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In cryptography, HMAC (Hash-based Message Authentication Code), is a specific construction for calculating a message authentication code (MAC) involving a cryptographic hash function in combination with a secret key. As with any MAC, it may be used to simultaneously verify both the data integrity and the authenticity 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 length in bits and on the size and quality of the cryptographic 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 (128 or 160 bits in the case of MD5 or SHA-1, respectively), 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,[1] 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-SHA-1 and HMAC-MD5 are used within the IPsec and TLS protocols.


Definition (from RFC 2104)


  • H(·) be a cryptographic hash function
  • K be 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 be the message to be authenticated
  • ∥ denote concatenation
  • ⊕ denote exclusive or (XOR)
  • opad be the outer padding (0x5c5c5c…5c5c, one-block-long hexadecimal constant)
  • ipad be the inner padding (0x363636…3636, one-block-long hexadecimal constant)

Then HMAC(K,m) is mathematically defined by


The following pseudocode demonstrates how HMAC may be implemented.

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