The OCB Authenticated-Encryption Algorithm

Internet Research Task Force (IRTF)                           T. Krovetz
Request for Comments: 7253                              Sacramento State
Category: Informational                                       P. Rogaway
ISSN: 2070-1721                                                 UC Davis
                                                                May 2014


               The OCB Authenticated-Encryption Algorithm

Abstract

   This document specifies OCB, a shared-key blockcipher-based
   encryption scheme that provides confidentiality and authenticity for
   plaintexts and authenticity for associated data.  This document is a
   product of the Crypto Forum Research Group (CFRG).

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 Research Task Force
   (IRTF).  The IRTF publishes the results of Internet-related research
   and development activities.  These results might not be suitable for
   deployment.  This RFC represents the consensus of the Crypto Forum
   Research Group of the Internet Research Task Force (IRTF).  Documents
   approved for publication by the IRSG are not 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/rfc7253.

Copyright Notice

   Copyright (c) 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.

Table of Contents

   1. Introduction ....................................................2
   2. Notation and Basic Operations ...................................4
   3. OCB Global Parameters ...........................................5
      3.1. Named OCB Parameter Sets and RFC 5116 Constants ............6
   4. OCB Algorithms ..................................................6
      4.1. Processing Associated Data: HASH ...........................6
      4.2. Encryption: OCB-ENCRYPT ....................................8
      4.3. Decryption: OCB-DECRYPT ....................................9
   5. Security Considerations ........................................11
      5.1. Nonce Requirements ........................................12
   6. IANA Considerations ............................................13
   7. Acknowledgements ...............................................13
   8. References .....................................................14
      8.1. Normative References ......................................14
      8.2. Informative References ....................................14
   Appendix A.  Sample Results .......................................15

1.  Introduction

   Schemes for authenticated encryption (AE) simultaneously provide for
   confidentiality and authentication.  While this goal would
   traditionally be achieved by melding separate encryption and
   authentication mechanisms, each using its own key, integrated AE
   schemes intertwine what is needed for confidentiality and what is
   needed for authenticity.  By conceptualizing AE as a single
   cryptographic goal, AE schemes are less likely to be misused than
   conventional encryption schemes.  Also, integrated AE schemes can be
   significantly faster than what one sees from composing separate
   confidentiality and authenticity means.

   When an AE scheme allows for the authentication of unencrypted data
   at the same time that a plaintext is being encrypted and
   authenticated, the scheme is an authenticated encryption with
   associated data (AEAD) scheme.  Associated data can be useful when,
   for example, a network packet has unencrypted routing information and
   an encrypted payload.

   OCB is an AEAD scheme that depends on a blockcipher.  This document
   fully defines OCB encryption and decryption except for the choice of
   the blockcipher and the length of authentication tag that is part of
   the ciphertext.  The blockcipher must have a 128-bit blocksize.  Each
   choice of blockcipher and tag length specifies a different variant of
   OCB.  Several AES-based variants are defined in Section 3.1.

   OCB encryption and decryption employ a nonce N, which must be
   distinct for each invocation of the OCB encryption operation.  OCB
   requires the associated data A to be specified when one encrypts or
   decrypts, but it may be zero-length.  The plaintext P and the
   associated data A can have any bitlength.  The ciphertext C one gets
   by encrypting P in the presence of A consists of a ciphertext-core
   having the same length as P, plus an authentication tag.  One can
   view the resulting ciphertext as either the pair (ciphertext-core,
   tag) or their concatenation (ciphertext-core || tag), the difference
   being purely how one assembles and parses ciphertexts.  This document
   uses concatenation.

   OCB encryption protects the confidentiality of P and the authenticity
   of A, N, and P.  It does this using, on average, about a + m + 1.02
   blockcipher calls, where a is the blocklength of A, m is the
   blocklength of P, and the nonce N is implemented as a counter (if N
   is random, then OCB uses a + m + 2 blockcipher calls).  If A is fixed
   during a session, then, after preprocessing, there is effectively no
   cost to having A authenticated on subsequent encryptions, and the
   mode will average m + 1.02 blockcipher calls.  OCB requires a single
   key K for the underlying blockcipher, and all blockcipher calls are
   keyed by K.  OCB is online.  In particular, one need not know the
   length of A or P to proceed with encryption, nor need one know the
   length of A or C to proceed with decryption.  OCB is parallelizable:
   the bulk of its blockcipher calls can be performed simultaneously.
   Computational work beyond blockcipher calls consists of a small and
   fixed number of logical operations per call.  OCB enjoys provable
   security: the mode of operation is secure assuming that the
   underlying blockcipher is secure.  As with most modes of operation,
   security degrades as the number of blocks processed gets large (see
   Section 5 for details).

   For reasons of generality, OCB is defined to operate on arbitrary
   bitstrings.  But for reasons of simplicity and efficiency, most
   implementations will assume that strings operated on are bytestrings
   (i.e., strings that are a multiple of 8 bits).  To promote
   interoperability, implementations of OCB that communicate with
   implementations of unknown capabilities should restrict all provided
   values (nonces, tags, plaintexts, ciphertexts, and associated data)
   to bytestrings.

   The version of OCB defined in this document is a refinement of two
   prior schemes.  The original OCB version was published in 2001 [OCB1]
   and was listed as an optional component in IEEE 802.11i.  A second
   version was published in 2004 [OCB2] and is specified in ISO 19772.
   The scheme described here is called OCB3 in the 2011 paper describing
   the mode [OCB3]; it shall be referred to simply as OCB throughout
   this document.  The only difference between the algorithm of this RFC
   and that of the [OCB3] paper is that the tag length is now encoded
   into the internally formatted nonce.  See [OCB3] for complete
   references, timing information, and a discussion of the differences
   between the algorithms.  OCB was initially the acronym for Offset
   Codebook but is now the algorithm's full name.

   OCB has received years of in-depth analysis previous to its
   submission to the CFRG and has been under review by the members of
   the CFRG for over a year.  It is the consensus of the CFRG that the
   security mechanisms provided by the OCB AEAD algorithm described in
   this document are suitable for use in providing confidentiality and
   authentication.

2.  Notation and Basic Operations

   There are two types of variables used in this specification, strings
   and integers.  Although strings processed by most implementations of
   OCB will be strings of bytes, bit-level operations are used
   throughout this specification document for defining OCB.  String
   variables are always written with an initial uppercase letter while
   integer variables are written in all lowercase.  Following C's
   convention, a single equals ("=") indicates variable assignment and
   double equals ("==") is the equality relation.  Whenever a variable
   is followed by an underscore ("_"), the underscore is intended to
   denote a subscript, with the subscripted expression requiring
   evaluation to resolve the meaning of the variable.  For example, when
   i == 2, then P_i refers to the variable P_2.

   c^i           The integer c raised to the i-th power.

   bitlen(S)     The length of string S in bits (e.g., bitlen(101) ==
                 3).

   zeros(n)      The string made of n zero bits.

   ntz(n)        The number of trailing zero bits in the base-2
                 representation of the positive integer n.  More
                 formally, ntz(n) is the largest integer x for which 2^x
                 divides n.

   S xor T       The string that is the bitwise exclusive-or of S and T.
                 Strings S and T will always have the same length.

   S[i]          The i-th bit of the string S (indices begin at 1, so if
                 S is 011, then S[1] == 0, S[2] == 1, S[3] == 1).

   S[i..j]       The substring of S consisting of bits i through j,
                 inclusive.

   S || T        String S concatenated with string T (e.g., 000 || 111
                 == 000111).

   str2num(S)    The base-2 interpretation of bitstring S (e.g.,
                 str2num(1110) == 14).

   num2str(i,n)  The n-bit string whose base-2 interpretation is i
                 (e.g., num2str(14,4) == 1110 and num2str(1,2) == 01).

   double(S)     If S[1] == 0, then double(S) == (S[2..128] || 0);
                 otherwise, double(S) == (S[2..128] || 0) xor
                 (zeros(120) || 10000111).

3.  OCB Global Parameters

   To be complete, the algorithms in this document require specification
   of two global parameters: a blockcipher operating on 128-bit blocks
   and the length of authentication tags in use.

   Specifying a blockcipher implicitly defines the following symbols.

   KEYLEN         The blockcipher's key length in bits.

   ENCIPHER(K,P)  The blockcipher function mapping 128-bit plaintext
                  block P to its corresponding ciphertext block using
                  KEYLEN-bit key K.

   DECIPHER(K,C)  The inverse blockcipher function mapping 128-bit
                  ciphertext block C to its corresponding plaintext
                  block using KEYLEN-bit key K.

   The TAGLEN parameter specifies the length of authentication tag used
   by OCB and may be any value up to 128.  Greater values for TAGLEN
   provide greater assurances of authenticity, but ciphertexts produced
   by OCB are longer than their corresponding plaintext by TAGLEN bits.
   See Section 5 for details about TAGLEN and security.

   As an example, if 128-bit authentication tags and AES with 192-bit
   keys are to be used, then KEYLEN is 192, ENCIPHER refers to the
   AES-192 cipher, DECIPHER refers to the AES-192 inverse cipher, and
   TAGLEN is 128 [AES].

3.1.  Named OCB Parameter Sets and RFC 5116 Constants

   The following table gives names to common OCB global parameter sets.
   Each of the AES variants is defined in [AES].

           +----------------------------+-------------+--------+
           | Name                       | Blockcipher | TAGLEN |
           +----------------------------+-------------+--------+
           | AEAD_AES_128_OCB_TAGLEN128 |   AES-128   |  128   |
           | AEAD_AES_128_OCB_TAGLEN96  |   AES-128   |   96   |
           | AEAD_AES_128_OCB_TAGLEN64  |   AES-128   |   64   |
           | AEAD_AES_192_OCB_TAGLEN128 |   AES-192   |  128   |
           | AEAD_AES_192_OCB_TAGLEN96  |   AES-192   |   96   |
           | AEAD_AES_192_OCB_TAGLEN64  |   AES-192   |   64   |
           | AEAD_AES_256_OCB_TAGLEN128 |   AES-256   |  128   |
           | AEAD_AES_256_OCB_TAGLEN96  |   AES-256   |   96   |
           | AEAD_AES_256_OCB_TAGLEN64  |   AES-256   |   64   |
           +----------------------------+-------------+--------+

   RFC 5116 defines an interface for authenticated-encryption schemes
   [RFC5116].  RFC 5116 requires the specification of certain constants
   for each named AEAD scheme.  For each of the OCB parameter sets
   listed above: P_MAX, A_MAX, and C_MAX are all unbounded; N_MIN is 1
   byte, and N_MAX is 15 bytes.  The parameter sets indicating the use
   of AES-128, AES-192, and AES-256 have K_LEN equal to 16, 24, and 32
   bytes, respectively.

   Each ciphertext is longer than its corresponding plaintext by exactly
   TAGLEN bits, and TAGLEN is given at the end of each name.  For
   instance, an AEAD_AES_128_OCB_TAGLEN64 ciphertext is exactly 64 bits
   longer than its corresponding plaintext.

4.  OCB Algorithms

   OCB is described in this section using pseudocode.  Given any
   collection of inputs of the required types, following the pseudocode
   description for a function will produce the correct output of the
   promised type.

4.1.  Processing Associated Data: HASH

   OCB has the ability to authenticate unencrypted associated data at
   the same time that it provides for authentication and encrypts a
   plaintext.  The following hash function is central to providing this
   functionality.  If an application has no associated data, then the
   associated data should be considered to exist and to be the empty
   string.  HASH, conveniently, always returns zeros(128) when the
   associated data is the empty string.

   Function name:
     HASH
   Input:
     K, string of KEYLEN bits                      // Key
     A, string of any length                       // Associated data
   Output:
     Sum, string of 128 bits                       // Hash result

   Sum is defined as follows.

     //
     // Key-dependent variables
     //
     L_* = ENCIPHER(K, zeros(128))
     L_$ = double(L_*)
     L_0 = double(L_$)
     L_i = double(L_{i-1}) for every integer i > 0

     //
     // Consider A as a sequence of 128-bit blocks
     //
     Let m be the largest integer so that 128m <= bitlen(A)
     Let A_1, A_2, ..., A_m and A_* be strings so that
       A == A_1 || A_2 || ... || A_m || A_*, and
       bitlen(A_i) == 128 for each 1 <= i <= m.
       Note: A_* may possibly be the empty string.

     //
     // Process any whole blocks
     //
     Sum_0 = zeros(128)
     Offset_0 = zeros(128)
     for each 1 <= i <= m
        Offset_i = Offset_{i-1} xor L_{ntz(i)}
        Sum_i = Sum_{i-1} xor ENCIPHER(K, A_i xor Offset_i)
     end for

     //
     // Process any final partial block; compute final hash value
     //
     if bitlen(A_*) > 0 then
        Offset_* = Offset_m xor L_*
        CipherInput = (A_* || 1 || zeros(127-bitlen(A_*))) xor Offset_*
        Sum = Sum_m xor ENCIPHER(K, CipherInput)
     else
        Sum = Sum_m
     end if

4.2.  Encryption: OCB-ENCRYPT

   This function computes a ciphertext (which includes a bundled
   authentication tag) when given a plaintext, associated data, nonce,
   and key.  For each invocation of OCB-ENCRYPT using the same key K,
   the value of the nonce input N must be distinct.

   Function name:
     OCB-ENCRYPT
   Input:
     K, string of KEYLEN bits                      // Key
     N, string of no more than 120 bits            // Nonce
     A, string of any length                       // Associated data
     P, string of any length                       // Plaintext
   Output:
     C, string of length bitlen(P) + TAGLEN bits   // Ciphertext

   C is defined as follows.

     //
     // Key-dependent variables
     //
     L_* = ENCIPHER(K, zeros(128))
     L_$ = double(L_*)
     L_0 = double(L_$)
     L_i = double(L_{i-1}) for every integer i > 0

     //
     // Consider P as a sequence of 128-bit blocks
     //
     Let m be the largest integer so that 128m <= bitlen(P)
     Let P_1, P_2, ..., P_m and P_* be strings so that
       P == P_1 || P_2 || ... || P_m || P_*, and
       bitlen(P_i) == 128 for each 1 <= i <= m.
       Note: P_* may possibly be the empty string.

     //
     // Nonce-dependent and per-encryption variables
     //
     Nonce = num2str(TAGLEN mod 128,7) || zeros(120-bitlen(N)) || 1 || N
     bottom = str2num(Nonce[123..128])
     Ktop = ENCIPHER(K, Nonce[1..122] || zeros(6))
     Stretch = Ktop || (Ktop[1..64] xor Ktop[9..72])
     Offset_0 = Stretch[1+bottom..128+bottom]
     Checksum_0 = zeros(128)
     //
     // Process any whole blocks
     //
     for each 1 <= i <= m
        Offset_i = Offset_{i-1} xor L_{ntz(i)}
        C_i = Offset_i xor ENCIPHER(K, P_i xor Offset_i)
        Checksum_i = Checksum_{i-1} xor P_i
     end for

     //
     // Process any final partial block and compute raw tag
     //
     if bitlen(P_*) > 0 then
        Offset_* = Offset_m xor L_*
        Pad = ENCIPHER(K, Offset_*)
        C_* = P_* xor Pad[1..bitlen(P_*)]
        Checksum_* = Checksum_m xor (P_* || 1 || zeros(127-bitlen(P_*)))
        Tag = ENCIPHER(K, Checksum_* xor Offset_* xor L_$) xor HASH(K,A)
     else
        C_* = <empty string>
        Tag = ENCIPHER(K, Checksum_m xor Offset_m xor L_$) xor HASH(K,A)
     end if

     //
     // Assemble ciphertext
     //
     C = C_1 || C_2 || ... || C_m || C_* || Tag[1..TAGLEN]

4.3.  Decryption: OCB-DECRYPT

   This function computes a plaintext when given a ciphertext,
   associated data, nonce, and key.  An authentication tag is embedded
   in the ciphertext.  If the tag is not correct for the ciphertext,
   associated data, nonce, and key, then an INVALID signal is produced.

   Function name:
     OCB-DECRYPT
   Input:
     K, string of KEYLEN bits                      // Key
     N, string of no more than 120 bits            // Nonce
     A, string of any length                       // Associated data
     C, string of at least TAGLEN bits             // Ciphertext
   Output:
     P, string of length bitlen(C) - TAGLEN bits,  // Plaintext
          or INVALID indicating authentication failure

   P is defined as follows.

     //
     // Key-dependent variables
     //
     L_* = ENCIPHER(K, zeros(128))
     L_$ = double(L_*)
     L_0 = double(L_$)
     L_i = double(L_{i-1}) for every integer i > 0

     //
     // Consider C as a sequence of 128-bit blocks
     //
     Let m be the largest integer so that 128m <= bitlen(C) - TAGLEN
     Let C_1, C_2, ..., C_m, C_* and T be strings so that
       C == C_1 || C_2 || ... || C_m || C_* || T,
       bitlen(C_i) == 128 for each 1 <= i <= m, and
       bitlen(T) == TAGLEN.
       Note: C_* may possibly be the empty string.

     //
     // Nonce-dependent and per-decryption variables
     //
     Nonce = num2str(TAGLEN mod 128,7) || zeros(120-bitlen(N)) || 1 || N
     bottom = str2num(Nonce[123..128])
     Ktop = ENCIPHER(K, Nonce[1..122] || zeros(6))
     Stretch = Ktop || (Ktop[1..64] xor Ktop[9..72])
     Offset_0 = Stretch[1+bottom..128+bottom]
     Checksum_0 = zeros(128)

     //
     // Process any whole blocks
     //
     for each 1 <= i <= m
        Offset_i = Offset_{i-1} xor L_{ntz(i)}
        P_i = Offset_i xor DECIPHER(K, C_i xor Offset_i)
        Checksum_i = Checksum_{i-1} xor P_i
     end for

     //
     // Process any final partial block and compute raw tag
     //
     if bitlen(C_*) > 0 then
        Offset_* = Offset_m xor L_*
        Pad = ENCIPHER(K, Offset_*)
        P_* = C_* xor Pad[1..bitlen(C_*)]
        Checksum_* = Checksum_m xor (P_* || 1 || zeros(127-bitlen(P_*)))
        Tag = ENCIPHER(K, Checksum_* xor Offset_* xor L_$) xor HASH(K,A)
     else
        P_* = <empty string>
        Tag = ENCIPHER(K, Checksum_m xor Offset_m xor L_$) xor HASH(K,A)
     end if

     //
     // Check for validity and assemble plaintext
     //
     if (Tag[1..TAGLEN] == T) then
        P = P_1 || P_2 || ... || P_m || P_*
     else
        P = INVALID
     end if

5.  Security Considerations

   OCB achieves two security properties, confidentiality and
   authenticity.  Confidentiality is defined via "indistinguishability
   from random bits", meaning that an adversary is unable to distinguish
   OCB outputs from an equal number of random bits.  Authenticity is
   defined via "authenticity of ciphertexts", meaning that an adversary
   is unable to produce any valid nonce-ciphertext pair that it has not
   already acquired.  The security guarantees depend on the underlying
   blockcipher being secure in the sense of a strong pseudorandom
   permutation.  Thus, if OCB is used with a blockcipher that is not
   secure as a strong pseudorandom permutation, the security guarantees
   vanish.  The need for the strong pseudorandom permutation property
   means that OCB should be used with a conservatively designed, well-
   trusted blockcipher, such as AES.

   Both the confidentiality and the authenticity properties of OCB
   degrade as per s^2 / 2^128, where s is the total number of blocks
   that the adversary acquires.  The consequence of this formula is that
   the proven security disappears when s becomes as large as 2^64.
   Thus, the user should never use a key to generate an amount of
   ciphertext that is near to, or exceeds, 2^64 blocks.  In order to
   ensure that s^2 / 2^128 remains small, a given key should be used to
   encrypt at most 2^48 blocks (2^55 bits or 4 petabytes), including the
   associated data.  To ensure these limits are not crossed, automated
   key management is recommended in systems exchanging large amounts of
   data [RFC4107].

   When a ciphertext decrypts as INVALID, it is the implementor's
   responsibility to make sure that no information beyond this fact is
   made adversarially available.

   OCB encryption and decryption produce an internal 128-bit
   authentication tag.  The parameter TAGLEN determines how many bits of
   this internal tag are included in ciphertexts and used for
   authentication.  The value of TAGLEN has two impacts: an adversary
   can trivially forge with probability 2^{-TAGLEN}, and ciphertexts are
   TAGLEN bits longer than their corresponding plaintexts.  It is up to
   the application designer to choose an appropriate value for TAGLEN.
   Long tags cost no more computationally than short ones.

   Normally, a given key should be used to create ciphertexts with a
   single tag length, TAGLEN, and an application should reject any
   ciphertext that claims authenticity under the same key but a
   different tag length.  While the ciphertext core and all of the bits
   of the tag do depend on the tag length, this is done for added
   robustness to misuse and should not suggest that receivers accept
   ciphertexts employing variable tag lengths under a single key.

   Timing attacks are not a part of the formal security model and an
   implementation should take care to mitigate them in contexts where
   this is a concern.  To render timing attacks impotent, the amount of
   time to encrypt or decrypt a string should be independent of the key
   and the contents of the string.  The only explicitly conditional OCB
   operation that depends on private data is double(), which means that
   using constant-time blockcipher and double() implementations
   eliminates most (if not all) sources of timing attacks on OCB.
   Power-usage attacks are likewise out of the scope of the formal model
   and should be considered for environments where they are threatening.

   The OCB encryption scheme reveals in the ciphertext the length of the
   plaintext.  Sometimes the length of the plaintext is a valuable piece
   of information that should be hidden.  For environments where
   "traffic analysis" is a concern, techniques beyond OCB encryption
   (typically involving padding) would be necessary.

   Defining the ciphertext that results from OCB-ENCRYPT to be the pair
   (C_1 || C_2 || ... || C_m || C_*, Tag[1..TAGLEN]) instead of the
   concatenation C_1 || C_2 || ... || C_m || C_* || Tag[1..TAGLEN]
   introduces no security concerns.  Because TAGLEN is fixed, both
   versions allow ciphertexts to be parsed unambiguously.

5.1.  Nonce Requirements

   It is crucial that, as one encrypts, one does not repeat a nonce.
   The inadvertent reuse of the same nonce by two invocations of the OCB
   encryption operation, with the same key, but with distinct plaintext
   values, undermines the confidentiality of the plaintexts protected in
   those two invocations and undermines all of the authenticity and
   integrity protection provided by that key.  For this reason, OCB
   should only be used whenever nonce uniqueness can be provided with
   certainty.  Note that it is acceptable to input the same nonce value
   multiple times to the decryption operation.  We emphasize that the
   security consequences are quite serious if an attacker observes two
   ciphertexts that were created using the same nonce and key values,
   unless the plaintext and associated data values in both invocations
   of the encrypt operation were identical.  First, a loss of
   confidentiality ensues because the attacker will be able to infer
   relationships between the two plaintext values.  Second, a loss of
   authenticity ensues because the attacker will be able to recover
   secret information used to provide authenticity, making subsequent
   forgeries trivial.  Note that there are AEAD schemes, particularly
   the Synthetic Initialization Vector (SIV) [RFC5297], appropriate for
   environments where nonces are unavailable or unreliable.  OCB is not
   such a scheme.

   Nonces need not be secret, and a counter may be used for them.  If
   two parties send OCB-encrypted plaintexts to one another using the
   same key, then the space of nonces used by the two parties must be
   partitioned so that no nonce that could be used by one party to
   encrypt could be used by the other to encrypt (e.g., odd and even
   counters).

6.  IANA Considerations

   The Internet Assigned Numbers Authority (IANA) has defined a registry
   for Authenticated Encryption with Associated Data parameters.  The
   IANA has added the following entries to the AEAD Registry.  Each name
   refers to a set of parameters defined in Section 3.1.

         +----------------------------+-------------+------------+
         | Name                       |  Reference  | Numeric ID |
         +----------------------------+-------------+------------+
         | AEAD_AES_128_OCB_TAGLEN128 | Section 3.1 |     20     |
         | AEAD_AES_128_OCB_TAGLEN96  | Section 3.1 |     21     |
         | AEAD_AES_128_OCB_TAGLEN64  | Section 3.1 |     22     |
         | AEAD_AES_192_OCB_TAGLEN128 | Section 3.1 |     23     |
         | AEAD_AES_192_OCB_TAGLEN96  | Section 3.1 |     24     |
         | AEAD_AES_192_OCB_TAGLEN64  | Section 3.1 |     25     |
         | AEAD_AES_256_OCB_TAGLEN128 | Section 3.1 |     26     |
         | AEAD_AES_256_OCB_TAGLEN96  | Section 3.1 |     27     |
         | AEAD_AES_256_OCB_TAGLEN64  | Section 3.1 |     28     |
         +----------------------------+-------------+------------+

7.  Acknowledgements

   The design of the original OCB scheme [OCB1] was done while Rogaway
   was at Chiang Mai University, Thailand.  Follow-up work [OCB2] was
   done with support of NSF grant 0208842 and a gift from Cisco.  The
   final work by Krovetz and Rogaway [OCB3] that has resulted in this
   specification was supported by NSF grant 0904380.  Thanks go to the
   many members of the Crypto Forum Research Group (CFRG) who provided
   feedback on earlier drafts.  Thanks in particular go to David McGrew
   for contributing some text and for managing the RFC approval process,
   to James Manger for initiating a productive discussion on tag-length
   dependency and for greatly improving Appendix A, to Matt Caswell and
   Peter Dettman for writing implementations and verifying test vectors,
   and to Stephen Farrell and Spencer Dawkins for their careful reading
   and suggestions.

8.  References

8.1.  Normative References

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

   [RFC5116]  McGrew, D., "An Interface and Algorithms for Authenticated
              Encryption", RFC 5116, January 2008.

8.2.  Informative References

   [OCB1]     Rogaway, P., Bellare, M., Black, J., and T. Krovetz, "OCB:
              A Block-Cipher Mode of Operation for Efficient
              Authenticated Encryption", ACM Conference on Computer and
              Communications Security 2001 - CCS 2001, ACM Press, 2001.

   [OCB2]     Rogaway, P., "Efficient Instantiations of Tweakable
              Blockciphers and Refinements to Modes OCB and PMAC",
              Advances in Cryptology - ASIACRYPT 2004, Springer, 2004.

   [OCB3]     Krovetz, T. and P. Rogaway, "The Software Performance of
              Authenticated-Encryption Modes", Fast Software Encryption
              - FSE 2011 Springer, 2011.

   [RFC4107]  Bellovin, S. and R. Housley, "Guidelines for Cryptographic
              Key Management", BCP 107, RFC 4107, June 2005.

   [RFC5297]  Harkins, D., "Synthetic Initialization Vector (SIV)
              Authenticated Encryption Using the Advanced Encryption
              Standard (AES)", RFC 5297, October 2008.

Appendix A.  Sample Results

   This section gives sample output values for various inputs when using
   OCB with AES as per the parameters defined in Section 3.1.  All
   strings are represented in hexadecimal (e.g., 0F represents the
   bitstring 00001111).

   The following 16 (N,A,P,C) tuples show the ciphertext C that results
   from OCB-ENCRYPT(K,N,A,P) for various lengths of associated data (A)
   and plaintext (P).  The key (K) has a fixed value, the tag length is
   128 bits, and the nonce (N) increments.

     K : 000102030405060708090A0B0C0D0E0F

   An empty entry indicates the empty string.

     N: BBAA99887766554433221100
     A:
     P:
     C: 785407BFFFC8AD9EDCC5520AC9111EE6

     N: BBAA99887766554433221101
     A: 0001020304050607
     P: 0001020304050607
     C: 6820B3657B6F615A5725BDA0D3B4EB3A257C9AF1F8F03009

     N: BBAA99887766554433221102
     A: 0001020304050607
     P:
     C: 81017F8203F081277152FADE694A0A00

     N: BBAA99887766554433221103
     A:
     P: 0001020304050607
     C: 45DD69F8F5AAE72414054CD1F35D82760B2CD00D2F99BFA9

     N: BBAA99887766554433221104
     A: 000102030405060708090A0B0C0D0E0F
     P: 000102030405060708090A0B0C0D0E0F
     C: 571D535B60B277188BE5147170A9A22C3AD7A4FF3835B8C5
        701C1CCEC8FC3358

     N: BBAA99887766554433221105
     A: 000102030405060708090A0B0C0D0E0F
     P:
     C: 8CF761B6902EF764462AD86498CA6B97
     N: BBAA99887766554433221106
     A:
     P: 000102030405060708090A0B0C0D0E0F
     C: 5CE88EC2E0692706A915C00AEB8B2396F40E1C743F52436B
        DF06D8FA1ECA343D

     N: BBAA99887766554433221107
     A: 000102030405060708090A0B0C0D0E0F1011121314151617
     P: 000102030405060708090A0B0C0D0E0F1011121314151617
     C: 1CA2207308C87C010756104D8840CE1952F09673A448A122
        C92C62241051F57356D7F3C90BB0E07F

     N: BBAA99887766554433221108
     A: 000102030405060708090A0B0C0D0E0F1011121314151617
     P:
     C: 6DC225A071FC1B9F7C69F93B0F1E10DE

     N: BBAA99887766554433221109
     A:
     P: 000102030405060708090A0B0C0D0E0F1011121314151617
     C: 221BD0DE7FA6FE993ECCD769460A0AF2D6CDED0C395B1C3C
        E725F32494B9F914D85C0B1EB38357FF

     N: BBAA9988776655443322110A
     A: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F
     P: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F
     C: BD6F6C496201C69296C11EFD138A467ABD3C707924B964DE
        AFFC40319AF5A48540FBBA186C5553C68AD9F592A79A4240

     N: BBAA9988776655443322110B
     A: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F
     P:
     C: FE80690BEE8A485D11F32965BC9D2A32

     N: BBAA9988776655443322110C
     A:
     P: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F
     C: 2942BFC773BDA23CABC6ACFD9BFD5835BD300F0973792EF4
        6040C53F1432BCDFB5E1DDE3BC18A5F840B52E653444D5DF
     N: BBAA9988776655443322110D
     A: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F2021222324252627
     P: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F2021222324252627
     C: D5CA91748410C1751FF8A2F618255B68A0A12E093FF45460
        6E59F9C1D0DDC54B65E8628E568BAD7AED07BA06A4A69483
        A7035490C5769E60

     N: BBAA9988776655443322110E
     A: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F2021222324252627
     P:
     C: C5CD9D1850C141E358649994EE701B68

     N: BBAA9988776655443322110F
     A:
     P: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F2021222324252627
     C: 4412923493C57D5DE0D700F753CCE0D1D2D95060122E9F15
        A5DDBFC5787E50B5CC55EE507BCB084E479AD363AC366B95
        A98CA5F3000B1479

   Next are several internal values generated during the OCB-ENCRYPT
   computation for the last test vector listed above.

     L_*       : C6A13B37878F5B826F4F8162A1C8D879
     L_$       : 8D42766F0F1EB704DE9F02C54391B075
     L_0       : 1A84ECDE1E3D6E09BD3E058A8723606D
     L_1       : 3509D9BC3C7ADC137A7C0B150E46C0DA
     bottom    : 15 (decimal)
     Ktop      : 9862B0FDEE4E2DD56DBA6433F0125AA2
     Stretch   : 9862B0FDEE4E2DD56DBA6433F0125AA2FAD24D13A063F8B8
     Offset_0  : 587EF72716EAB6DD3219F8092D517D69
     Offset_1  : 42FA1BF908D7D8D48F27FD83AA721D04
     Offset_2  : 77F3C24534AD04C7F55BF696A434DDDE
     Offset_*  : B152F972B3225F459A1477F405FC05A7
     Checksum_1: 000102030405060708090A0B0C0D0E0F
     Checksum_2: 10101010101010101010101010101010
     Checksum_*: 30313233343536379010101010101010
   The next tuple shows a result with a tag length of 96 bits and a
   different key.

     K: 0F0E0D0C0B0A09080706050403020100

     N: BBAA9988776655443322110D
     A: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F2021222324252627
     P: 000102030405060708090A0B0C0D0E0F1011121314151617
        18191A1B1C1D1E1F2021222324252627
     C: 1792A4E31E0755FB03E31B22116E6C2DDF9EFD6E33D536F1
        A0124B0A55BAE884ED93481529C76B6AD0C515F4D1CDD4FD
        AC4F02AA

   The following algorithm tests a wider variety of inputs.  Results are
   given for each parameter set defined in Section 3.1.

      K = zeros(KEYLEN-8) || num2str(TAGLEN,8)
      C = <empty string>
      for i = 0 to 127 do
         S = zeros(8i)
         N = num2str(3i+1,96)
         C = C || OCB-ENCRYPT(K,N,S,S)
         N = num2str(3i+2,96)
         C = C || OCB-ENCRYPT(K,N,<empty string>,S)
         N = num2str(3i+3,96)
         C = C || OCB-ENCRYPT(K,N,S,<empty string>)
      end for
      N = num2str(385,96)
      Output : OCB-ENCRYPT(K,N,C,<empty string>)

   Iteration i of the loop adds 2i + (3 * TAGLEN / 8) bytes to C,
   resulting in an ultimate length for C of 22,400 bytes when TAGLEN ==
   128, 20,864 bytes when TAGLEN == 192, and 19,328 bytes when TAGLEN ==
   64.  The final OCB-ENCRYPT has an empty plaintext component, so
   serves only to authenticate C.  The output should be:

     AEAD_AES_128_OCB_TAGLEN128 Output: 67E944D23256C5E0B6C61FA22FDF1EA2
     AEAD_AES_192_OCB_TAGLEN128 Output: F673F2C3E7174AAE7BAE986CA9F29E17
     AEAD_AES_256_OCB_TAGLEN128 Output: D90EB8E9C977C88B79DD793D7FFA161C
     AEAD_AES_128_OCB_TAGLEN96 Output : 77A3D8E73589158D25D01209
     AEAD_AES_192_OCB_TAGLEN96 Output : 05D56EAD2752C86BE6932C5E
     AEAD_AES_256_OCB_TAGLEN96 Output : 5458359AC23B0CBA9E6330DD
     AEAD_AES_128_OCB_TAGLEN64 Output : 192C9B7BD90BA06A
     AEAD_AES_192_OCB_TAGLEN64 Output : 0066BC6E0EF34E24
     AEAD_AES_256_OCB_TAGLEN64 Output : 7D4EA5D445501CBE

Authors' Addresses

   Ted Krovetz
   Computer Science Department
   California State University, Sacramento
   6000 J Street
   Sacramento, CA  95819-6021
   USA

   EMail: ted@krovetz.net


   Phillip Rogaway
   Computer Science Department
   University of California, Davis
   One Shields Avenue
   Davis, CA  95616-8562
   USA

   EMail: rogaway@cs.ucdavis.edu