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cryptographyhmac

Could HMAC output be the same for different key and message pairs

Could the output of the HMAC be the same if I used different keys and messages?

Example:

Out1 = HMAC(key1, msg1)
Out2 = HMAC(key2, msg2)

Could Out1=Out2 under any condition?

Solution

  • In short, you can't find such pairs better than negligible probability when the search is computationally bounded.

    HMAC is a Pseudo-Random Function (PRF) under the assumption that the used hash function is PRF.

    What you are looking for a collision for the HMAC. In theory, it is possible to find such pairs that they will collide.

    If you use a n bit output then the collision probability of two pairs is 1/2^n for the fixed key. If HMAC is initiated with SHA256 then the collision of two random pairs will be 1/2^256. By the birthday paradox, you will need around 2^128 pairs to find a collision with 50% under the same key.

    A similar calculation can be performed with random keys, too.