JunHyuk Song
Radha Poovendran
University of Washington
Jicheol Lee
Samsung Electronics
Tetsu Iwata
INTERNET DRAFT Ibaraki University
Expires: June 8, 2006 December 9 2005
The AES-CMAC Algorithm
draft-songlee-aes-cmac-03.txt
Status of This Memo
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Copyright Notice
Copyright (C) The Internet Society (2005).
Abstract
National Institute of Standards and Technology (NIST) has newly
specified the Cipher-based Message Authentication Code (CMAC)
which is equivalent to the One-Key CBC MAC1 (OMAC1) submitted by
Iwata and Kurosawa. This memo specifies the authentication algorithm
based on CMAC with 128-bit Advanced Encryption Standard (AES).
This new authentication algorithm is named AES-CMAC.
The purpose of this document is to make the AES-CMAC algorithm
conveniently available to the Internet Community.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 2
2. Specification of AES-CMAC . . . . . . . . . . . . . . . . 3
2.1 Basic definitions . . . . . . . . . . . . . . . . . . . . 3
2.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Subkey Generation Algorithm . . . . . . . . . . . . . . . 5
2.4 MAC Generation Algorithm . . . . . . . . . . . . . . . . . 7
2.5 MAC Verification Algorithm . . . . . . . . . . . . . . . . 9
3. Security Considerations . . . . . . . . . . . . . . . . . . 10
4. Test Vector . . . . . . . . . . . . . . . . . . . . . . . . 11
5. Acknowledgement . . . . . . . . . . . . . . . . . . . . . . 11
6. Authors address . . . . . . . . . . . . . . . . . . . . . . 12
7. References . . . . . . . . . . . . . . . . . . . . . . . . 13
Appendix A. Test Code . . . . . . . . . . . . . . . . . . . . 14
1. Introduction
National Institute of Standards and Technology (NIST) has newly
specified the Cipher-based Message Authentication Code (CMAC).
CMAC [NIST-CMAC] is a keyed hash function that is based on a
symmetric key block cipher such as the Advanced Encryption
Standard [NIST-AES]. CMAC is equivalent to the One-Key CBC MAC1
(OMAC1) submitted by Iwata and Kurosawa [OMAC1a, OMAC1b]. OMAC1
is an improvement of the eXtended Cipher Block Chaining mode (XCBC)
submitted by Black and Rogaway [XCBCa, XCBCb], which itself is an
improvement of the basic CBC-MAC. XCBC efficiently addresses the
security deficiencies of CBC-MAC, and OMAC1 efficiently reduces the
key size of XCBC.
AES-CMAC provides stronger assurance of data integrity than a
checksum or an error detecting code. The verification of a checksum
or an error detecting code detects only accidental modifications of
the data, while CMAC is designed to detect intentional, unauthorized
modifications of the data, as well as accidental modifications.
AES-CMAC achieves the similar security goal of HMAC [RFC-HMAC].
Since AES-CMAC is based on a symmetric key block cipher, AES,
while HMAC is based on a hash function, such as SHA-1, AES-CMAC
is appropriate for information systems in which AES is more readily
available than a hash function.
This memo specifies the authentication algorithm based on CMAC with
AES-128. This new authentication algorithm is named AES-CMAC.
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2. Specification of AES-CMAC
2.1 Basic definitions
The following table describes the basic definitions necessary to
explain the specification of AES-CMAC.
x || y Concatenation.
x || y is the string x concatenated with string y.
0000 || 1111 is 00001111.
x XOR y Exclusive-OR operation.
For two equal length strings x and y,
x XOR y is their bit-wise exclusive-OR.
ceil(x) Ceiling function.
The smallest integer no smaller than x.
ceil(3.5) is 4. ceil(5) is 5.
x << 1 Left-shift of the string x by 1 bit.
The most significant bit disappears and a zero
comes into the least significant bit.
10010001 << 1 is 00100010.
0^n The string that consists of n zero-bits.
0^3 means that 000 in binary format.
10^4 means that 10000 in binary format.
10^i means that 1 followed by i-times repeated
zero's.
MSB(x) The most-significant bit of the string x.
MSB(10010000) means 1.
padding(x) 10^i padded output of input x.
It is described in detail in section 2.4.
Key 128 bits (16 bytes) long key for AES-128.
Denoted by K.
First subkey 128 bits (16 bytes) long first subkey,
derived through the subkey
generation algorithm from the key K.
Denoted by K1.
Second subkey 128 bits (16 bytes) long second subkey,
derived through the subkey
generation algorithm from the key K.
Denoted by K2.
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Message A message to be authenticated.
Denoted by M.
The message can be null, which means that the length
of M is 0.
Message length The length of the message M in bytes.
Denoted by len.
Minimum value of the length can be 0. The maximum
value of the length is not specified in this document.
AES-128(K,M) AES-128(K,M) is the 128-bit ciphertext of AES-128
for a 128-bit key K and a 128-bit message M.
MAC A 128-bit string which is the output of AES-CMAC.
Denoted by T.
Validating the MAC provides assurance of the
integrity and authenticity over the message from
the source.
MAC length By default, the length of the output of AES-CMAC is
128 bits. It is possible to truncate the MAC.
Result of truncation should be taken in most
significant bits first order. MAC length must be
specified before the communication starts, and
it must not be changed during the life time of the key.
2.2 Overview
AES-CMAC uses the Advanced Encryption Standard [NIST-AES] as a
building block. To generate a MAC, AES-CMAC takes a secret key,
a message of variable length and the length of the message in bytes
as inputs, and returns a fixed bit string called a MAC.
The core of AES-CMAC is the basic CBC-MAC. For a message M to be
authenticated, the CBC-MAC is applied to M. There are two cases of
operation in CMAC. Figure 2.1 illustrated the operation of CBC-MAC
with two cases. If the size of input message block is equal to
multiple of block size namely 128 bits, the last block processing
shall be exclusive-OR'ed with K1. Otherwise, the last block shall
be padded with 10^i (notation is described in section 2.1) and
exclusive-OR'ed with K2. The result of the previous process will be
the input of the last CBC operation. The output of AES-CMAC provides
data integrity over whole input message.
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+-----+ +-----+ +-----+ +-----+ +-----+ +---+----+
| M_1 | | M_2 | | M_n | | M_1 | | M_2 | |M_n|10^i|
+-----+ +-----+ +-----+ +-----+ +-----+ +---+----+
| | | +--+ | | | +--+
| +--->(+) +--->(+)<-|K1| | +--->(+) +--->(+)<-|K2|
| | | | | +--+ | | | | | +--+
+-----+ | +-----+ | +-----+ +-----+ | +-----+ | +-----+
|AES_K| | |AES_K| | |AES_K| |AES_K| | |AES_K| | |AES_K|
+-----+ | +-----+ | +-----+ +-----+ | +-----+ | +-----+
| | | | | | | | | |
+-----+ +-----+ | +-----+ +-----+ |
| |
+-----+ +-----+
| T | | T |
+-----+ +-----+
(a) positive multiple block length (b) otherwise
Figure 2.1 Illustration of two cases of AES-CMAC.
AES_K is AES-128 with key K.
The message M is divided into blocks M_1,...,M_n,
where M_i is the i-th message block.
The length of M_i is 128 bits for i = 1,...,n-1, and
the length of the last block M_n is less than or equal to 128 bits.
K1 is the subkey for the case (a), and
K2 is the subkey for the case (b).
K1 and K2 are generated by the subkey generation algorithm
described in section 2.3.
2.3 Subkey Generation Algorithm
The subkey generation algorithm, Generate_Subkey(), takes a secret
key, K, which is just the key for AES-128.
The output of the subkey generation algorithm is two subkeys, K1
and K2. We write (K1,K2) := Generate_Subkey(K).
Subkeys K1 and K2 are used in both MAC generation and MAC
verification algorithms. K1 is used for the case where the length
of the last block is equal to the block length. K2 is used for the
case where the length of the last block is less than the block
length.
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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Algorithm Generate_Subkey +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ +
+ Input : K (128-bit key) +
+ Output : K1 (128-bit first subkey) +
+ K2 (128-bit second subkey) +
+-------------------------------------------------------------------+
+ +
+ Constants: const_Zero is 0x00000000000000000000000000000000 +
+ const_Rb is 0x00000000000000000000000000000087 +
+ Variables: L for output of AES-128 applied to 0^128 +
+ +
+ Step 1. L := AES-128(K, const_Zero); +
+ Step 2. if MSB(L) is equal to 0 +
+ then K1 := L << 1; +
+ else K1 := (L << 1) XOR const_Rb; +
+ Step 3. if MSB(K1) is equal to 0 +
+ then K2 := K1 << 1; +
+ else K2 := (K1 << 1) XOR const_Rb; +
+ Step 4. return K1, K2; +
+ +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Figure 2.2 Algorithm Generate_Subkey
Figure 2.2 specifies the subkey generation algorithm.
In step 1, AES-128 is applied to all zero bits with the input
key K.
In step 2, K1 is derived through the following operation:
If the most significant bit of L is equal to 0, K1 is
the left-shift of L by 1-bit.
Otherwise, K1 is the exclusive-OR of const_Rb and
the left-shift of L by 1-bit.
In step 3, K2 is derived through the following operation:
If the most significant bit of K1 is equal to 0, K2 is
the left-shift of K1 by 1-bit.
Otherwise, K2 is the exclusive-OR of const_Rb and
the left-shift of K1 by 1-bit.
In step 4, (K1,K2) := Generate_Subkey(K) is returned.
The mathematical meaning of procedure in step 2 and step 3
including const_Rb can be found in [OMAC1a].
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2.4 MAC Generation Algorithm
The MAC generation algorithm, AES-CMAC(), takes three inputs,
a secret key, a message, and the length of the message in bytes.
The secret key, denoted by K, is just the key for AES-128.
The message and its length in bytes are denoted by M and len,
respectively. The message M is denoted by the sequence of M_i
where M_i is the i-th message block. That is, if M consists of
n blocks, then M is written as
- M = M_1 || M_2 || ... || M_{n-1} || M_n
The length of M_i is 128 bits for i = 1,...,n-1, and the length of
the last block M_n is less than or equal to 128 bits.
The output of the MAC generation algorithm is a 128-bit string,
called a MAC, which can be used to validate the input message.
The MAC is denoted by T and we write T := AES-CMAC(K,M,len).
Validating the MAC provides assurance of the integrity and
authenticity over the message from the source.
It is possible to truncate the MAC. According to [NIST-CMAC] at
least 64-bit MAC should be used for against guessing attack.
Result of truncation should be taken in most significant bits first
order.
The block length of AES-128 is 128 bits (16 bytes). There is a
special treatment in case that the length of the message is
not a positive multiple of the block length. The special treatment
is to pad 10^i bit-string for adjusting the length of the last
block up to the block length.
For the input string x of r-bytes, where r < 16, the padding
function, padding(x), is defined as follows.
- padding(x) = x || 10^i where i is 128-8*r-1
That is, padding(x) is the concatenation of x and a single '1'
followed by the minimum number of '0's so that the total length is
equal to 128 bits.
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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Algorithm AES-CMAC +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ +
+ Input : K ( 128-bit key ) +
+ : M ( message to be authenticated ) +
+ : len ( length of the message in bytes ) +
+ Output : T ( message authenticated code ) +
+ +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Constants: const_Zero is 0x00000000000000000000000000000000 +
+ const_Rb is 0x00000000000000000000000000000087 +
+ const_Bsize is 16 +
+ +
+ Variables: K1, K2 for 128-bit subkeys +
+ M_i is the i-th block (i=1..ceil(len/const_Bsize)) +
+ M_last is the last block xor-ed with K1 or K2 +
+ n for number of blocks to be processed +
+ r for number of bytes of last block +
+ flag for denoting if last block is complete or not +
+ +
+ Step 1. (K1,K2) := Generate_Subkey(K); +
+ Step 2. n := ceil(len/const_Bsize); +
+ Step 3. if n = 0 +
+ then +
+ n := 1; +
+ flag := false; +
+ else +
+ if len mod const_Bsize is 0 +
+ then flag := true; +
+ else flag := false; +
+ +
+ Step 4. if flag is true +
+ then M_last := M_n XOR K1; +
+ else M_last := padding(M_n) XOR K2; +
+ Step 5. X := const_Zero; +
+ Step 6. for i := 1 to n-1 do +
+ begin +
+ Y := X XOR M_i; +
+ X := AES-128(K,Y); +
+ end +
+ Y := M_last XOR X; +
+ T := AES-128(K,Y); +
+ Step 7. return T; +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Figure 2.3 Algorithm AES-CMAC
Figure 2.3 describes the MAC generation algorithm.
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In step 1, subkeys K1 and K2 are derived from K through the subkey
generation algorithm.
In step 2, the number of blocks, n, is calculated. The number of
blocks is the smallest integer value greater than or equal to
quotient by dividing length parameter by the block length, 16
bytes.
In step 3, the length of the input message is checked.
If the input length is less than 128 bits (including null), the
number of blocks to be processed shall be 1 and mark the flag as
not-complete-block (false). Otherwise, if the last block length
is 128 bits, mark the flag as complete-block (true), else mark the
flag as not-complete-block (false).
In step 4, M_last is calculated by exclusive-OR'ing
M_n and previously calculated subkeys. If the last block is a
complete block (true), then M_last is the exclusive-OR of M_n and
K1. Otherwise, M_last is the exclusive-OR of padding(M_n) and K2.
In step 5, the variable X is initialized.
In step 6, the basic CBC-MAC is applied to M_1,...,M_{n-1},M_last.
In step 7, the 128-bit MAC, T := AES-CMAC(K,M,len), is returned.
If necessary, truncation of the MAC is done before returning the
MAC.
2.5 MAC Verification Algorithm
The verification of the MAC is simply done by a MAC recomputation.
We use the MAC generation algorithm which is described in section
2.4.
The MAC verification algorithm, Verify_MAC(), takes four inputs,
a secret key, a message, the length of the message in bytes, and
the received MAC.
They are denoted by K, M, len, and T' respectively.
The output of the MAC verification algorithm is either INVALID or
VALID.
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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Algorithm Verify_MAC +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ +
+ Input : K ( 128-bit Key ) +
+ : M ( message to be verified ) +
+ : len ( length of the message in bytes ) +
+ : T' ( the received MAC to be verified ) +
+ Output : INVALID or VALID +
+ +
+-------------------------------------------------------------------+
+ +
+ Step 1. T* := AES-CMAC(K,M,len); +
+ Step 2. if T* = T' +
+ then +
+ return VALID; +
+ else +
+ return INVALID; +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Figure 2.4 Algorithm Verify_MAC
Figure 2.4 describes the MAC verification algorithm.
In step 1, T* is derived from K, M and len through the MAC generation
algorithm.
In step 2, T* and T' are compared. If T*=T', then return VALID,
otherwise return INVALID.
If the output is INVALID, then the message is definitely not
authentic, i.e., it did not originate from a source that executed
the generation process on the message to produce the purported MAC.
If the output is VALID, then the design of the AES-CMAC provides
assurance that the message is authentic and, hence, was not
corrupted in transit; however, this assurance, as for any MAC
algorithm, is not absolute.
3. Security Considerations
The security provided by AES-CMAC are built on strong cryptographic
algorithm AES. However as is true with any cryptographic algorithm,
part of its strength lies in the secret key, 'K' and the correctness
of the implementation in all of the participating systems.
If the secret key 'K' is compromised or inappropriately shared, it
no longer guarantee either authentication or integrity of message.
The secret key shall be generated in a way that meet the pseudo
randomness requirement of RFC 4086 [RFC4086] and should be kept
in safe. If and only if AES-CMAC used properly it can provide the
Authentication and Integrity that meet the best current practice
of message authentication.
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4. Test Vectors
Following test vectors are the same as those of [NIST-CMAC].
The following vectors are also output of the test program in
appendix A.
--------------------------------------------------
Subkey Generation
K 2b7e1516 28aed2a6 abf71588 09cf4f3c
AES-128(key,0) 7df76b0c 1ab899b3 3e42f047 b91b546f
K1 fbeed618 35713366 7c85e08f 7236a8de
K2 f7ddac30 6ae266cc f90bc11e e46d513b
--------------------------------------------------
--------------------------------------------------
Example 1: len = 0
M <empty string>
AES-CMAC bb1d6929 e9593728 7fa37d12 9b756746
--------------------------------------------------
Example 2: len = 16
M 6bc1bee2 2e409f96 e93d7e11 7393172a
AES-CMAC 070a16b4 6b4d4144 f79bdd9d d04a287c
--------------------------------------------------
Example 3: len = 40
M 6bc1bee2 2e409f96 e93d7e11 7393172a
ae2d8a57 1e03ac9c 9eb76fac 45af8e51
30c81c46 a35ce411
AES-CMAC dfa66747 de9ae630 30ca3261 1497c827
--------------------------------------------------
Example 4: len = 64
M 6bc1bee2 2e409f96 e93d7e11 7393172a
ae2d8a57 1e03ac9c 9eb76fac 45af8e51
30c81c46 a35ce411 e5fbc119 1a0a52ef
f69f2445 df4f9b17 ad2b417b e66c3710
AES-CMAC 51f0bebf 7e3b9d92 fc497417 79363cfe
--------------------------------------------------
5. Acknowledgement
Portions of this text here in is borrowed from [NIST-CMAC].
We appreciate OMAC1 authors and SP 800-38B author, and Russ Housley
for his useful comments and guidance that have been incorporated
herein. We also appreciate David Johnston for providing code of
the AES block cipher.
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6. Author's Address
Junhyuk Song
University of Washington
Samsung Electronics
(206) 853-5843
songlee@ee.washington.edu
junhyuk.song@samsung.com
Jicheol Lee
Samsung Electronics
+82-31-279-3605
jicheol.lee@samsung.com
Radha Poovendran
Network Security Lab
University of Washington
(206) 221-6512
radha@ee.washington.edu
Tetsu Iwata
Ibaraki University
iwata@cis.ibaraki.ac.jp
7. References
7.1. Normative References
[NIST-CMAC] NIST, Special Publication 800-38B Draft,"Recommendation
for Block Cipher Modes of Operation: The CMAC Method
for Authentication," March 9, 2005
[NIST-AES] NIST, FIPS 197, "Advanced Encryption Standard (AES),"
November 2001.
http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf
[OMAC1] "OMAC: One-Key CBC MAC," Tetsu Iwata and Kaoru Kurosawa,
Department of Computer and Information Sciences,
Ilbaraki University, March 10, 2003.
[XCBC] Black, J. and P. Rogaway, "A Suggestion for Handling
Arbitrary-Length Messages with the CBC MAC," NIST
Second Modes of Operation Workshop, August 2001.
http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/
xcbc-mac/xcbc-mac-spec.pdf
[RFC4086] Eastlake 3rd, D., Crocker, S., and J. Schiller,
"Randomness Requirements for Security", RFC 4086
June 2005
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7.2. Informative References
[OMAC1a] Tetsu Iwata and Kaoru Kurosawa, "OMAC: One-Key CBC MAC,"
Fast Software Encryption, FSE 2003, LNCS 2887,
pp. 129-153, Springer-Verlag, 2003.
[RFC-HMAC] Hugo Krawczyk, Mihir Bellare and Ran Canetti,
"HMAC: Keyed-Hashing for Message Authentication,"
RFC2104, February 1997.
[OMAC1b] Tetsu Iwata and Kaoru Kurosawa, "OMAC: One-Key CBC MAC,"
Submission to NIST, December 2002.
Available from the NIST modes of operation web site at
http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/
omac/omac-spec.pdf
[XCBCa] John Black and Phillip Rogaway, "A Suggestion for
Handling Arbitrary-Length Messages with the CBC MAC,"
NIST Second Modes of Operation Workshop, August 2001.
Available from the NIST modes of operation web site at
http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/
xcbc-mac/xcbc-mac-spec.pdf
[XCBCb] John Black and Phillip Rogaway, "CBC MACs for
Arbitrary-Length Messages: The Three-Key
Constructions," Journal of Cryptology, Vol. 18, No. 2,
pp. 111-132, Springer-Verlag, Spring 2005.
[RFC1750] Eastlake 3rd, D., Crocker, S., and J. Schiller,
"Randomness Recommendations for Security", RFC 1750,
December 1994.
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Appendix A. Test Code
/****************************************************************/
/* AES-CMAC with AES-128 bit */
/* AES-128 from David Johnston (802.16) */
/* CMAC Algorithm described in SP800-38B draft */
/* Author: Junhyuk Song (junhyuk.song@samsung.com) */
/* Jicheol Lee (jicheol.lee@samsung.com) */
/****************************************************************/
#include <stdio.h>
/******** SBOX Table *********/
unsigned char sbox_table[256] = {
0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5,
0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0,
0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc,
0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a,
0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0,
0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b,
0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,
0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85,
0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,
0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5,
0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,
0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17,
0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,
0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88,
0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,
0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c,
0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9,
0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,
0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6,
0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,
0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e,
0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,
0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94,
0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,
0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68,
0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16
};
Song et al. Expires June 2006 [Page 14]
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/* For CMAC Calculation */
unsigned char const_Rb[16] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x87
};
unsigned char const_Zero[16] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
};
/*****************************/
/**** Function Prototypes ****/
/*****************************/
void xor_128(unsigned char *a, unsigned char *b, unsigned char *out);
void xor_32(unsigned char *a, unsigned char *b, unsigned char *out);
unsigned char sbox(unsigned char a);
void next_key(unsigned char *key, int round);
void byte_sub(unsigned char *in, unsigned char *out);
void shift_row(unsigned char *in, unsigned char *out);
void mix_column(unsigned char *in, unsigned char *out);
void add_round_key( unsigned char *shiftrow_in,
unsigned char *mcol_in,
unsigned char *block_in,
int round,
unsigned char *out);
void AES_128(unsigned char *key, unsigned char *data, unsigned char
*ciphertext);
void leftshift_onebit(unsigned char *input,unsigned char *output);
/****************************************/
/* AES_128() */
/* Performs a 128 bit AES encrypt with */
/* 128 bit data. */
/****************************************/
void xor_128(unsigned char *a, unsigned char *b, unsigned char *out)
{
int i;
for (i=0;i<16; i++)
{
out[i] = a[i] ^ b[i];
}
}
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void xor_32(unsigned char *a, unsigned char *b, unsigned char *out)
{
int i;
for (i=0;i<4; i++)
{
out[i] = a[i] ^ b[i];
}
}
unsigned char sbox(unsigned char a)
{
return sbox_table[(int)a];
}
void next_key(unsigned char *key, int round)
{
unsigned char rcon;
unsigned char sbox_key[4];
unsigned char rcon_table[12] = {
0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
0x1b, 0x36, 0x36, 0x36
};
sbox_key[0] = sbox(key[13]);
sbox_key[1] = sbox(key[14]);
sbox_key[2] = sbox(key[15]);
sbox_key[3] = sbox(key[12]);
rcon = rcon_table[round];
xor_32(&key[0], sbox_key, &key[0]);
key[0] = key[0] ^ rcon;
xor_32(&key[4], &key[0], &key[4]);
xor_32(&key[8], &key[4], &key[8]);
xor_32(&key[12], &key[8], &key[12]);
}
void byte_sub(unsigned char *in, unsigned char *out)
{
int i;
for (i=0; i< 16; i++)
{
out[i] = sbox(in[i]);
}
}
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void shift_row(unsigned char *in, unsigned char *out)
{
out[0] = in[0];
out[1] = in[5];
out[2] = in[10];
out[3] = in[15];
out[4] = in[4];
out[5] = in[9];
out[6] = in[14];
out[7] = in[3];
out[8] = in[8];
out[9] = in[13];
out[10] = in[2];
out[11] = in[7];
out[12] = in[12];
out[13] = in[1];
out[14] = in[6];
out[15] = in[11];
}
void mix_column(unsigned char *in, unsigned char *out)
{
int i;
unsigned char add1b[4];
unsigned char add1bf7[4];
unsigned char rotl[4];
unsigned char swap_halfs[4];
unsigned char andf7[4];
unsigned char rotr[4];
unsigned char temp[4];
unsigned char tempb[4];
for (i=0 ; i<4; i++)
{
if ((in[i] & 0x80)== 0x80)
add1b[i] = 0x1b;
else
add1b[i] = 0x00;
}
swap_halfs[0] = in[2]; /* Swap halfs */
swap_halfs[1] = in[3];
swap_halfs[2] = in[0];
swap_halfs[3] = in[1];
rotl[0] = in[3]; /* Rotate left 8 bits */
rotl[1] = in[0];
rotl[2] = in[1];
rotl[3] = in[2];
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andf7[0] = in[0] & 0x7f;
andf7[1] = in[1] & 0x7f;
andf7[2] = in[2] & 0x7f;
andf7[3] = in[3] & 0x7f;
for (i = 3; i>0; i--) /* logical shift left 1 bit */
{
andf7[i] = andf7[i] << 1;
if ((andf7[i-1] & 0x80) == 0x80)
{
andf7[i] = (andf7[i] | 0x01);
}
}
andf7[0] = andf7[0] << 1;
andf7[0] = andf7[0] & 0xfe;
xor_32(add1b, andf7, add1bf7);
xor_32(in, add1bf7, rotr);
temp[0] = rotr[0]; /* Rotate right 8 bits */
rotr[0] = rotr[1];
rotr[1] = rotr[2];
rotr[2] = rotr[3];
rotr[3] = temp[0];
xor_32(add1bf7, rotr, temp);
xor_32(swap_halfs, rotl,tempb);
xor_32(temp, tempb, out);
}
void AES_128(unsigned char *key, unsigned char *data, unsigned char
*ciphertext)
{
int round;
int i;
unsigned char intermediatea[16];
unsigned char intermediateb[16];
unsigned char round_key[16];
for(i=0; i<16; i++) round_key[i] = key[i];
for (round = 0; round < 11; round++)
{
if (round == 0)
{
xor_128(round_key, data, ciphertext);
next_key(round_key, round);
}
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else if (round == 10)
{
byte_sub(ciphertext, intermediatea);
shift_row(intermediatea, intermediateb);
xor_128(intermediateb, round_key, ciphertext);
}
else /* 1 - 9 */
{
byte_sub(ciphertext, intermediatea);
shift_row(intermediatea, intermediateb);
mix_column(&intermediateb[0], &intermediatea[0]);
mix_column(&intermediateb[4], &intermediatea[4]);
mix_column(&intermediateb[8], &intermediatea[8]);
mix_column(&intermediateb[12], &intermediatea[12]);
xor_128(intermediatea, round_key, ciphertext);
next_key(round_key, round);
}
}
}
void print_hex(char *str, unsigned char *buf, int len)
{
int i;
for ( i=0; i<len; i++ ) {
if ( (i % 16) == 0 && i != 0 ) printf(str);
printf("%02x", buf[i]);
if ( (i % 4) == 3 ) printf(" ");
if ( (i % 16) == 15 ) printf("\n");
}
if ( (i % 16) != 0 ) printf("\n");
}
void print128(unsigned char *bytes)
{
int j;
for (j=0; j<16;j++) {
printf("%02x",bytes[j]);
if ( (j%4) == 3 ) printf(" ");
}
}
void print96(unsigned char *bytes)
{
int j;
for (j=0; j<12;j++) {
printf("%02x",bytes[j]);
if ( (j%4) == 3 ) printf(" ");
}
}
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/* AES-CMAC Generation Function */
void leftshift_onebit(unsigned char *input,unsigned char *output)
{
int i;
unsigned char overflow = 0;
for ( i=15; i>=0; i-- ) {
output[i] = input[i] << 1;
output[i] |= overflow;
overflow = (input[i] & 0x80)?1:0;
}
return;
}
void generate_subkey(unsigned char *key, unsigned char *K1, unsigned
char *K2)
{
unsigned char L[16];
unsigned char Z[16];
unsigned char tmp[16];
int i;
for ( i=0; i<16; i++ ) Z[i] = 0;
AES_128(key,Z,L);
if ( (L[0] & 0x80) == 0 ) { /* If MSB(L) = 0, then K1 = L << 1 */
leftshift_onebit(L,K1);
} else { /* Else K1 = ( L << 1 ) (+) Rb */
leftshift_onebit(L,tmp);
xor_128(tmp,const_Rb,K1);
}
if ( (K1[0] & 0x80) == 0 ) {
leftshift_onebit(K1,K2);
} else {
leftshift_onebit(K1,tmp);
xor_128(tmp,const_Rb,K2);
}
return;
}
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void padding ( unsigned char *lastb, unsigned char *pad, int length )
{
int j;
/* original last block */
for ( j=0; j<16; j++ ) {
if ( j < length ) {
pad[j] = lastb[j];
} else if ( j == length ) {
pad[j] = 0x80;
} else {
pad[j] = 0x00;
}
}
}
void AES_CMAC ( unsigned char *key, unsigned char *input, int length,
unsigned char *mac )
{
unsigned char X[16],Y[16], M_last[16], padded[16];
unsigned char K1[16], K2[16];
int n, i, flag;
generate_subkey(key,K1,K2);
n = (length+15) / 16; /* n is number of rounds */
if ( n == 0 ) {
n = 1;
flag = 0;
} else {
if ( (length%16) == 0 ) { /* last block is a complete block */
flag = 1;
} else { /* last block is not complete block */
flag = 0;
}
}
if ( flag ) { /* last block is complete block */
xor_128(&input[16*(n-1)],K1,M_last);
} else {
padding(&input[16*(n-1)],padded,length%16);
xor_128(padded,K2,M_last);
}
for ( i=0; i<16; i++ ) X[i] = 0;
for ( i=0; i<n-1; i++ ) {
xor_128(X,&input[16*i],Y); /* Y := Mi (+) X */
AES_128(key,Y,X); /* X := AES-128(KEY, Y); */
}
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xor_128(X,M_last,Y);
AES_128(key,Y,X);
for ( i=0; i<16; i++ ) {
mac[i] = X[i];
}
}
int main()
{
unsigned char L[16], K1[16], K2[16], T[16], TT[12];
unsigned char M[64] = {
0x6b, 0xc1, 0xbe, 0xe2, 0x2e, 0x40, 0x9f, 0x96,
0xe9, 0x3d, 0x7e, 0x11, 0x73, 0x93, 0x17, 0x2a,
0xae, 0x2d, 0x8a, 0x57, 0x1e, 0x03, 0xac, 0x9c,
0x9e, 0xb7, 0x6f, 0xac, 0x45, 0xaf, 0x8e, 0x51,
0x30, 0xc8, 0x1c, 0x46, 0xa3, 0x5c, 0xe4, 0x11,
0xe5, 0xfb, 0xc1, 0x19, 0x1a, 0x0a, 0x52, 0xef,
0xf6, 0x9f, 0x24, 0x45, 0xdf, 0x4f, 0x9b, 0x17,
0xad, 0x2b, 0x41, 0x7b, 0xe6, 0x6c, 0x37, 0x10
};
unsigned char key[16] = {
0x2b, 0x7e, 0x15, 0x16, 0x28, 0xae, 0xd2, 0xa6,
0xab, 0xf7, 0x15, 0x88, 0x09, 0xcf, 0x4f, 0x3c
};
printf("--------------------------------------------------\n");
printf("K "); print128(key); printf("\n");
printf("\nSubkey Generation\n");
AES_128(key,const_Zero,L);
printf("AES_128(key,0) "); print128(L); printf("\n");
generate_subkey(key,K1,K2);
printf("K1 "); print128(K1); printf("\n");
printf("K2 "); print128(K2); printf("\n");
printf("\nExample 1: len = 0\n");
printf("M "); printf("<empty string>\n");
AES_CMAC(key,M,0,T);
printf("AES_CMAC "); print128(T); printf("\n");
printf("\nExample 2: len = 16\n");
printf("M "); print_hex(" ",M,16);
AES_CMAC(key,M,16,T);
printf("AES_CMAC "); print128(T); printf("\n");
printf("\nExample 3: len = 40\n");
printf("M "); print_hex(" ",M,40);
AES_CMAC(key,M,40,T);
printf("AES_CMAC "); print128(T); printf("\n");
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printf("\nExample 4: len = 64\n");
printf("M "); print_hex(" ",M,64);
AES_CMAC(key,M,64,T);
printf("AES_CMAC "); print128(T); printf("\n");
printf("--------------------------------------------------\n");
return 0;
}
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Song et al. Expires June 2006 [Page 23]
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Copyright Statement
Copyright (C) The Internet Society (2005). This document is subject
to the rights, licenses and restrictions contained in BCP 78, and
except as set forth therein, the authors retain all their rights.
Acknowledgment
Funding for the RFC Editor function is currently provided by the
Internet Society.
Song et al. Expires June 2006 [Page 24]
