In cryptography, a keyed-hash message authentication code is a specific construction for calculating
a message authentication code involving a cryptographic hash function in combination
with a secret cryptographic key.
As with any MAC, it may be used to simultaneously verify both the data integrity and the authentication
of a message.
Any cryptographic hash function, such as MD5 or SHA-1, may be used in the calculation of
an HMAC; the resulting MAC algorithm is termed HMAC-MD5 or HMAC-SHA1 accordingly.
The cryptographic strength of the HMAC depends upon the cryptographic strength of the underlying
hash function, the size of its hash output, and on the size and quality of the key.
An iterative hash function breaks up a message into blocks of a fixed size and iterates over
them with a compression function.
For example, MD5 and SHA-1 operate on 512-bit blocks.
The size of the output of HMAC is the same as that of the underlying hash function, although
it can be truncated if desired.
The definition and analysis of the HMAC construction was first published in 1996 by Mihir Bellare,
Ran Canetti, and Hugo Krawczyk, who also wrote RFC 2104.
This paper also defined a variant called NMAC that is rarely, if ever, used.
FIPS PUB 198 generalizes and standardizes the use of HMACs.
HMAC-SHA1 and HMAC-MD5 are used within the IPsec and TLS protocols.
Definition
where H is a cryptographic hash function,
K is a secret key padded to the right with extra zeros to the input block size of the
hash function, or the hash of the original key if it's longer than that block size,
m is the message to be authenticated, | denotes concatenation,
⊕ denotes exclusive or, opad is the outer padding,
and ipad is the inner padding.
Implementation The following pseudocode demonstrates how
HMAC may be implemented.
Blocksize is 64 when using one of the following hash functions: SHA-1, MD5, RIPEMD-128/160.
function hmac if > blocksize) then
key = hash(key) keys longer than blocksize are shortened
end if if < blocksize) then
key = key ∥ [0x00 *)] keys shorter than blocksize are zero-padded
end if
o_key_pad = [0x5c * blocksize] ⊕ key Where blocksize is that of the underlying hash function
i_key_pad = [0x36 * blocksize] ⊕ key Where ⊕ is exclusive or
return hash(o_key_pad ∥ hash(i_key_pad ∥ message)) Where ∥ is concatenation
end function
The following is a Python implementation of HMAC-MD5:
Python includes a hmac module, so the function above can be replaced by a shorter version.
Example usage A business that suffers from attackers that
place fraudulent Internet orders may insist that all its customers deposit a secret symmetric
key with them.
Along with an order, a customer must supply the order's HMAC digest, computed using the
customer's key.
The business, knowing the customer's key, can then verify that the order originated
from the stated customer and has not been tampered with.
Design principles The design of the HMAC specification was motivated
by the existence of attacks on more trivial mechanisms for combining a key with a hash
function.
For example, one might assume the same security that HMAC provides could be achieved with
MAC = H(key ∥ message).
However, this method suffers from a serious flaw: with most hash functions, it is easy
to append data to the message without knowing the key and obtain another valid MAC.
The alternative, appending the key using MAC = H(message ∥ key), suffers from the problem
that an attacker who can find a collision in the hash function has a collision in the
MAC.
Using MAC = H(key ∥ message ∥ key) is better, however various security papers have
suggested vulnerabilities with this approach, even when two different keys are used.
No known extensions attacks have been found against the current HMAC specification which
is defined as H(key ∥ H(key ∥ message)) because the outer application of the hash
function masks the intermediate result of the internal hash.
The values of ipad and opad are not critical to the security of the algorithm, but were
defined in such a way to have a large Hamming distance from each other and so the inner
and outer keys will have fewer bits in common.
The security reduction of HMAC does require them to be different in at least one bit.
The Keccak hash function, that was selected by NIST as the SHA-3 competition winner, doesn't
need this nested approach and can be used to generate a MAC by simply prepending the
key to the message.
Security The cryptographic strength of the HMAC depends
upon the size of the secret key that is used.
The most common attack against HMACs is brute force to uncover the secret key.
HMACs are substantially less affected by collisions than their underlying hashing algorithms alone.
Therefore, HMAC-MD5 does not suffer from the same weaknesses that have been found in MD5.
In 2006, Jongsung Kim, Alex Biryukov, Bart Preneel, and Seokhie Hong showed how to distinguish
HMAC with reduced versions of MD5 and SHA-1 or full versions of HAVAL, MD4, and SHA-0
from a random function or HMAC with a random function.
Differential distinguishers allow an attacker to devise a forgery attack on HMAC.
Furthermore, differential and rectangle distinguishers can lead to second-preimage attacks.
HMAC with the full version of MD4 can be forged with this knowledge.
These attacks do not contradict the security proof of HMAC, but provide insight into HMAC
based on existing cryptographic hash functions.
In improperly-secured systems a timing attack can be performed to find out a HMAC digit
by digit.
Examples of HMAC Here are some empty HMAC values:
HMAC_MD5("", "") = 0x74e6f7298a9c2d168935f58c001bad88 HMAC_SHA1("", "") = 0xfbdb1d1b18aa6c08324b7d64b71fb76370690e1d
HMAC_SHA256("", "") = 0xb613679a0814d9ec772f95d778c35fc5ff1697c493715653c6c712144292c5ad
Here are some non-empty HMAC values, assuming 8-bit ASCII or UTF-8 encoding:
HMAC_MD5("key", "The quick brown fox jumps over the lazy dog") = 0x80070713463e7749b90c2dc24911e275
HMAC_SHA1("key", "The quick brown fox jumps over the lazy dog") = 0xde7c9b85b8b78aa6bc8a7a36f70a90701c9db4d9
HMAC_SHA256("key", "The quick brown fox jumps over the lazy dog") = 0xf7bc83f430538424b13298e6aa6fb143ef4d59a14946175997479dbc2d1a3cd8
References
Notes
External links RFC2104
Online HMAC Calculator for dozens of underlying hashing algorithms
Online HMAC Generator / Tester Tool FIPS PUB 198-1, The Keyed-Hash Message Authentication
Code PHP HMAC implementation
Python HMAC implementation Perl HMAC implementation
Ruby HMAC implementation C HMAC implementation
C++ HMAC implementation Java implementation
JavaScript MD5 and SHA HMAC implementation JavaScript SHA-only HMAC implementation
.NET's System.Security.Cryptography.HMAC