type.  The output of HMAC-SHA-256 is
   truncated to 128 bits, and the output of HMAC-SHA-384 is truncated to
   192 bits.  Sample test vectors are given in Appendix A.

   Decryption is performed by removing the HMAC, verifying the HMAC
   against the cipher state concatenated with the ciphertext, and then
   decrypting the ciphertext if the HMAC is correct.  Finally, the first
   16 octets of the decryption output (the confounder) is discarded, and
   the remainder is returned as the plaintext decryption output.

   The following parameters apply to the encryption types
   aes128-cts-hmac-sha256-128 and aes256-cts-hmac-sha384-192.

   protocol key format: as defined in Section 2.

   specific key structure: three derived keys: { Kc, Ke, Ki }.

   Kc: the checksum key, inputted into HMAC to provide the checksum
   mechanism defined in Section 6.

   Ke: the encryption key, inputted into AES encryption and decryption
   as defined in "encryption function" and "decryption function" below.

   Ki: the integrity key, inputted into HMAC to provide authenticated
   encryption as defined in "encryption function" and "decryption
   function" below.

   required checksum mechanism: as defined in Section 6.

   key-generation seed length: key size (128 or 256 bits).

   string-to-key function: as defined in Section 4.

   default string-to-key parameters: iteration count of decimal 32768.

   random-to-key function: identity function.

   key-derivation function: KDF-HMAC-SHA2 as defined in Section 3.  The
   key usage number is expressed as 4 octets in big-endian order.

   If the enctype is aes128-cts-hmac-sha256-128:
   Kc = KDF-HMAC-SHA2(base-key, usage | 0x99, 128)
   Ke = KDF-HMAC-SHA2(base-key, usage | 0xAA, 128)
   Ki = KDF-HMAC-SHA2(base-key, usage | 0x55, 128)

   If the enctype is aes256-cts-hmac-sha384-192:
   Kc = KDF-HMAC-SHA2(base-key, usage | 0x99, 192)
   Ke = KDF-HMAC-SHA2(base-key, usage | 0xAA, 256)
   Ki = KDF-HMAC-SHA2(base-key, usage | 0x55, 192)

   cipher state: a 128-bit CBC initialization vector derived from a
   previous ciphertext (if any) using the same encryption key, as
   specified below.

   initial cipher state: all bits zero.

   encryption function: as follows, where E() is AES encryption in
   CBC-CS3 mode, and h is the size of truncated HMAC (128 bits or 192
   bits as described above).

      N = random value of length 128 bits (the AES block size)
      IV = cipher state
      C = E(Ke, N | plaintext, IV)
      H = HMAC(Ki, IV | C)
      ciphertext = C | H[1..h]
      Steps to compute the 128-bit cipher state:
         L = length of C in bits
         portion C into 128-bit blocks, placing any remainder of less
         than 128 bits into a final block
         if L == 128: cipher state = C
         else if L mod 128 > 0: cipher state = last full (128-bit) block
                                             of C (the next-to-last
                                             block)
         else if L mod 128 == 0: cipher state = next-to-last block of C

         (Note that L will never be less than 128 because of the
         presence of N in the encryption input.)

   decryption function: as follows, where D() is AES decryption in
   CBC-CS3 mode, and h is the size of truncated HMAC.

      (C, H) = ciphertext
          (Note: H is the last h bits of the ciphertext.)
      IV = cipher state
      if H != HMAC(Ki, IV | C)[1..h]
          stop, report error
      (N, P) = D(Ke, C, IV)

      (Note: N is set to the first block of the decryption output; P is
      set to the rest of the output.)

      cipher state = same as described above in encryption function

   pseudorandom function:
      If the enctype is aes128-cts-hmac-sha256-128:
      PRF = KDF-HMAC-SHA2(input-key, "prf", octet-string, 256)

      If the enctype is aes256-cts-hmac-sha384-192:
      PRF = KDF-HMAC-SHA2(input-key, "prf", octet-string, 384)

      where "prf" is the octet-string 0x707266

6.  Checksum Parameters

   The following parameters apply to the checksum types
   hmac-sha256-128-aes128 and hmac-sha384-192-aes256, which are the
   associated checksums for aes128-cts-hmac-sha256-128 and
   aes256-cts-hmac-sha384-192, respectively.

   associated cryptosystem: aes128-cts-hmac-sha256-128 or
   aes256-cts-hmac-sha384-192 as appropriate.

   get_mic: HMAC(Kc, message)[1..h].
      where h is 128 bits for checksum type hmac-sha256-128-aes128 and
      192 bits for checksum type hmac-sha384-192-aes256

   verify_mic: get_mic and compare.

7.  IANA Considerations

   IANA has assigned encryption type numbers as follows in the "Kerberos
   Encryption Type Numbers" registry.

      etype   encryption type              Reference
      -----   ---------------              ---------
      19      aes128-cts-hmac-sha256-128   RFC 8009
      20      aes256-cts-hmac-sha384-192   RFC 8009

   IANA has assigned checksum type numbers as follows in the "Kerberos
   Checksum Type Numbers" registry.

      sumtype   Checksum type            checksum  Reference
      value                              size
      -------   -------------            --------  ---------
      19        hmac-sha256-128-aes128   16        RFC 8009
      20        hmac-sha384-192-aes256   24        RFC 8009

8.  Security Considerations

   This specification requires implementations to generate random
   values.  The use of inadequate pseudorandom number generators (PRNGs)
   can result in little or no security.  The generation of quality
   random numbers is difficult.  [RFC4086] offers guidance on random
   number generation.

   This document specifies a mechanism for generating keys from
   passphrases or passwords.  The use of PBKDF2, a salt, and a large
   iteration count adds some resistance to offline dictionary attacks by
   passive eavesdroppers.  Salting prevents "rainbow table" attacks,
   while large iteration counts slow password-guess attempts.
   Nonetheless, computing power continues to rapidly improve, including
   the potential for use of graphics processing units (GPUs) in
   password-guess attempts.  It is important to choose strong
   passphrases.  Use of Kerberos extensions that protect against offline
   dictionary attacks should also be considered, as should the use of
   public key cryptography for initial Kerberos authentication [RFC4556]
   to eliminate the use of passwords or passphrases within the Kerberos
   protocol.

   The NIST guidance in Section 5.3 of [SP800-38A], requiring that CBC
   initialization vectors be unpredictable, is satisfied by the use of a
   random confounder as the first block of plaintext.  The confounder
   fills the cryptographic role typically played by an initialization
   vector.  This approach was chosen to align with other Kerberos
   cryptosystem approaches.

8.1.  Random Values in Salt Strings

   The NIST guidance in Section 5.1 of [SP800-132] requires at least 128
   bits of the salt to be randomly generated.  The string-to-key
   function as defined in [RFC3961] requires the salt to be valid UTF-8
   strings [RFC3629].  Not every 128-bit random string will be valid
   UTF-8, so a UTF-8-compatible encoding would be needed to encapsulate
   the random bits.  However, using a salt containing a random portion
   may have the following issues with some implementations:

   *  Keys for cross-realm krbtgt services [RFC4120] are typically
      managed by entering the same password at two Key Distribution
      Centers (KDCs) to get the same keys.  If each KDC uses a random
      salt, they won't have the same keys.

   *  Random salts may interfere with checking of password history.

8.2.  Algorithm Rationale

   This document has been written to be consistent with common
   implementations of AES and SHA-2.  The encryption and hash algorithm
   sizes have been chosen to create a consistent level of protection,
   with consideration to implementation efficiencies.  So, for instance,
   SHA-384, which would normally be matched to AES-192, is instead
   matched to AES-256 to leverage the fact that there are efficient
   hardware implementations of AES-256.  Note that, as indicated by the
   enc-type name "aes256-cts-hmac-sha384-192", the truncation of the
   HMAC-SHA-384 output to 192 bits results in an overall 192-bit level
   of security.

9.  References

9.1.  Normative References

   [FIPS180]    National Institute of Standards and Technology, "Secure
                Hash Standard", FIPS PUB 180-4,
                DOI 10.6028/NIST.FIPS.180-4, August 2015.

   [FIPS197]    National Institute of Standards and Technology,
                "Advanced Encryption Standard (AES)", FIPS PUB 197,
                November 2001.

   [RFC2104]    Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
                Hashing for Message Authentication", RFC 2104,
                DOI 10.17487/RFC2104, February 1997,
                <http://www.rfc-editor.org/info/rfc2104>.

   [RFC2898]    Kaliski, B., "PKCS #5: Password-Based Cryptography
                Specification Version 2.0", RFC 2898,
                DOI 10.17487/RFC2898, September 2000,
                <http://www.rfc-editor.org/info/rfc2898>.

   [RFC3629]    Yergeau, F., "UTF-8, a transformation format of ISO
                10646", STD 63, RFC 3629, DOI 10.17487/RFC3629, November
                2003, <http://www.rfc-editor.org/info/rfc3629>.

   [RFC3961]    Raeburn, K., "Encryption and Checksum Specifications for
                Kerberos 5", RFC 3961, DOI 10.17487/RFC3961, February
                2005, <http://www.rfc-editor.org/info/rfc3961>.

   [RFC3962]    Raeburn, K., "Advanced Encryption Standard (AES)
                Encryption for Kerberos 5", RFC 3962,
                DOI 10.17487/RFC3962, February 2005,
                <http://www.rfc-editor.org/info/rfc3962>.

   [SP800-38A+] National Institute of Standards and Technology,
                "Recommendation for Block Cipher Modes of Operation:
                Three Variants of Ciphertext Stealing for CBC Mode",
                NIST Special Publication 800-38A Addendum, October 2010.

   [SP800-108]  National Institute of Standards and Technology,
                "Recommendation for Key Derivation Using Pseudorandom
                Functions", NIST Special Publication 800-108, October
                2009.

9.2.  Informative References

   [RFC4086]    Eastlake 3rd, D., Schiller, J., and S. Crocker,
                "Randomness Requirements for Security", BCP 106,
                RFC 4086, DOI 10.17487/RFC4086, June 2005,
                <http://www.rfc-editor.org/info/rfc4086>.

   [RFC4120]    Neuman, C., Yu, T., Hartman, S., and K. Raeburn, "The
                Kerberos Network Authentication Service (V5)", RFC 4120,
                DOI 10.17487/RFC4120, July 2005,
                <http://www.rfc-editor.org/info/rfc4120>.

   [RFC4556]    Zhu, L. and B. Tung, "Public Key Cryptography for
                Initial Authentication in Kerberos (PKINIT)", RFC 4556,
                DOI 10.17487/RFC4556, June 2006,
                <http://www.rfc-editor.org/info/rfc4556>.

   [SP800-38A]  National Institute of Standards and Technology,
                "Recommendation for Block Cipher Modes of Operation:
                Methods and Techniques", NIST Special Publication
                800-38A, December 2001.

   [SP800-132]  National Institute of Standards and Technology,
                "Recommendation for Password-Based Key Derivation, Part
                1: Storage Applications", NIST Special Publication
                800-132, June 2010.

Appendix A.  Test Vectors

   Sample results for string-to-key conversion:
   --------------------------------------------

   Iteration count = 32768
   Pass phrase = "password"
   Saltp for creating 128-bit base-key:
      61 65 73 31 32 38 2D 63 74 73 2D 68 6D 61 63 2D
      73 68 61 32 35 36 2D 31 32 38 00 10 DF 9D D7 83
      E5 BC 8A CE A1 73 0E 74 35 5F 61 41 54 48 45 4E
      41 2E 4D 49 54 2E 45 44 55 72 61 65 62 75 72 6E

   (The saltp is "aes128-cts-hmac-sha256-128" | 0x00 |
    random 16-byte valid UTF-8 sequence | "ATHENA.MIT.EDUraeburn")
   128-bit base-key:
      08 9B CA 48 B1 05 EA 6E A7 7C A5 D2 F3 9D C5 E7

   Saltp for creating 256-bit base-key:
      61 65 73 32 35 36 2D 63 74 73 2D 68 6D 61 63 2D
      73 68 61 33 38 34 2D 31 39 32 00 10 DF 9D D7 83
      E5 BC 8A CE A1 73 0E 74 35 5F 61 41 54 48 45 4E
      41 2E 4D 49 54 2E 45 44 55 72 61 65 62 75 72 6E
   (The saltp is "aes256-cts-hmac-sha384-192" | 0x00 |
    random 16-byte valid UTF-8 sequence | "ATHENA.MIT.EDUraeburn")
   256-bit base-key:
      45 BD 80 6D BF 6A 83 3A 9C FF C1 C9 45 89 A2 22
      36 7A 79 BC 21 C4 13 71 89 06 E9 F5 78 A7 84 67
   Sample results for key derivation:
   ----------------------------------

   enctype aes128-cts-hmac-sha256-128:
   128-bit base-key:
      37 05 D9 60 80 C1 77 28 A0 E8 00 EA B6 E0 D2 3C
   Kc value for key usage 2 (label = 0x0000000299):
      B3 1A 01 8A 48 F5 47 76 F4 03 E9 A3 96 32 5D C3
   Ke value for key usage 2 (label = 0x00000002AA):
      9B 19 7D D1 E8 C5 60 9D 6E 67 C3 E3 7C 62 C7 2E
   Ki value for key usage 2 (label = 0x0000000255):
      9F DA 0E 56 AB 2D 85 E1 56 9A 68 86 96 C2 6A 6C

   enctype aes256-cts-hmac-sha384-192:
   256-bit base-key:
      6D 40 4D 37 FA F7 9F 9D F0 D3 35 68 D3 20 66 98
      00 EB 48 36 47 2E A8 A0 26 D1 6B 71 82 46 0C 52
   Kc value for key usage 2 (label = 0x0000000299):
      EF 57 18 BE 86 CC 84 96 3D 8B BB 50 31 E9 F5 C4
      BA 41 F2 8F AF 69 E7 3D
   Ke value for key usage 2 (label = 0x00000002AA):
      56 AB 22 BE E6 3D 82 D7 BC 52 27 F6 77 3F 8E A7
      A5 EB 1C 82 51 60 C3 83 12 98 0C 44 2E 5C 7E 49
   Ki value for key usage 2 (label = 0x0000000255):
      69 B1 65 14 E3 CD 8E 56 B8 20 10 D5 C7 30 12 B6
      22 C4 D0 0F FC 23 ED 1F
   Sample encryptions (all using the default cipher state):
   --------------------------------------------------------

   These sample encryptions use the above sample key derivation results,
   including use of the same base-key and key usage values.

   The following test vectors are for
   enctype aes128-cts-hmac-sha256-128:

   Plaintext: (empty)
   Confounder:
      7E 58 95 EA F2 67 24 35 BA D8 17 F5 45 A3 71 48
   128-bit AES key (Ke):
      9B 19 7D D1 E8 C5 60 9D 6E 67 C3 E3 7C 62 C7 2E
   128-bit HMAC key (Ki):
      9F DA 0E 56 AB 2D 85 E1 56 9A 68 86 96 C2 6A 6C
   AES Output:
      EF 85 FB 89 0B B8 47 2F 4D AB 20 39 4D CA 78 1D
   Truncated HMAC Output:
      AD 87 7E DA 39 D5 0C 87 0C 0D 5A 0A 8E 48 C7 18
   Ciphertext (AES Output | HMAC Output):
      EF 85 FB 89 0B B8 47 2F 4D AB 20 39 4D CA 78 1D
      AD 87 7E DA 39 D5 0C 87 0C 0D 5A 0A 8E 48 C7 18

   Plaintext: (length less than block size)
      00 01 02 03 04 05
   Confounder:
      7B CA 28 5E 2F D4 13 0F B5 5B 1A 5C 83 BC 5B 24
   128-bit AES key (Ke):
      9B 19 7D D1 E8 C5 60 9D 6E 67 C3 E3 7C 62 C7 2E
   128-bit HMAC key (Ki):
      9F DA 0E 56 AB 2D 85 E1 56 9A 68 86 96 C2 6A 6C
   AES Output:
      84 D7 F3 07 54 ED 98 7B AB 0B F3 50 6B EB 09 CF
      B5 54 02 CE F7 E6
   Truncated HMAC Output:
      87 7C E9 9E 24 7E 52 D1 6E D4 42 1D FD F8 97 6C
   Ciphertext:
      84 D7 F3 07 54 ED 98 7B AB 0B F3 50 6B EB 09 CF
      B5 54 02 CE F7 E6 87 7C E9 9E 24 7E 52 D1 6E D4
      42 1D FD F8 97 6C
   Plaintext: (length equals block size)
      00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   Confounder:
      56 AB 21 71 3F F6 2C 0A 14 57 20 0F 6F A9 94 8F
   128-bit AES key (Ke):
      9B 19 7D D1 E8 C5 60 9D 6E 67 C3 E3 7C 62 C7 2E
   128-bit HMAC key (Ki):
      9F DA 0E 56 AB 2D 85 E1 56 9A 68 86 96 C2 6A 6C
   AES Output:
      35 17 D6 40 F5 0D DC 8A D3 62 87 22 B3 56 9D 2A
      E0 74 93 FA 82 63 25 40 80 EA 65 C1 00 8E 8F C2
   Truncated HMAC Output:
      95 FB 48 52 E7 D8 3E 1E 7C 48 C3 7E EB E6 B0 D3
   Ciphertext:
      35 17 D6 40 F5 0D DC 8A D3 62 87 22 B3 56 9D 2A
      E0 74 93 FA 82 63 25 40 80 EA 65 C1 00 8E 8F C2
      95 FB 48 52 E7 D8 3E 1E 7C 48 C3 7E EB E6 B0 D3

   Plaintext: (length greater than block size)
      00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
      10 11 12 13 14
   Confounder:
      A7 A4 E2 9A 47 28 CE 10 66 4F B6 4E 49 AD 3F AC
   128-bit AES key (Ke):
      9B 19 7D D1 E8 C5 60 9D 6E 67 C3 E3 7C 62 C7 2E
   128-bit HMAC key (Ki):
      9F DA 0E 56 AB 2D 85 E1 56 9A 68 86 96 C2 6A 6C
   AES Output:
      72 0F 73 B1 8D 98 59 CD 6C CB 43 46 11 5C D3 36
      C7 0F 58 ED C0 C4 43 7C 55 73 54 4C 31 C8 13 BC
      E1 E6 D0 72 C1
   Truncated HMAC Output:
      86 B3 9A 41 3C 2F 92 CA 9B 83 34 A2 87 FF CB FC
   Ciphertext:
      72 0F 73 B1 8D 98 59 CD 6C CB 43 46 11 5C D3 36
      C7 0F 58 ED C0 C4 43 7C 55 73 54 4C 31 C8 13 BC
      E1 E6 D0 72 C1 86 B3 9A 41 3C 2F 92 CA 9B 83 34
      A2 87 FF CB FC
   The following test vectors are for enctype
   aes256-cts-hmac-sha384-192:

   Plaintext: (empty)
   Confounder:
      F7 64 E9 FA 15 C2 76 47 8B 2C 7D 0C 4E 5F 58 E4
   256-bit AES key (Ke):
      56 AB 22 BE E6 3D 82 D7 BC 52 27 F6 77 3F 8E A7
      A5 EB 1C 82 51 60 C3 83 12 98 0C 44 2E 5C 7E 49
   192-bit HMAC key (Ki):
      69 B1 65 14 E3 CD 8E 56 B8 20 10 D5 C7 30 12 B6
      22 C4 D0 0F FC 23 ED 1F
   AES Output:
      41 F5 3F A5 BF E7 02 6D 91 FA F9 BE 95 91 95 A0
   Truncated HMAC Output:
      58 70 72 73 A9 6A 40 F0 A0 19 60 62 1A C6 12 74
      8B 9B BF BE 7E B4 CE 3C
   Ciphertext:
      41 F5 3F A5 BF E7 02 6D 91 FA F9 BE 95 91 95 A0
      58 70 72 73 A9 6A 40 F0 A0 19 60 62 1A C6 12 74
      8B 9B BF BE 7E B4 CE 3C

   Plaintext: (length less than block size)
      00 01 02 03 04 05
   Confounder:
      B8 0D 32 51 C1 F6 47 14 94 25 6F FE 71 2D 0B 9A
   256-bit AES key (Ke):
      56 AB 22 BE E6 3D 82 D7 BC 52 27 F6 77 3F 8E A7
      A5 EB 1C 82 51 60 C3 83 12 98 0C 44 2E 5C 7E 49
   192-bit HMAC key (Ki):
      69 B1 65 14 E3 CD 8E 56 B8 20 10 D5 C7 30 12 B6
      22 C4 D0 0F FC 23 ED 1F
   AES Output:
      4E D7 B3 7C 2B CA C8 F7 4F 23 C1 CF 07 E6 2B C7
      B7 5F B3 F6 37 B9
   Truncated HMAC Output:
      F5 59 C7 F6 64 F6 9E AB 7B 60 92 23 75 26 EA 0D
      1F 61 CB 20 D6 9D 10 F2
   Ciphertext:
      4E D7 B3 7C 2B CA C8 F7 4F 23 C1 CF 07 E6 2B C7
      B7 5F B3 F6 37 B9 F5 59 C7 F6 64 F6 9E AB 7B 60
      92 23 75 26 EA 0D 1F 61 CB 20 D6 9D 10 F2
   Plaintext: (length equals block size)
      00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   Confounder:
      53 BF 8A 0D 10 52 65 D4 E2 76 42 86 24 CE 5E 63
   256-bit AES key (Ke):
      56 AB 22 BE E6 3D 82 D7 BC 52 27 F6 77 3F 8E A7
      A5 EB 1C 82 51 60 C3 83 12 98 0C 44 2E 5C 7E 49
   192-bit HMAC key (Ki):
      69 B1 65 14 E3 CD 8E 56 B8 20 10 D5 C7 30 12 B6
      22 C4 D0 0F FC 23 ED 1F
   AES Output:
      BC 47 FF EC 79 98 EB 91 E8 11 5C F8 D1 9D AC 4B
      BB E2 E1 63 E8 7D D3 7F 49 BE CA 92 02 77 64 F6
   Truncated HMAC Output:
      8C F5 1F 14 D7 98 C2 27 3F 35 DF 57 4D 1F 93 2E
      40 C4 FF 25 5B 36 A2 66
   Ciphertext:
      BC 47 FF EC 79 98 EB 91 E8 11 5C F8 D1 9D AC 4B
      BB E2 E1 63 E8 7D D3 7F 49 BE CA 92 02 77 64 F6
      8C F5 1F 14 D7 98 C2 27 3F 35 DF 57 4D 1F 93 2E
      40 C4 FF 25 5B 36 A2 66

   Plaintext: (length greater than block size)
      00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
      10 11 12 13 14
   Confounder:
      76 3E 65 36 7E 86 4F 02 F5 51 53 C7 E3 B5 8A F1
   256-bit AES key (Ke):
      56 AB 22 BE E6 3D 82 D7 BC 52 27 F6 77 3F 8E A7
      A5 EB 1C 82 51 60 C3 83 12 98 0C 44 2E 5C 7E 49
   192-bit HMAC key (Ki):
      69 B1 65 14 E3 CD 8E 56 B8 20 10 D5 C7 30 12 B6
      22 C4 D0 0F FC 23 ED 1F
   AES Output:
      40 01 3E 2D F5 8E 87 51 95 7D 28 78 BC D2 D6 FE
      10 1C CF D5 56 CB 1E AE 79 DB 3C 3E E8 64 29 F2
      B2 A6 02 AC 86
   Truncated HMAC Output:
      FE F6 EC B6 47 D6 29 5F AE 07 7A 1F EB 51 75 08
      D2 C1 6B 41 92 E0 1F 62
   Ciphertext:
      40 01 3E 2D F5 8E 87 51 95 7D 28 78 BC D2 D6 FE
      10 1C CF D5 56 CB 1E AE 79 DB 3C 3E E8 64 29 F2
      B2 A6 02 AC 86 FE F6 EC B6 47 D6 29 5F AE 07 7A
      1F EB 51 75 08 D2 C1 6B 41 92 E0 1F 62
   Sample checksums:
   -----------------

   These sample checksums use the above sample key derivation results,
   including use of the same base-key and key usage values.

   Checksum type: hmac-sha256-128-aes128
   128-bit HMAC key (Kc):
      B3 1A 01 8A 48 F5 47 76 F4 03 E9 A3 96 32 5D C3
   Plaintext:
      00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
      10 11 12 13 14
   Checksum:
      D7 83 67 18 66 43 D6 7B 41 1C BA 91 39 FC 1D EE

   Checksum type: hmac-sha384-192-aes256
   192-bit HMAC key (Kc):
      EF 57 18 BE 86 CC 84 96 3D 8B BB 50 31 E9 F5 C4
      BA 41 F2 8F AF 69 E7 3D
   Plaintext:
      00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
      10 11 12 13 14
   Checksum:
      45 EE 79 15 67 EE FC A3 7F 4A C1 E0 22 2D E8 0D
      43 C3 BF A0 66 99 67 2A
   Sample pseudorandom function (PRF) invocations:
   -----------------------------------------------

   PRF input octet-string: "test" (0x74657374)

   enctype aes128-cts-hmac-sha256-128:
   input-key value / HMAC-SHA-256 key:
      37 05 D9 60 80 C1 77 28 A0 E8 00 EA B6 E0 D2 3C
   HMAC-SHA-256 input message:
      00 00 00 01 70 72 66 00 74 65 73 74 00 00 01 00
   PRF output:
      9D 18 86 16 F6 38 52 FE 86 91 5B B8 40 B4 A8 86
      FF 3E 6B B0 F8 19 B4 9B 89 33 93 D3 93 85 42 95

   enctype aes256-cts-hmac-sha384-192:
   input-key value / HMAC-SHA-384 key:
      6D 40 4D 37 FA F7 9F 9D F0 D3 35 68 D3 20 66 98
      00 EB 48 36 47 2E A8 A0 26 D1 6B 71 82 46 0C 52
   HMAC-SHA-384 input message:
      00 00 00 01 70 72 66 00 74 65 73 74 00 00 01 80
   PRF output:
      98 01 F6 9A 36 8C 2B F6 75 E5 95 21 E1 77 D9 A0
      7F 67 EF E1 CF DE 8D 3C 8D 6F 6A 02 56 E3 B1 7D
      B3 C1 B6 2A D1 B8 55 33 60 D1 73 67 EB 15 14 D2

Acknowledgements

   Kelley Burgin was employed at the National Security Agency during
   much of the work on this document.

Authors' Addresses

   Michael J. Jenkins
   National Security Agency

   Email: mjjenki@tycho.ncsc.mil


   Michael A. Peck
   The MITRE Corporation

   Email: mpeck@mitre.org


   Kelley W. Burgin

   Email: kelley.burgin@gmail.com