Internet Draft                                       IPsec Working Group
June 2002                                               S. Frankel, NIST
Expiration Date: December 2002                         H. Herbert, Intel

          The AES-XCBC-MAC-96 Algorithm and Its Use With IPsec

Status of this Memo

   This document is an Internet-Draft and is in full conformance with
   all provisions of Section 10 of RFC2026.  Internet Drafts are working
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   Distribution of this memo is unlimited.

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                             Table of Contents

 1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . .   3
 2. Specification of Requirements  . . . . . . . . . . . . . . . . .   3
 3. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .   3
 4. Basic CBC-MAC with Obligatory 10* Padding  . . . . . . . . . . .   4
 5. AES-XCBC-MAC-96  . . . . . . . . . . . . . . . . . . . . . . . .   4
    5.1 Keying Material  . . . . . . . . . . . . . . . . . . . . . .   5
    5.2 Padding  . . . . . . . . . . . . . . . . . . . . . . . . . .   6
    5.3 Truncation . . . . . . . . . . . . . . . . . . . . . . . . .   6
    5.4 Interaction with the ESP Cipher Mechanism  . . . . . . . . .   7
    5.5 Performance  . . . . . . . . . . . . . . . . . . . . . . . .   7
    5.6 Test Vectors . . . . . . . . . . . . . . . . . . . . . . . .   7
 6. Security Considerations  . . . . . . . . . . . . . . . . . . . .   8
 7. IANA Considerations  . . . . . . . . . . . . . . . . . . . . . .   8
 8. Intellectual Property Rights Statement . . . . . . . . . . . . .   8
 9. Acknowledgments  . . . . . . . . . . . . . . . . . . . . . . . .   9
10. References . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
11. Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . .  10
12. Full Copyright Statement . . . . . . . . . . . . . . . . . . . .  11

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1. Abstract

   A Message Authentication Code (MAC) is a key-dependent one way hash
   function.  One popular way to construct a MAC algorithm is to use a
   block cipher in conjunction with the Cipher-Block-Chaining (CBC) mode
   of operation.  The classic CBC-MAC algorithm, while secure for mes-
   sages of a pre-selected fixed length, has been shown to be insecure
   across messages of varying lengths such as the type found in typical
   IP datagrams.  This memo specifies the use of AES in CBC mode with a
   set of extensions to overcome this limitation.  This new algorithm is
   named AES-XCBC-MAC-96.

2. Specification of Requirements

   The keywords "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   appear in this document are to be interpreted as described in

3. Introduction

   Message authentication provides data integrity and data origin au-
   thentication with respect to the original message source.  A Message
   Authentication Code (MAC) is a key-dependent one way hash function.
   One popular way to construct a MAC algorithm is to use a block cipher
   in conjunction with the Cipher-Block-Chaining (CBC) mode of opera-
   tion.  The classic CBC-MAC algorithm, while secure for messages of a
   pre-selected fixed length, has been shown to be insecure across mes-
   sages of varying lengths such as the type found in typical IP data-
   grams.  In fact, it is trivial to produce forgeries for a second mes-
   sage given the MAC of a prior message.

   This memo specifies the use of AES [AES] in CBC mode [MODES] with a
   set of extensions [XCBC-MAC-1] to overcome this limitation.  This new
   algorithm is named AES-XCBC-MAC-96.  Using the AES block cipher, with
   its increased block size (128 bits) and increased key length (128
   bits), provides the new algorithm with the ability to withstand con-
   tinuing advances in crypto-analytic techniques and computational ca-
   pability.  AES-XCBC-MAC-96 is used as an authentication mechanism
   within the context of the IPsec Encapsulating Security Payload (ESP)
   and the Authentication Header (AH) protocols.  For further informa-
   tion on ESP, refer to [ESP] and [ROADMAP].  For further information
   on AH, refer to [AH] and [ROADMAP].

   The goal of AES-XCBC-MAC-96 is to ensure that the datagram is authen-
   tic and cannot be modified in transit.  Data integrity and data ori-
   gin authentication as provided by AES-XCBC-MAC-96 are dependent upon
   the scope of the distribution of the secret key. If the key is known
   only by the source and destination, this algorithm will provide both
   data origin authentication and data integrity for datagrams sent be-
   tween the two parties.  In addition, only a party with the identical
   key can verify the hash.

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4. Basic CBC-MAC with Obligatory 10* Padding

   CBC-MAC uses a block cipher for encryption; the block cipher trans-
   forms b bits of plaintext to b bits of ciphertext.  The basic CBC-MAC
   [CBC-MAC-1, CBC-MAC-2] with Obligatory 10* Padding over a b-bit block
   cipher is calculated as follows for a message M:

     (1)  Append a single 1 bit to M.  Then append the minimum number of
          0 bits to M such that the length of M is a multiple of b.
          [NOTE: This is 1 of several padding schemes that can be used
          for CBC-MAC. Several others are described in [MODES].]

     (2)  Break M into n blocks, M[1] ... M[n], where the blocksize of
          blocks M[1] ... M[n] is b bits

     (3)  Define E[0] = 0x00000000000000000000000000000000

     (4)  For each block M[i], where i = 1 ... n:
             XOR M[i] with E[i-1], then encrypt the result with Key K,
             yielding E[i].

     (5)  E[n] is the b-bit authenticator.

   Basic CBC-MAC with obligatory 10* padding has been shown to be secure
   for messages up to (but not including) a pre-selected fixed length,
   in which the length is a multiple of the blocksize.  This algorithm
   is not suitable for IPsec for the following reasons:

     +    Any IPsec authenticator must be able to handle messages of
          arbitrary length.  However, the basic CBC-MAC cannot securely
          handle messages that exceed the pre-selected fixed length.

     +    For messages shorter than the selected length, padding the
          message to the selected length may necessitate additional
          encryption operations, adding an unacceptable computational


   [AES] describes the underlying AES algorithm, while [CBC-MAC-2] and
   [XCBC-MAC-1] describe the AES-XCBC-MAC algorithm.

   The AES-XCBC-MAC-96 algorithm is a variant of the basic CBC-MAC with
   obligatory 10* padding; however, AES-XCBC-MAC-96 is secure for mes-
   sages of arbitrary length.  The AES-XCBC-MAC-96 calculations require
   numerous encryption operations; this encryption MUST be accomplished
   using AES with a 128-bit key.  Given a 128-bit secret key K, AES-
   XCBC-MAC-96 is calculated as follows for a message M that consists of
   n blocks, M[1] ... M[n], in which the blocksize of blocks M[1] ...
   M[n-1] is 128 bits and the blocksize of block M[n] is between 1 and
   128 bits:

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     (1)  Derive 3 128-bit keys (K1, K2 and K3) from the 128-bit secret
          key K, as follows:
            K1 = 0x01010101010101010101010101010101 encrypted with Key K
            K2 = 0x02020202020202020202020202020202 encrypted with Key K
            K3 = 0x03030303030303030303030303030303 encrypted with Key K

     (2)  Define E[0] = 0x00000000000000000000000000000000

     (3)  For each block M[i], where i = 1 ... n-1:
             XOR M[i] with E[i-1], then encrypt the result with Key K1,
             yielding E[i].

     (4)  For block M[n]:

          (a)  If the blocksize of M[n] is 128 bits:
                  XOR M[n] with E[n-1] and Key K2, then encrypt the
                  result with Key K1, yielding E[n].

          (b)  If the blocksize of M[n] is less than 128 bits:

               (i)  Pad M[n] with a single "1" bit, followed by the num-
                    ber of "0" bits (possibly none) required to increase
                    M[n]'s blocksize to 128 bits.

               (ii) XOR M[n] with E[n-1] and Key K3, then encrypt the
                    result with Key K1, yielding E[n].

     (5)  The authenticator value is the leftmost 96 bits of the 128-bit

   NOTE1: If M is the empty string, pad and encrypt as in (4)(b) to cre-
   ate M[1] and E[1]. This will never be the case for ESP or AH, but is
   included for completeness sake.

   NOTE2: [CBC-MAC-2] defines K1 as follows:
                  K1 = Constant1A encrypted with Key K |
                     Constant1B encrypted with Key K.
           However, the second encryption operation is only needed for
           AES-XCBC-MAC with keys greater than 128 bits; thus, it is not
           included in the definition of AES-XCBC-MAC-96.

   AES-XCBC-MAC-96 verification is performed as follows:
      Upon receipt of the AES-XCBC-MAC-96 authenticator, the entire
      128-bit value is computed and the first 96 bits are compared to
      the value stored in the authenticator field.

5.1 Keying Material

   AES-XCBC-MAC-96 is a secret key algorithm. For use with either ESP or
   AH a fixed key length of 128-bits MUST be supported. Key lengths
   other than 128-bits MUST NOT be supported (i.e. only 128-bit keys are
   to be used by AES-XCBC-MAC-96).

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   AES-XCBC-MAC-96 actually requires 384 bits of keying material (128
   bits for the AES keysize + 2 times the blocksize). This keying mate-
   rial can either be provided through the key generation mechanism or
   it can be generated from a single 128-bit key. The latter approach
   has been selected for AES-XCBC-MAC-96, since it is analogous to other
   authenticators used within IPsec.  The reason AES-XCBC-MAC-96 uses 3
   keys is so the length of the input stream does not need to be known
   in advance. This may be useful for systems that do one-pass assembly
   of large packets.

   A strong pseudo-random function MUST be used to generate the required
   128-bit key. This key, along with the 3 derived keys (K1, K2 and K3),
   should be used for no purposes other than those specified in the
   algorithm.  In particular, they should not be used as keys in another
   cryptographic setting.  Such abuses will invalidate the security of
   the authentication algorithm.

   At the time of this writing there are no specified weak keys for use
   with AES-XCBC-MAC-96. This does not mean to imply that weak keys do
   not exist.  If, at some point, a set of weak keys for AES-XCBC-MAC-96
   are identified, the use of these weak keys MUST be rejected followed
   by a request for replacement keys or a newly negotiated Security

   [ARCH] describes the general mechanism for obtaining keying material
   when multiple keys are required for a single SA (e.g. when an ESP SA
   requires a key for confidentiality and a key for authentication).

   In order to provide data origin authentication, the key distribution
   mechanism must ensure that unique keys are allocated and that they
   are distributed only to the parties participating in the communica-

   Current attacks do not necessitate a specific recommended frequency
   for key changes. However, periodic key refreshment is a fundamental
   security practice that helps against potential weaknesses of the
   function and the keys, reduces the information available to a crypt-
   analyst, and limits the damage resulting from a compromised key.

5.2 Padding

   AES-XCBC-MAC-96 operates on 128-bit blocks of data. Padding require-
   ments are specified in [CBC-MAC-2] and are part of the XCBC algo-
   rithm. If you build AES-XCBC-MAC-96 according to [CBC-MAC-2] you do
   not need to add any additional padding as far as AES-XCBC-MAC-96 is
   concerned. With regard to "implicit packet padding" as defined in
   [AH], no implicit packet padding is required.

5.3 Truncation

   AES-XCBC-MAC produces a 128-bit authenticator value.  AES-XCBC-MAC-96
   is derived by truncating this 128-bit value as described in [HMAC]
   and verified in [XCBC-MAC-2].  For use with either ESP or AH, a

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   truncated value using the first 96 bits MUST be supported.  Upon
   sending, the truncated value is stored within the authenticator
   field. Upon receipt, the entire 128-bit value is computed and the
   first 96 bits are compared to the value stored in the authenticator
   field. No other authenticator value lengths are supported by AES-

   The length of 96 bits was selected because it is the default authen-
   ticator length as specified in [AH] and meets the security require-
   ments described in [XCBC-MAC-2].

5.4 Interaction with the ESP Cipher Mechanism

   As of this writing, there are no known issues which preclude the use
   of AES-XCBC-MAC-96 with any specific cipher algorithm.

5.5 Performance

   For any CBC MAC variant, the major computational effort is expended
   in computing the underlying block cipher.  This algorithm uses a min-
   imum number of AES invocations, one for each block of the message or
   fraction thereof, resulting in performance equivalent to classic CBC-

   The key expansion requires 3 additional AES encryption operations,
   but these can be performed once in advance for each secret key.

5.6 Test Vectors

   These test cases were provided by John Black, co-author of the XCBC-
   MAC algorithm, who verified them with 2 independent implementations.
   All values are hexadecimal numbers.

   Test Case #1   : AES-XCBC-MAC-96 with 0-byte input
   Key (K)        : 000102030405060708090a0b0c0d0e0f
   Message (M)    : <empty string>
   AES-XCBC-MAC   : 75f0251d528ac01c4573dfd584d79f29
   AES-XCBC-MAC-96: 75f0251d528ac01c4573dfd5

   Test Case #2   : AES-XCBC-MAC-96 with 3-byte input
   Key (K)        : 000102030405060708090a0b0c0d0e0f
   Message (M)    : 000102
   AES-XCBC-MAC   : 5b376580ae2f19afe7219ceef172756f
   AES-XCBC-MAC-96: 5b376580ae2f19afe7219cee

   Test Case #3   : AES-XCBC-MAC-96 with 16-byte input
   Key (K)        : 000102030405060708090a0b0c0d0e0f
   Message (M)    : 000102030405060708090a0b0c0d0e0f
   AES-XCBC-MAC   : d2a246fa349b68a79998a4394ff7a263
   AES-XCBC-MAC-96: d2a246fa349b68a79998a439

   Test Case #4   : AES-XCBC-MAC-96 with 20-byte input
   Key (K)        : 000102030405060708090a0b0c0d0e0f
   Message (M)    : 000102030405060708090a0b0c0d0e0f10111213

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   AES-XCBC-MAC   : 47f51b4564966215b8985c63055ed308
   AES-XCBC-MAC-96: 47f51b4564966215b8985c63

   Test Case #5   : AES-XCBC-MAC-96 with 32-byte input
   Key (K)        : 000102030405060708090a0b0c0d0e0f
   Message (M)    : 000102030405060708090a0b0c0d0e0f10111213141516171819
   AES-XCBC-MAC   : f54f0ec8d2b9f3d36807734bd5283fd4
   AES-XCBC-MAC-96: f54f0ec8d2b9f3d36807734b

   Test Case #6   : AES-XCBC-MAC-96 with 34-byte input
   Key (K)        : 000102030405060708090a0b0c0d0e0f
   Message (M)    : 000102030405060708090a0b0c0d0e0f10111213141516171819
   AES-XCBC-MAC   : becbb3bccdb518a30677d5481fb6b4d8
   AES-XCBC-MAC-96: becbb3bccdb518a30677d548

   Test Case #7   : AES-XCBC-MAC-96 with 1000-byte input
   Key (K)        : 000102030405060708090a0b0c0d0e0f
   Message (M)    : 00000000000000000000 ... 00000000000000000000
                    [1000 bytes]
   AES-XCBC-MAC   : f0dafee895db30253761103b5d84528f
   AES-XCBC-MAC-96: f0dafee895db30253761103b

6. Security Considerations

   The security provided by AES-XCBC-MAC-96 is based upon the strength
   of AES.  At the time of this writing there are no practical crypto-
   graphic attacks against AES or AES-XCBC-MAC-96.

   As is true with any cryptographic algorithm, part of its strength
   lies in the correctness of the algorithm implementation, the security
   of the key management mechanism and its implementation, the strength
   of the associated secret key, and upon the correctness of the imple-
   mentation in all of the participating systems.  This draft contains
   test vectors to assist in verifying the correctness of AES-XCBC-
   MAC-96 code.

7. IANA Considerations

   IANA has assigned AH Transform Identifier XX to AH_AES-XCBC-MAC.
   IANA has assigned AH/ESP Authentication Algorithm Value XX to AES-

8. Intellectual Property Rights Statement

   Pursuant to the provisions of [RFC-2026], the authors represent that
   they have disclosed the existence of any proprietary or intellectual
   property rights in the contribution that are reasonably and person-
   ally known to the authors.  The authors do not represent that they
   personally know of all potentially pertinent proprietary and intel-
   lectual property rights owned or claimed by the organizations they
   represent or third parties.

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   The IETF takes no position regarding the validity or scope of any
   intellectual property or other rights that might be claimed to per-
   tain to the implementation or use of the technology described in this
   document or the extent to which any license under such rights might
   or might not be available; neither does it represent that it has made
   any effort to identify any such rights.  Information on the IETF's
   procedures with respect to rights in standards-track and standards-
   related documentation can be found in BCP-11.  Copies of claims of
   rights made available for publication and any assurances of licenses
   to be made available, or the result of an attempt made to obtain a
   general license or permission for the use of such proprietary rights
   by implementers or users of this specification can be obtained from
   the IETF Secretariat.

9. Acknowledgments

   Portions of this text were unabashedly borrowed from [HMAC-SHA].

   Thanks to the XCBC-MAC authors for their expert advice and rapid
   response to our queries: to Phil Rogaway for providing values for the
   XCBC-MAC constants; and to John Black for detailed corrections to the
   algorithm specifications and for providing the test cases. Thanks
   also to Andrew Krywaniuk for insisting on (and providing wording for)
   a rationale for the 3-key approach.

10. References

     [AES]       NIST, FIPS PUB 197, "Advanced Encryption Standard
                 (AES)," November 2001.{ps,pdf}

     [AH]        Kent, S. and R. Atkinson, "IP Authentication Header",
                 RFC 2402, November 1998.

     [ARCH]      Kent, S. and R. Atkinson, "Security Architecture for
                 the Internet Protocol", RFC 2401, November 1998.

     [CBC-MAC-1] Bellare, M., J. Kilian and P. Rogaway, "The Security of
                 the Cipher Block Chaining Message Authentication Code,"
                 Journal of Computer and System Sciences (JCSS), Vol.
                 61, No. 3, December 2000, pp. 362-399.

     [CBC-MAC-2] Black, J. and P. Rogaway, "CBC MACs for Arbitrary-
                 Length Messages: The Three-Key Constructions," in M.
                 Bellare, editor, Advances in Cryptology -- CRYPTO '00,
                 volume 1880 of Lecture Notes in Computer Science, p.
                 0197, August 2000, Springer-Verlag.

     [ESP]       Kent, S. and R. Atkinson, "IP Encapsulating Security
                 Payload (ESP)", RFC 2406, November 1998.

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     [HMAC]      Krawczyk, H., M. Bellare and R. Canetti, "HMAC: Keyed-
                 Hashing for Message Authentication," RFC 2104, February

     [HMAC-SHA]  Madson, C. and R. Glenn, "The Use of HMAC-SHA-1-96
                 within ESP and AH," RFC 2404, November 1998.

     [MODES]     Dworkin, M., "Recommendation for Block Cipher Modes of
                 Operation: Methods and Techniques," NIST Special
                 Publication 800-38A, December 2001.

     [RFC-2026]  Bradner, S., "The Internet Standards Process --
                 Revision 3", RFC2026, October 1996.

     [RFC-2119]  Bradner, S., "Key words for use in RFCs to Indicate
                 Requirement Levels", RFC 2119, March 1997.

     [ROADMAP]   Thayer, R., N. Doraswamy, and R. Glenn, "IP Security
                 Document Roadmap", RFC 2411, November 1998.

                 Black, J. and P. Rogaway, "A Suggestion for Handling
                 Arbitrary-Length Messages with the CBC MAC," NIST
                 Second Modes of Operation Workshop, August 2001.

                 Rogaway, Phil, email communications, October 2001.

11. Authors' Addresses

        Sheila Frankel
        820 West Diamond Ave.
        Room 680
        Gaithersburg, MD 20899
        Phone: +1 (301) 975-3297

        Howard C. Herbert
        Intel Corporation
        Lan Access Division
        5000 West Chandler Blvd.
        Chandler, Arizona 85226
        Phone: +1 (480) 554-3116

   The IPsec working group can be contacted through the chairs:

Frankel,Herbert                                                [Page 10]

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        Barbara Fraser
        Cisco Systems Inc.

        Theodore Ts'o
        Massachusetts Institute of Technology

12. Full Copyright Statement

   Copyright (C) The Internet Society (1998).  All Rights Reserved.

   This document and translations of it may be copied and furnished to
   others, and derivative works that comment on or otherwise explain it
   or assist in its implementation may be prepared, copied, published
   and distributed, in whole or in part, without restriction of any
   kind, provided that the above copyright notice and this paragraph are
   included on all such copies and derivative works.  However, this doc-
   ument itself may not be modified in any way, such as by removing the
   copyright notice or references to the Internet Society or other In-
   ternet organizations, except as needed for the purpose of developing
   Internet standards in which case the procedures for copyrights de-
   fined in the Internet Standards process must be followed, or as re-
   quired to translate it into languages other than English.

   The limited permissions granted above are perpetual and will not be
   revoked by the Internet Society or its successors or assigns.

   This document and the information contained herein is provided on an

Frankel,Herbert                                                [Page 11]