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What is more important, in terms of security, the size of the MAC or the size of the key that it uses? I'm asking this because I have to answer the following homework question:

What is more secure? A MAC with a 12-byte key and 6-byte MAC length, or a MAC with a 8-byte key and 12-byte MAC length?

For the first one, it's easier to find a pre-image of the result. But for the second one, it's easier to find the key.

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    $\begingroup$ Hint: Is finding pre-images a problem for the security of a MAC (ie can you use it to break the security definition)? $\endgroup$ – SEJPM Jun 22 '17 at 15:53

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