Network Working Group                                          K. Burgin                                         M. Jenkins
Internet Draft                                  National Security Agency
Intended Status: Informational                                   M. Peck
Expires: December 30, 2013 November 7, 2014                          The MITRE Corporation
                                                           June 28, 2013
                                                               K. Burgin
                                                             May 6, 2014

              AES Encryption with HMAC-SHA2 for Kerberos 5
                 draft-ietf-kitten-aes-cts-hmac-sha2-01
                 draft-ietf-kitten-aes-cts-hmac-sha2-02

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 Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on December 30, 2013. January 20, 2014.

Copyright and License Notice

   Copyright (c) 2013 2014 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
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   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.

Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Protocol Key Representation  . . . . . . . . . . . . . . . . .  3
   3.  Key Generation from Pass Phrases Derivation Function  . . . . . . . . . . . . . . .  3
   4.  Key Derivation Function . . . .  3
   4.  Key Generation from Pass Phrases . . . . . . . . . . . . . . .  4
   5.  Kerberos Algorithm Protocol Parameters . . . . . . . . . . . .  5
   6.  Checksum Parameters  . . . . . . . . . . . . . . . . . . . . .  8  6
   7.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . .  9  7
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . .  9  7
     8.1.  Random Values in Salt Strings  . . . . . . . . . . . . . .  9  7
   9.  References  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . .  8
   10.  References  . . . 10
     9.1. . . . . . . . . . . . . . . . . . . . . . .  8
     10.1.  Normative References  . . . . . . . . . . . . . . . . . . . 10
     9.2.  8
     10.2.  Informative References  . . . . . . . . . . . . . . . . . . 10  8
   Appendix A.  Test Vectors  . . . . . . . . . . . . . . . . . . . . 11  9
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 15

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 variant to CBC mode
   defined in [SP800-38A+] (this mode is [SP800-38A+], also referred to as CTS). ciphertext stealing or
   CTS mode.  The new types conform to the framework specified in
   [RFC3961], but do not use the simplified profile.

   Note that [SP800-38A+] requires the plaintext length to be greater
   than the block size, so the encryption types have two cases.

   The encryption and checksum types defined in this document are
   intended to support NSA's Suite B Profile for Kerberos [suiteb-
   kerberos] which requires the environments that desire to use of SHA-256 or SHA-384 SHA-
   384 as the hash algorithm.  Differences between the encryption and
   checksum types defined in this document and existing the pre-existing Kerberos
   AES encryption and checksum types specified in [RFC3962] are:

   *  The pseudorandom function used by PBKDF2 is HMAC-SHA-256 or HMAC-
      SHA-384.

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

   *  The IV used during content encryption is sent as part of the
      ciphertext, instead of using a confounder. This saves one
      encryption and decryption operation per message.

   *  The HMAC is calculated over the cipherstate 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 Generation from Pass Phrases

   The pseudorandom Derivation Function

   We use a key derivation function used by PBKDF2 will be the SHA-256 or SHA-
   384 HMAC from Section 5.1 of [SP800-108]
   which uses the passphrase and salt. If the enctype is "aes128-cts-
   hmac-sha256-128", then HMAC-SHA-256 is used HMAC algorithm as the PRF.  If the
   enctype is "aes256-cts-hmac-sha384-192", then HMAC-SHA-384  The counter i is used expressed
   as
   the PRF. four octets in big-endian order.  The final key derivation step uses length of the algorithm KDF-HMAC-SHA2
   defined below output key in Section 4.

   If no string-to-key parameters are specified, the default number of
   iterations
   bits (denoted as k) is raised to 32,768.

   To ensure that different long-term keys are used with different
   enctypes, we prepend the enctype name to the salt string, 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 key is derived as follows

     saltp = enctype-name | 0x00 | salt
     tkey = random-to-key(PBKDF2(passphrase, saltp,
                              iter_count, keylength))
     key = KDF-HMAC-SHA2(tkey, "kerberos") where "kerberos" is the
           byte string {0x6b65726265726f73}.

   where 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, and the algorithm KDF-HMAC-SHA2 is defined in
   Section 4.

4.  Key Derivation Function

   We use a key derivation function from Section 5.1 of [SP800-108]
   which uses the HMAC algorithm as the PRF.  The counter i is expressed
   as four octets in big-endian order.  The length of the output key in
   bits (denoted as k) is also represented as four octets in big-endian
   order.  The "Label" input also represented as four octets in big-endian
   order.  The "Label" input to the KDF is the usage constant supplied
   to the key derivation function, and the "Context" input is null.
   Each application of the KDF only requires a single iteration of the
   PRF, so n = 1 in the notation of [SP800-108].

   In the following summary, | indicates concatenation.  The random-to-
   key function is the identity function, as defined in Section 3. function.  The k-truncate function is
   defined in [RFC3961], Section 5.1.

   When the encryption type is aes128-cts-hmac-sha256-128, the output
   key length k is 128 bits for all applications of KDF-HMAC-SHA2(key,
   constant) which is computed as follows:

     K1 = HMAC-SHA-256(key, 00 00 00 01 | constant | 0x00 00 | 00 00 00 80)
     KDF-HMAC-SHA2(key, constant) = random-to-key(k-truncate(K1))

   When the encryption type is aes256-cts-hmac-sha384-192, the output
   key length k is 256 bits when computing deriving the base-key (from a
   passphrase as described in Section 4) and Ke, and the output key
   length k is 192 bits when deriving Kc and Ki.  KDF-HMAC-
   SHA2(key,  KDF-HMAC-SHA2(key,
   constant) is computed as follows:

     If deriving Kc or Ki (the constant ends with 0x99 or 0x55):
     k = 192
     K1 = HMAC-SHA-384(key, 00 00 00 01 | constant | 0x00 00 | 00 00 00 C0)
     KDF-HMAC-SHA2(key, constant) = random-to-key(k-truncate(K1))

     Otherwise (if deriving Ke or

     If deriving the base-key from a
                passphrase as described in Section 3): (the constant is "kerberos", the byte
     string 0x6B65726265726F73) or Ke (the constant ends with 0xAA):
     k = 256
     K1 = HMAC-SHA-384(key, 00 00 00 01 | constant | 0x00 00 | 00 00 01 00)
     KDF-HMAC-SHA2(key, constant) = random-to-key(k-truncate(K1))

   The constants

4.  Key Generation from Pass Phrases

     PBKDF2 [RFC2898] is used for key derivation to derive the base-key from a passphrase
     and salt.

     If no string-to-key parameters are specified, the same as those default number of
     iterations is 32,768.

     To ensure that different long-term base-keys are used in with
     different enctypes, we prepend the simplified profile.

5.  Kerberos Algorithm Protocol Parameters

   In cases where enctype name to the plaintext length salt,
     separated by a null byte.  The enctype-name is greater than "aes128-cts-hmac-
     sha256-128" or "aes256-cts-hmac-sha384-192" (without the block size:

      Each encryption will use a 16-octet nonce generated at random quotes).
     The user's long-term base-key is derived as follows

     saltp = enctype-name | 0x00 | salt
     tkey = random-to-key(PBKDF2(passphrase, saltp,
                              iter_count, keylength))
     base-key = KDF-HMAC-SHA2(tkey, "kerberos") where "kerberos" is the
                byte string {0x6B65726265726F73}.

   where the pseudorandom function used by PBKDF2 is HMAC-SHA-256 when
   the message originator. 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 cipherstate is used as the formal initialization vector (IV) used by
      AES
   input into CBC-CS3.  The plaintext is obtained by xoring the prepended with a 16-octet
   random nonce with generated by the cipherstate. message originator, known as a
   confounder.

   The ciphertext is the a concatenation of the random nonce, the output of AES in CBC-CS3 mode,
   mode and the HMAC of the nonce cipherstate concatenated with the AES
   output.  The HMAC is computed using either SHA-256 or SHA-384. SHA-384
   depending on the encryption type.  The output of SHA-256 HMAC-SHA-256 is
   truncated to 128 bits and the output of SHA-384 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 remainder, cipherstate concatenated with the ciphertext, and then
   decrypting the remainder ciphertext if the HMAC is correct.

   In cases where the plaintext length is less than or equal to the
   block size, a different algorithm is specified.

      Each encryption will use a 16-octet nonce generated at random by
      the message originator.  The initialization vector (IV) used by
      AES is obtained by xoring  Finally, the random nonce with first
   16 octets of the cipherstate.

      The plaintext decryption output (the confounder) is padded with zeros so the length of discarded, and
   the result remainder is
      one block length (no zeros are added if returned as the plaintext length
      equals the block length). decryption output.

   The padded plaintext is xored with following parameters apply to the
      IV, then encrypted using AES in ECB mode.  The output of AES is
      split into two parts, so that the length of the first part equals
      the length of the unpadded plaintext.  The nonce is also split
      into two parts, so that the length of the first part equals the
      length of the unpadded plaintext.

      The ciphertext is the concatenation of the first part of the
      random nonce, the second part of the AES output followed by the
      first part of the AES output, and the HMAC of the concatenation of
      the first part of the random nonce, the second part of the AES
      output followed by the first part of the AES output.  The HMAC is
      computed using either SHA-256 or SHA-384.  The output of SHA-256
      is truncated to 128 bits and the output of SHA-384 is truncated to
      192 bits. Sample test vectors are given in Appendix A.

      Decryption is performed by first removing the HMAC, and verifying
      the HMAC against the remainder.  If the HMAC is correct, separate
      the remainder into N' and C' by taking the first 16 bytes as N',
      and the following bytes as C'.  Split N' into two parts, so that
      the length of the first part equals the length of C'.  Decrypt the
      concatenation of C' with the second part of N' using ECB mode to
      get a value P' whose length is one block length.  The nonce is
      recovered by taking the concatenation of the first part of N' with
      the second part of P' xored with the cipherState (where again, the
      length of the first part equals the length of C').  The IV is
      recovered as the nonce xored with cipherState, and the plaintext
      is recovered as the first part of P' xored with the IV.

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

   protocol key format: as defined 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 protocol-format keys: { Kc, Ke, Ki }.

   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 3. 4.

   default string-to-key parameters: 00 00 80 00.

   random-to-key function: identity function.

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

   Kc = KDF-HMAC-SHA2(base-key, usage | 0x99)
   Ke = KDF-HMAC-SHA2(base-key, usage | 0xAA)
   Ki = KDF-HMAC-SHA2(base-key, usage | 0x55)

   cipherState:

   cipherstate: a 128-bit random nonce. CBC initialization vector.

   initial cipherState: cipherstate: all bits zero.

   encryption function: as follows.  When the plaintext length is
   greater than the block size, CTS mode follows, where E() is used. When the plaintext AES encryption in
   CBC-CS3 mode, h is less than or equal to the block size, ECB mode is used.

   h = size of truncated HMAC
   E() = encryption function
   D() = decryption function HMAC, and c = block size of is the encryption algorithm
   L(x) = length of x
   < = less-than operator; true == 1, false == 0
   zeroblock = one AES
   block (length c) of zeros
   o[start:len] = sub-string operation returning the substring of
                  length len of string o starting at byte start
                  (zero-based)

   encryption function: size.

      N = random nonce of length 128 bits c (128 bits)
      IV = N XOR cipherState
      if (L(P) > c)
          PC = 0
          P' = P cipherstate
      C = E(Ke, P', IV)
              // using CBC-CS3-Encrypt defined
              // in [SP800-38A+]
          N' = N
          C' = C
      else
          PC = c - L(P)
          P' = P | zeroblock[0:PC]
          C = E(Ke, P' XOR plaintext, IV)
              // using ECB mode
          N' = N[0:c - PC] | C[c - PC:PC]
          C' = C[0:c - PC]
      H = HMAC(Ki, N' IV | C') C)
      ciphertext =  N' | C'  C | H[1..h]
      cipherState
      cipherstate = N next-to-last 128-bit block of C
      Note: if C is only a single block, then cipherstate = C

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

      (C, H) = ciphertext
      IV = cipherstate
      if (H H != HMAC(Ki, N' IV | C')[1..h]) C)[1..h]
          stop, report error

      if (L(C') > c)
          // Not short-plaintext
          IV = N' XOR cipherState
          P
      (N, P) = D(Ke, C', C, IV)
              // using CBC-CS3-Decrypt defined
              // in [SP800-38A+]
          cipherState = N'
          stop, output P, success
      else
      // Short plaintext
      PC = c - L(C')
      C = C' | N'[c - PC:PC]
      P' = D(Ke, C)
           // using ECB mode

      // P' here == (P | zeroblock[0:PC]) XOR IV
      // so IV[c - PC:PC] == P'[c - PC:PC]
      // In the non-short-pt case we'd recover
      // IV as N XOR cipherState, but here we only know
      // a head of
      Note: N and tail is set to the first block of IV.

      N = N'[0:c -PC] | (P' XOR cipherState)[c - PC:PC]
      IV = N XOR cipherState the decryption output,
      P is set to the rest of the output.
      cipherstate = (P' XOR IV)[0:PC]
      cipherState next-to-last 128-bit block of C
      Note: if C is only a single block, then cipherstate = N
      stop, output P, success C

   pseudo-random function:
      Kp  = KDF-HMAC-SHA2(protocol-key, "prf")
      PRF = HMAC(Kp, octet-string)

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: AES-128-CTS or AES-256-CTS as appropriate appropriate.

   get_mic: HMAC(Kc, message)[1..h] message)[1..h].

   verify_mic: get_mic and compare compare.

7.  IANA Considerations

   IANA is requested to assign:

   Encryption type numbers for aes128-cts-hmac-sha256-128 and
   aes256-cts-hmac-sha384-192 in the Kerberos Encryption Type Numbers
   registry.

      Etype   encryption type              Reference
      -----   ---------------              ---------
      TBD1    aes128-cts-hmac-sha256-128   [this document]
      TBD2    aes256-cts-hmac-sha384-192   [this document]

   Checksum type numbers for hmac-sha256-128-aes128 and hmac-sha384-192-
   aes256 in the Kerberos Checksum Type Numbers registry.

      Sumtype   Checksum type            Size   Reference
      -------   -------------            ----   ---------
      TBD3      hmac-sha256-128-aes128   16     [this document]
      TBD4      hmac-sha384-192-aes256   24     [this document]

8.  Security Considerations

   This specification requires implementations to generate random
   values.  The use of inadequate pseudo-random number generators
   (PRNGs) can result in little or no security.  The generation of
   quality random numbers is difficult.  NIST Special Publication 800-90
   [SP800-90] and  [RFC4086] offer offers random number
   generation guidance.

   This document specifies a mechanism for generating keys from pass
   phrases or passwords.  The salt and iteration count resist brute
   force and dictionary attacks, however, it is still important to
   choose or generate strong passphrases.

   NIST guidance in section 5.3 of [SP800-38A] requires CBC
   initialization vectors be unpredictable.  This specification does not
   formally comply with that guidance.  However, the use of a confounder
   as the first block of plaintext 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

   NIST guidance in Section 5.1 of [SP800-132] requires the salt used as
   input to the PBKDF to contain at least 128 bits of random.  Some
   known issues with including random values in Kerberos encryption type
   salt strings are:

   *  Cross-realm TGTs are currently managed by entering the same
      password at two KDCs to get the same keys.  If each KDC uses a
      random salt, they won't have the same keys.

   *  The string-to-key function as defined in [RFC3961] requires the
      salt to be valid UTF-8 strings.  Not every 128-bit random string
      will be valid UTF-8.

   *  Current implementations of password history checking will not
      work.

   *  ktutil's add_entry command assumes the default salt.

9.  Acknowledgements

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

10.  References

9.1.

10.1.  Normative References

   [RFC2898]    Kaliski, B., "PKCS #5: Password-Based Cryptography
                Specification Version 2.0", RFC 2898, September 2000.

   [RFC3961]    Raeburn, K., "Encryption and Checksum Specifications for
                Kerberos 5", RFC 3961, February 2005.

   [RFC4086]    Eastlake 3rd, D., Schiller, J., and S. Crocker,
                "Randomness Requirements

   [RFC3962]    Raeburn, K., "Advanced Encryption Standard (AES)
                Encryption for Security", BCP 106, Kerberos 5", RFC 4086, June 3962, February 2005.

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

9.2.  Informative References

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

   [SP800-90]

   [SP800-108]  National Institute of Standards and Technology,
                Recommendation
                "Recommendation for Random Number Generation Key Derivation Using
                Deterministic Random Bit Generators (Revised), Pseudorandom
                Functions", NIST Special Publication 800-90, March 2007.

   [SP800-108] 800-108, October
                2009.

10.2.  Informative References

   [RFC4086]    Eastlake 3rd, D., Schiller, J., and S. Crocker,
                "Randomness Requirements for Security", BCP 106, RFC
                4086, June 2005.

   [SP800-38A]  National Institute of Standards and Technology,
                "Recommendation for Key Derivation Using Pseudorandom
                Functions", Block Cipher Modes of Operation:
                Methods and Techniques", NIST Special Publication 800-108, October
                2009.
                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.

   [suiteb-kerberos]
                Burgin, K. and K. Igoe, "Suite B Profile for
                Kerberos 5", internet-draft draft-burgin-kerberos-
                suiteb-01, 2012.

Appendix A.  Test Vectors

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

   Iteration count = 32768
   Pass phrase = "password"
   Saltp for creating 128-bit master key: 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 master key:
      3C 44 03 85 28 06 BF 5C EE E6 36 base-key:
      08 9B CA 48 6C 29 2F D6 B1 05 EA 6E A7 7C A5 D2 F3 9D C5 E7

   Saltp for creating 256-bit master key: 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 master key:
      53 96 0C AF 44 D5 57 4D base-key:
      45 BD 80 6D BF 6A 83 3A 9C FF 4D 44 37 38 75 C1 C9 45 89 A2 22 B0
      7F 5B 02 5C 5E 65 BF EF 29 C2 B4 28 98 3B 37 08
      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 master key: base-key:
      37 05 D9 60 80 C1 77 28 A0 E8 00 EA B6 E0 D2 3C

   Kc value for key usage 2 (constant = 0x0000000299):
      B3 1A 01 8A 48 F5 47 76 F4 03 E9 A3 96 32 5D C3
   Ke value for key usage 2 (constant = 0x00000002AA):
      9B 19 7D D1 E8 C5 60 9D 6E 67 C3 E3 7C 62 C7 2E
   Ki value for key usage 2 (constant = 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 master key: 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 (constant = 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 (constant = 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 (constant = 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 (using (all using the default cipher state):
   ----------------------------------------------------

   128-bit AES key:
      2B 7E 15 16 28 AE D2 A6 AB F7 15 88 09 CF 4F 3C
   128-bit HMAC key:
      67 C3 31 A4 D7 AB 52 EF 3A A9 73 E0 39 AD D3 32
   Nonce:

   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
   Plaintext: (length less than block size)
      49 6E 63 6F
   128-bit AES key:
      9B 19 7D D1 E8 C5 60 9D 6E 63 65 69 76 61 67 C3 E3 7C 62 C7 2E
   128-bit HMAC key:
      9F DA 0E 56 AB 2D 85 E1 56 9A 68 86 96 C2 6A 6C 65
   AES Output:
      1C 17 3E AD FC 67 C8 BC B3 A5 93 02 98 CB FC 60
   HMAC Output (truncated):
      35 E8 32 B2 EB F4 6A 46 C2 E6 50 D2 50
      EF 85 FB 89 0B B8 47 2F 4D AB 84 43
   Ciphertext: (Nonce* | AES Output** | 20 39 4D CA 78 1D
   Truncated HMAC Output)
      7E 58 95 EA F2 67 24 35 BA D8 17 F5 45 CB FC 60
      1C 17 3E Output:
      AD FC 67 C8 BC B3 A5 93 02 98 35 E8 32
      B2 EB F4 6A 46 C2 E6 50 D2 50 AB 84 43

   *   Only the first 13 bytes of Nonce are sent.
   **  The AES 87 7E DA 39 D5 0C 87 0C 0D 5A 0A 8E 48 C7 18
   Ciphertext (AES Output is split and rearranged as described in Section 5
       since the plaintext length is | 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 the block size. 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:
      2B 7E 15 16 28 AE D2
      4E FD A6 52 4E 6B 56 B4 F2 12 61 FB FC 93 21 AB F7 15 88 09 CF 4F 3C

   128-bit HMAC key:
      67 C3 31 A4
      29 1B 0C 37 73 D7 6E E6 BA 2C CF 1E 03 93 F6 3E
   AES Output:
      AB 52 EF 3A A9 73 E0 39 AD D3 32
   Nonce:
      7E 58 95 EA F2 67 24 35 70 F4 BA D8 17 F5 45 A3 71 48
   Plaintext: (length equals block size)
      67 61 73 74 72 6F 69 6E 74 65 73 74 69 9D 76 55 AF 24 B5 76 E4 6E 61 6C
   AES Output:
      F6 71 0B 75 0C 60 FB 7A 98
      F1 4B 93 65 E8 2E BF F8 9D DC E0 C9 B9 1B
   Truncated HMAC Output (truncated):
      7B 2C D9 70 E6 DF 18 F5 E0 3D 8B 8E 40 02 Output:
      A0 C5 F4 C0 7C AA 84 42 19 F9 08 AD ED EF 52 5B 71
   Ciphertext: (Nonce | AES Output | Truncated HMAC Output)
      7E 58 95 EA F2 67 24 35
      AB 70 F4 BA D8 17 F5 45 A3 71 48
      F6 71 0B 75 0C 60 9D 76 55 AF 24 B5 76 E4 6E FB 7A 98
      F1 4B 93 65 E8 2E BF F8 9D DC E0 C9 B9
      7B 2C D9 70 E6 DF 18 F5 E0 3D 8B 8E 40 02 1B A0 C5 F4 C0

   256-bit AES key:
      60 3D EB 10 15 CA 7C AA 84 42 19 F9 08
      AD ED EF 52 5B 71 BE 2B 73 AE F0 85 7D 77 81
      1F 35 2C

   Plaintext: (length equals block size)
      00 01 02 03 04 05 06 07 3B 61 08 D7 2D 98 10 A3 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:
      FF 82 40 42 4B CC BA 05 56 50 C0 39 3B 83 DF F4
   192-bit 3B
   128-bit HMAC key:
      37 16 14 EB 62 24 E1 F0 C4 72 6E E6 BE A7 A3 D2
      F4
      ED 15 62 C6 AC 66 42 A6 AC
   Nonce:
      7E 58 95 EA F2 67 24 35 BA D8 17 F5 8B 45 A3 71 48
   Plaintext: (length less than block size)
      49 6E 63 6F 6E 63 65 69 76 61 62 6C 65 35 8C BF 7F 50 E7 64 C2 6B 8A 1A
   AES Output:
      BD AE EC 5C F9 C9 B6 3C 9D DB A2 B7 9D 5C 6C 0B
   HMAC Output (truncated):
      65 D4 C7 07
      E7 34 8E 14 74 86 E5 A7 87 0F 51 2E 65 CA C8 65 75
      78 26 FF C0 EA 5B 28 A8 B9 60 8B C9 B3 C4 EA F5 F7 C2 6F
      ED 36 AC 7A 08 CD 59 19 2B
   Ciphertext: (Nonce* | AES Output* | E2 CC
   Truncated HMAC Output)
      7E 58 95 EA Output:
      C1 85 4E F2 67 24 F3 4D 02 35 BA D8 17 F5 45 5C 6C 0B
      BD AE EC 5C F9 C9 B6 3C 9D DB A2 B7 9D 65 D4 4E C7
      07 AA 53 BE 03 BE D5
   Ciphertext:
      E7 34 8E 14 74 86 E5 A7 87 0F 51 2E 65 CA C8 65 75
      78 26 FF C0 EA 5B 28 A8 B9 60 8B C9 B3 C4 EA F5 F7 C2 6F ED 36 AC
      7A 08 CD 59 19 2B

   *   Only the first 13 bytes of Nonce are sent.
   **  The AES Output is split and rearranged as described in Section 5
       since the plaintext length is less E2 CC
      C1 85 4E F2 F3 4D 02 35 4E C7 AA 53 BE 03 BE D5

   Plaintext: (length greater than the block size.

   256-bit AES key:
      60 3D EB size)
      00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
      10 15 CA 71 BE 2B 73 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:
      B5 9B 88 75 AD 5D CA FF F7 79 4D 93 F8 19 9D 79
   128-bit HMAC key:
      0A 42 1D 72 2F 8F C2 D6 84 8B 1C DA D1 5A 49 C9
   AES Output:
      C3 53 72 86 FF 9C FE 49 8D 2E FC FC 99 6D AC 2D
      52 CA 56 03 B3 E8 68 EA 1E 9C 54 E8 2A E5 CE 7A
      79 3E 21 09 7D
   Truncated HMAC Output:
      5B 03 5D 78 A7 E9 84 75 EC 91 0C E3 7A A0 2A 7D
   Ciphertext:
      C3 53 72 86 FF 9C FE 49 8D 2E FC FC 99 6D AC 2D
      52 CA 56 03 B3 E8 68 EA 1E 9C 54 E8 2A E5 CE 7A
      79 3E 21 09 7D 5B 03 5D 78 A7 E9 84 75 EC 91 0C
      E3 7A A0 2A 7D

   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:
      0F A2 0D 7D 03 33 EE 65 16 2C DA 67 E7 AD 0D 3C
      5E 03 1F 3B 66 70 E0 31 28 2F AC C2 87 9C 21 C7
   192-bit HMAC key:
      53 BF 30 6A 68 33 A3 25 18 FC B8 5F 63 1D 03 D5
      2E E3 1B 39 75 2F 57 ED
   AES Output:
      FE 6A 55 14 F3 99 7C 8C AA F2 2D 8E EE 28 6D 7D
   Truncated HMAC Output:
      81 1E AD AE F0 85 DA 7F B9 75 AD 96 C0 07 5A 98 83 F9
      AC 3A AB 06 97 FC E8 5A
   Ciphertext:
      FE 6A 55 14 F3 99 7C 8C AA F2 2D 8E EE 28 6D 7D 77
      81
      1F 35 2C 1E AD AE DA 7F B9 75 AD 96 C0 07 3B 61 08 D7 5A 98 83 F9
      AC 3A AB 06 97 FC E8 5A

   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 98 10 A3 09 0B 9A
   256-bit AES key:
      47 DA 4C A2 8B D1 C1 14 DF F4 D5 50 7E 55 81 86 CA 4F
      DB A0 DA E5 B2 4F 6D 68 89 D5 3A FB F1 D0 B8 36
   192-bit HMAC key:
      37 16 14 EB 62 24 E1 F0 C4 72 6E E6 BE A7 A3 D2
      F4 62 C6 AC
      13 6B 5C 83 C9 53 AE 29 E2 C2 31 6A 7B 34 B8 C2
      AD 26 E4 66 7F AB 42 A6 AC
   Nonce:
      7E 58 95 EA F2 67 24 35 BA D8 17 F5 45 A3 71 48
   Plaintext: (length equals block size)
      67 61 73 74 72 6F 69 6E 74 65 73 74 69 6E 61 6C
   AES Output:
      5D E5 49 BE D6 50 23 18 78 8F
      14 D2 E1 17 E0 5A
   HMAC Output (truncated): 78 CF 26 BA 5E 7D 3A 9D C7 99 7A 80 10 76 2C EA DF D5 B0 60 38 DE A9
      74 3B D4 BC 22 29 2D 7C 56 50 10
      C5 D6 D2 8D F6 21 E9 7A
   Ciphertext: (Nonce | AES Output | EC
   Truncated HMAC Output)
      7E 58 95 EA F2 67 24 35 BA D8 17 F5 45 A3 71 48
      5D E5 49 BE D6 50 23 18 78 8F 14 D2 E1 Output:
      17 E0 5A
      2C EA DF D5 2A B2 BB 12 B0 60 38 DE A9 22 0D BE C2 BF E6 29 2D 7C 56 50 10
      C5 D6 D2 8D F6 21 E9 7A

   128-bit AES key:
      9B 19 CF DD 62 EC
      3E 45 83 8F A9 FB AE 6E
   Ciphertext:
      14 78 CF 26 BA 5E 7D D1 E8 C5 60 3A 9D 6E 67 C3 E3 7C 62 C7 2E

   128-bit HMAC key:
      9F DA 0E 56 AB 2D 85 E1 56 9A 68 86 96 C2 6A 6C
   Nonce:
      8D 32 50 F6 36 AB 81 02 BE 6F AB 1E 57 D8 F8 99 7A 80 10 76 2C
      74 3B D4 BC 22 EC 17 2A B2 BB 12 B0 0D BE C2 BF
      E6 29 CF DD 62 EC 3E 45 83 8F A9 FB AE 6E

   Plaintext: (length greater than the 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 11 12 13 14
   AES Output:
      13 64 FB 39 DC C0 E3 D9 83 A7 DB 5B 4B 9F FB CA
      42 F6 52 65 88 29
   HMAC Output (truncated):
      F2 1F C8 95 75 AE 93 C7 57 18 AB 3C 7C FB 28 E1
   Ciphertext: (Nonce | AES Output | HMAC Output)
      8D 32 50 F6 36 AB 81 02 BE 6F AB 1E 57 D8 F8 17
      13 64 FB 39 DC C0 E3 D9 83 A7 DB 5B 4B 9F FB CA D4 E2 76 42 F6 65 88 29 F2 1F C8 95 75 AE 93 C7 57 18 AB
      3C 7C FB 28 E1 86 24 CE 5E 63
   256-bit AES key:
      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
      5E A6 16 D8 FD A2 33 F1 B4 99 79 A4 B9 FA 01 D3
      21 B1 3D 6F BD 6E 3B B7 2E 5C 7E 49 54 B4 85 E2 36 AF 23
   192-bit HMAC key:
      69 B1 65
      AD D3 8D C9 86 83 C5 CC 14 E3 CD 8E 56 B8 20 10 D5 C7 30 12 37 EA A7 06 47
      B3 19 71 0E 87 6A 38 77
   AES Output:
      B6
      22 C4 D0 0F FC 23 ED 1F
   Nonce:
      8D 32 50 F6 0B 6A A6 00 C2 D8 4B 03 A6 1C 18 DD A7 05 F0
      FE 90 B9 36 AB 81 02 BE B8 8C 4F EA 06 D7 1A 99 35 75 28 60
   Truncated HMAC Output:
      2F E5 BD 6E 41 78 17 D6 2A D2 C9 CF 50 8D FA E1
      B3 C9 6F AB 1E 57 4B 45 C1 9B 77
   Ciphertext:
      B6 0B 6A A6 00 C2 D8 F8 4B 03 A6 1C 18 DD A7 05 F0
      FE 90 B9 36 B8 8C 4F EA 06 D7 1A 99 35 75 28 60
      2F E5 BD 6E 41 78 17 D6 2A D2 C9 CF 50 8D FA E1
      B3 C9 6F 4B 45 C1 9B 77

   Plaintext: (length greater than the 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 Output:
      50 CB FF DC DF 38 69 D7 key:
      B3 A8 02 E3 40 61 3E F1 E0 EC E9 1A 15 7C 59 12
      6F BD C4 B8 C2 4C 8D 0B EA FF C3 2C 47 2E 5A 30 F0 1E 7E 34 88
   192-bit HMAC key:
      FC 0B C6
      5B 72 49 9B 83 55 A3 2A C3 37 2D
   HMAC Output (truncated):
      6E D7 C9 AC B6 64 93 63 EB
      5D BB A4 25 1A 75 B2 0A
   AES Output:
      4C F9 8B 5E DA 0D 94 9F B3 47 E9 0B BD 8F 31 F5 8E CD 67 DE 80 0F 79 58
      46 19 F9 69 EA CB 30 54 33 50 BA
      A1 41 64 6E 65 6C F6 7C
   Ciphertext: (Nonce | AES Output | 6B 9A D4 48 4B D9 5B
      E0 55 F5 69 EB
   Truncated HMAC Output)
      8D 32 50 F6 Output:
      7C F8 36 AB 81 02 BE 6F AB 1E 57 D8 70 75 8C BF DA 31 3C FE F8 17
      50 CB FF DC DF 38 69 D7 0B EA FF C3 2C 47 0B C6
      5B 72 C3 37 2D 6E D7 74 2B 11 74
      14 A7 DD 12 B4 96 64 2E
   Ciphertext:
      4C F9 8B 5E DA 0D 94 9F B3 47 E9 0B BD 8F 31 F5 8E CD 67 DE 80 0F 79
      58
      46 19 F9 69 EA CB 30 54 33 50 BA A1 41 64 6E 65 6C F6 6B 9A D4 48 4B D9 5B
      E0 55 F5 69 EB 7C F8 36 70 75 8C BF DA 31 3C FE
      F8 74 2B 11 74 14 A7 DD 12 B4 96 64 2E

   Sample checksums:
   -----------------
   Checksum type: hmac-sha256-128-aes128
   128-bit master key:
      37 05 D9 60 80 C1 77 28 A0 E8 00 EA B6 E0 D2 3C
   128-bit HMAC key (Kc, key usage 2): key:
      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
   256-bit master 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
   192-bit HMAC key (Kc, key usage 2): key:
      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

Authors' Addresses

   Kelley W. Burgin

   Michael J. Jenkins
   National Security Agency

   EMail: kwburgi@tycho.ncsc.mil mjjenki@tycho.ncsc.mil

   Michael A. Peck
   The MITRE Corporation

   EMail: mpeck@mitre.org

   Kelley W. Burgin

   Email: kelley.burgin@gmail.com