Internet Research Task Force T. Krovetz
Internet-Draft Sacramento State
Intended status: Informational P. Rogaway
Expires: December 14, 2013 UC Davis
June 12, 2013
The OCB Authenticated-Encryption Algorithm
draft-irtf-cfrg-ocb-03
Abstract
This document specifies OCB, a shared-key blockcipher-based
encryption scheme that provides privacy 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
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provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on December 14, 2013.
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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 . . . . . 5
4. OCB Algorithms . . . . . . . . . . . . . . . . . . . . . . . 6
4.1. Associated-Data Processing: HASH . . . . . . . . . . . . 6
4.2. Encryption: OCB-ENCRYPT . . . . . . . . . . . . . . . . . 7
4.3. Decryption: OCB-DECRYPT . . . . . . . . . . . . . . . . . 9
5. Security Considerations . . . . . . . . . . . . . . . . . . . 11
5.1. Nonce Requirements . . . . . . . . . . . . . . . . . . . 12
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 13
7. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 13
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 13
8.1. Normative References . . . . . . . . . . . . . . . . . . 14
8.2. Informative References . . . . . . . . . . . . . . . . . 14
Appendix A. Sample Results . . . . . . . . . . . . . . . . . . . 14
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 17
1. Introduction
Schemes for authenticated encryption (AE) simultaneously provide for
privacy 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 privacy 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 privacy 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.
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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 privacy 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 and 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 on-line: 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 in the
square of the number of blocks of texts divided by two to the
blocklength.
For reasons of generality, OCB is defined to operate on arbitrary
bit-strings. But for reasons of simplicity and efficiency, most
implementations will assume that strings operated on are byte-strings
(ie, 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 byte-strings.
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
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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 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 privacy 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 upper-case letter while
integer variables are written in all lower-case. 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 (eg, 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.
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S || T String S concatenated with string T (eg, 000 || 111 ==
000111).
str2num(S) The base-2 interpretation of bitstring S (eg,
str2num(1110) == 14).
num2str(i,n) The n-bit string whose base-2 interpretation is i (eg,
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].
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+----------------------------+-------------+--------+
| 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.
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. Associated-Data Processing: 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
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Sum is defined as follows.
//
// Key-dependent variables
//
L_* = ENCIPHER(K, zeros(128))
L_$ = double(L_*)
L_0 = double(L_$)
L_i = double(L_{i-1}) for every integer i > 0
//
// Consider A as a sequence of 128-bit blocks
//
Let m be the largest integer so that 128m <= bitlen(A)
Let A_1, A_2, ..., A_m and A_* be strings so that
A == A_1 || A_2 || ... || A_m || A_*, and
bitlen(A_i) == 128 for each 1 <= i <= m.
Note: A_* may possibly be the empty string.
//
// Process any whole blocks
//
Sum_0 = zeros(128)
Offset_0 = zeros(128)
for each 1 <= i <= m
Offset_i = Offset_{i-1} xor L_{ntz(i)}
Sum_i = Sum_{i-1} xor ENCIPHER(K, A_i xor Offset_i)
end for
//
// Process any final partial block; compute final hash value
//
if bitlen(A_*) > 0 then
Offset_* = Offset_m xor L_*
CipherInput = (A_* || 1 || zeros(127-bitlen(A_*))) xor Offset_*
Sum = Sum_m xor ENCIPHER(K, CipherInput)
else
Sum = Sum_m
end if
4.2. Encryption: OCB-ENCRYPT
This function computes a ciphertext (which includes a bundled
authentication tag) when given a plaintext, associated data, nonce
and key. For each invocation of OCB-ENCRYPT using the same key K,
the value of the nonce input N must be distinct.
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Function name:
OCB-ENCRYPT
Input:
K, string of KEYLEN bits // Key
N, string of no more than 120 bits // Nonce
A, string of any length // Associated data
P, string of any length // Plaintext
Output:
C, string of length bitlen(P) + TAGLEN bits // Ciphertext
C is defined as follows.
//
// Key-dependent variables
//
L_* = ENCIPHER(K, zeros(128))
L_$ = double(L_*)
L_0 = double(L_$)
L_i = double(L_{i-1}) for every integer i > 0
//
// Consider P as a sequence of 128-bit blocks
//
Let m be the largest integer so that 128m <= bitlen(P)
Let P_1, P_2, ..., P_m and P_* be strings so that
P == P_1 || P_2 || ... || P_m || P_*, and
bitlen(P_i) == 128 for each 1 <= i <= m.
Note: P_* may possibly be the empty string.
//
// Nonce-dependent and per-encryption variables
//
Nonce = num2str(TAGLEN mod 128,7) || zeros(120-bitlen(N)) || 1 || N
bottom = str2num(Nonce[123..128])
Ktop = ENCIPHER(K, Nonce[1..122] || zeros(6))
Stretch = Ktop || (Ktop[1..64] xor Ktop[9..72])
Offset_0 = Stretch[1+bottom..128+bottom]
Checksum_0 = zeros(128)
//
// Process any whole blocks
//
for each 1 <= i <= m
Offset_i = Offset_{i-1} xor L_{ntz(i)}
C_i = Offset_i xor ENCIPHER(K, P_i xor Offset_i)
Checksum_i = Checksum_{i-1} xor P_i
end for
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//
// Process any final partial block and compute raw tag
//
if bitlen(P_*) > 0 then
Offset_* = Offset_m xor L_*
Pad = ENCIPHER(K, Offset_*)
C_* = P_* xor Pad[1..bitlen(P_*)]
Checksum_* = Checksum_m xor (P_* || 1 || zeros(127-bitlen(P_*)))
Tag = ENCIPHER(K, Checksum_* xor Offset_* xor L_$) xor HASH(K,A)
else
C_* =
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_$)
L_i = double(L_{i-1}) for every integer i > 0
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//
// Consider C as a sequence of 128-bit blocks
//
Let m be the largest integer so that 128m <= bitlen(C) - TAGLEN
Let C_1, C_2, ..., C_m, C_* and T be strings so that
C == C_1 || C_2 || ... || C_m || C_* || T,
bitlen(C_i) == 128 for each 1 <= i <= m, and
bitlen(T) == TAGLEN.
Note: C_* may possibly be the empty string.
//
// Nonce-dependent and per-decryption variables
//
Nonce = num2str(TAGLEN mod 128,7) || zeros(120-bitlen(N)) || 1 || N
bottom = str2num(Nonce[123..128])
Ktop = ENCIPHER(K, Nonce[1..122] || zeros(6))
Stretch = Ktop || (Ktop[1..64] xor Ktop[9..72])
Offset_0 = Stretch[1+bottom..128+bottom]
Checksum_0 = zeros(128)
//
// Process any whole blocks
//
for each 1 <= i <= m
Offset_i = Offset_{i-1} xor L_{ntz(i)}
P_i = Offset_i xor DECIPHER(K, C_i xor Offset_i)
Checksum_i = Checksum_{i-1} xor P_i
end for
//
// Process any final partial block and compute raw tag
//
if bitlen(C_*) > 0 then
Offset_* = Offset_m xor L_*
Pad = ENCIPHER(K, Offset_*)
P_* = C_* xor Pad[1..bitlen(C_*)]
Checksum_* = Checksum_m xor (P_* || 1 || zeros(127-bitlen(P_*)))
Tag = ENCIPHER(K, Checksum_* xor Offset_* xor L_$) xor HASH(K,A)
else
P_* =
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_*
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else
P = INVALID
end if
5. Security Considerations
OCB achieves two security properties, privacy and authenticity.
Privacy 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 privacy 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
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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 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 allows 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 AD 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
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there are AEAD schemes, particularly 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 (eg, 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 Identifier |
+----------------------------+-------------+--------------------+
| AEAD_AES_128_OCB_TAGLEN128 | Section 3.1 | XX |
| AEAD_AES_128_OCB_TAGLEN96 | Section 3.1 | XX |
| AEAD_AES_128_OCB_TAGLEN64 | Section 3.1 | XX |
| AEAD_AES_192_OCB_TAGLEN128 | Section 3.1 | XX |
| AEAD_AES_192_OCB_TAGLEN96 | Section 3.1 | XX |
| AEAD_AES_192_OCB_TAGLEN64 | Section 3.1 | XX |
| AEAD_AES_256_OCB_TAGLEN128 | Section 3.1 | XX |
| AEAD_AES_256_OCB_TAGLEN96 | Section 3.1 | XX |
| AEAD_AES_256_OCB_TAGLEN64 | Section 3.1 | XX |
+----------------------------+-------------+--------------------+
7. Acknowledgements
The design of the original OCB scheme [OCB1] was done while Phil
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 spec was supported by NSF grant 0904380. Thanks go
to the Crypto Forum Research Group (CFRG) for providing feedback on
earlier drafts. Thanks in particular to David McGrew for
contributing text to Section 5, to James Manger for initiating a
productive discussion on tag-length dependency, and to Matt Caswell
for his careful reading and suggestions.
8. References
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8.1. Normative References
[RFC5116] McGrew, D., "An interface and algorithms for authenticated
encryption", RFC 5116, January 2008.
[AES] National Institute of Standards and Technology, "Advanced
Encryption Standard (AES)", FIPS PUB 197, November 2001.
8.2. Informative References
[RFC4107] Bellovin, S. and R. Housley, "Guidelines for cryptographic
key management", RFC 4107, June 2005.
[RFC5297] Harkins, D., "Synthetic Initialization Vector (SIV)
authenticated encryption using the Advanced Encryption
Standard (AES)", RFC 5297, October 2008.
[OCB3] Krovetz, T. and P. Rogaway, "The software performance of
authenticated-encryption modes", in Fast Software
Encryption - FSE 2011, Springer, 2011.
[OCB2] Rogaway, P., "Efficient instantiations of tweakable
blockciphers and refinements to modes OCB and PMAC", in
Advances in Cryptology - ASIACRYPT 2004, Springer, 2004.
[OCB1] Rogaway, P., Bellare, M., Black, J., and T. Krovetz, "OCB:
a block-cipher mode of operation for efficient
authenticated encryption", in ACM Conference on Computer
and Communications Security 2001 - CCS 2001, ACM Press,
2001.
[OCB1ALT] Rogaway, P., Bellare, M., Black, J., and T. Krovetz, "OCB
Mode: proposal to NIST for a block-cipher mode of
operation which simultaneously provides privacy and
authenticity", at http://eprint.iacr.org/2001/026, IACR
ePrint Archive, 2001.
Appendix A. Sample Results
This section gives sample output values for various inputs when using
the AEAD_AES_128_OCB_TAGLEN128 parameters defined in Section 3.1.
All strings are represented in hexadecimal (eg, 0F represents the
bitstring 00001111).
Each of the following (A,P,C) triples show the ciphertext C that
results from OCB-ENCRYPT(K,N,A,P) when K and N are fixed with the
values
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K : 000102030405060708090A0B0C0D0E0F
N : 000102030405060708090A0B
An empty entry indicates the empty string.
A:
P:
C: 197B9C3C441D3C83EAFB2BEF633B9182
A: 0001020304050607
P: 0001020304050607
C: 92B657130A74B85A16DC76A46D47E1EAD537209E8A96D14E
A: 0001020304050607
P:
C: 98B91552C8C009185044E30A6EB2FE21
A:
P: 0001020304050607
C: 92B657130A74B85A971EFFCAE19AD4716F88E87B871FBEED
A: 000102030405060708090A0B0C0D0E0F
P: 000102030405060708090A0B0C0D0E0F
C: BEA5E8798DBE7110031C144DA0B26122776C9924D6723A1F
C4524532AC3E5BEB
A: 000102030405060708090A0B0C0D0E0F
P:
C: 7DDB8E6CEA6814866212509619B19CC6
A:
P: 000102030405060708090A0B0C0D0E0F
C: BEA5E8798DBE7110031C144DA0B2612213CC8B747807121A
4CBB3E4BD6B456AF
A: 000102030405060708090A0B0C0D0E0F1011121314151617
P: 000102030405060708090A0B0C0D0E0F1011121314151617
C: BEA5E8798DBE7110031C144DA0B26122FCFCEE7A2A8D4D48
5FA94FC3F38820F1DC3F3D1FD4E55E1C
A: 000102030405060708090A0B0C0D0E0F1011121314151617
P:
C: 282026DA3068BC9FA118681D559F10F6
A:
P: 000102030405060708090A0B0C0D0E0F1011121314151617
C: BEA5E8798DBE7110031C144DA0B26122FCFCEE7A2A8D4D48
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6EF2F52587FDA0ED97DC7EEDE241DF68
A: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F
P: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F
C: BEA5E8798DBE7110031C144DA0B26122CEAAB9B05DF771A6
57149D53773463CBB2A040DD3BD5164372D76D7BB6824240
A: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F
P:
C: E1E072633BADE51A60E85951D9C42A1B
A:
P: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F
C: BEA5E8798DBE7110031C144DA0B26122CEAAB9B05DF771A6
57149D53773463CB4A3BAE824465CFDAF8C41FC50C7DF9D9
A: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F2021222324252627
P: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F2021222324252627
C: BEA5E8798DBE7110031C144DA0B26122CEAAB9B05DF771A6
57149D53773463CB68C65778B058A635659C623211DEEA0D
E30D2C381879F4C8
A: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F2021222324252627
P:
C: 7AEB7A69A1687DD082CA27B0D9A37096
A:
P: 000102030405060708090A0B0C0D0E0F1011121314151617
18191A1B1C1D1E1F2021222324252627
C: BEA5E8798DBE7110031C144DA0B26122CEAAB9B05DF771A6
57149D53773463CB68C65778B058A635060C8467F4ABAB5E
8B3C2067A2E115DC
Next are several internal values generated during the OCB-ENCRYPT
computation for the last test vector listed above.
bottom : 11
Checksum_1: 000102030405060708090A0B0C0D0E0F
Checksum_2: 10101010101010101010101010101010
Checksum_*: 30313233343536379010101010101010
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Ktop : 43E111498C0582BF99F1D966CEFCBCC6
L_* : C6A13B37878F5B826F4F8162A1C8D879
L_$ : 8D42766F0F1EB704DE9F02C54391B075
L_0 : 1A84ECDE1E3D6E09BD3E058A8723606D
L_1 : 3509D9BC3C7ADC137A7C0B150E46C0DA
Offset_0 : 088A4C602C15FCCF8ECB3677E5E63517
Offset_1 : 120EA0BE322892C633F533FD62C5557A
Offset_2 : 270779020E524ED5498938E86C8395A0
Offset_* : E1A6423589DD155726C6B98ACD4B4DD9
Stretch : 43E111498C0582BF99F1D966CEFCBCC6A2F058C589873D26
The following algorithm tests a wider variety of inputs. Results are
given for each parameter set defined in Section 3.1.
K = zeros(KEYLEN) // Keylength of AES in use
C =
for i = 0 to 127 do
S = zeros(8i) // i bytes of zeros
N = zeros(88) || num2str(i,8) // 11 byte zero then 1 byte i
C = C || OCB-ENCRYPT(K,N,S,S)
C = C || OCB-ENCRYPT(K,N,,S)
C = C || OCB-ENCRYPT(K,N,S,)
end for
N = zeros(96)
Output : OCB-ENCRYPT(K,N,C,)
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: B2B41CBF9B05037DA7F16C24A35C1C94
AEAD_AES_192_OCB_TAGLEN128 Output: 1529F894659D2B51B776740211E7D083
AEAD_AES_256_OCB_TAGLEN128 Output: 42B83106E473C0EEE086C8D631FD4C7B
AEAD_AES_128_OCB_TAGLEN96 Output: 1A4F0654277709A5BDA0D380
AEAD_AES_192_OCB_TAGLEN96 Output: AD819483E01DD648978F4522
AEAD_AES_256_OCB_TAGLEN96 Output: CD2E41379C7E7C4458CCFB4A
AEAD_AES_128_OCB_TAGLEN64 Output: B7ECE9D381FE437F
AEAD_AES_192_OCB_TAGLEN64 Output: DE0574C87FF06DF9
AEAD_AES_256_OCB_TAGLEN64 Output: 833E45FF7D332F7E
Authors' Addresses
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Ted Krovetz
Computer Science Department
California State University
6000 J Street
Sacramento, CA 95819-6021
USA
Email: ted@krovetz.net
Phillip Rogaway
Computer Science Department
University of California
One Shields Avenue
Davis, CA 95616-8562
USA
Email: rogaway@cs.ucdavis.edu
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