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Given $c' = \operatorname{HMACSHA512}(k, a\ ||\ b\ ||\ c\ ||\ d)$ and the 32-bit integers $a$, $b$, $c$, and $d$ is it feasible to alter $b$ and produce a valid MAC under the unknown key?

I understand that typically it wouldn't be, but I am mostly wondering if it's possible with 4 small independent inputs being used.

Would it change anything if I could observe many MACs over time with all variables constant except one?

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  • $\begingroup$ It works fine in your case, since a,b,c,d are all fixed length (even all-but-one of them being fixed-length would suffice), but in general, concatenation does not necessarily suffice, since for example ​ ​ ​ 01 || 0 ​ = ​ 0 || 10 ​ ​ . ​ ​ ​ ​ ​ ​ ​ ​ $\endgroup$
    – user991
    Commented Mar 11, 2016 at 1:16
  • $\begingroup$ @RickyDemer Indeed! I noticed that this would pose a problem for a different thing I was working on. Someone recommended using a separator value like a comma. $\endgroup$
    – Michael J. Gray
    Commented Mar 11, 2016 at 1:18
  • $\begingroup$ Another option is using a prefix-free code. ​ ​ $\endgroup$
    – user991
    Commented Mar 11, 2016 at 1:21

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Is is feasible to alter b and produce a valid MAC under the unknown key?

We most certainly hope not. The fundamental security property of a MAC is that, even if that attacker can get a huge number of valid (Message, MAC) pairs (where he gets to choose the messages), he still is unable to generate a MAC for a message he has not seen. This fundamental property doesn't change just because the inputs are 'small'.

We believe that HMAC-SHA512 is a secure MAC (assuming an unguessable key); hence we believe that it is secure in your case.

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  • $\begingroup$ I assumed this was the case. I figured it would not make any difference if there were small independent variables in the message that were changing in minor ways versus the message changing completely. $\endgroup$
    – Michael J. Gray
    Commented Mar 10, 2016 at 19:17

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