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I'm studying for a cryptography exam, I have this question from a past exam:

Consider the MAC with key $k$, based on a block cipher $E_{(k)}$ with block size $n$, and a collision-resistant hash function $h$ with output size $n$. The MAC on a message m is calculated as: $$ \text{MAC}(m) = E_{h(m)}(k) $$

  • Discuss the security of this MAC scheme.

Obviously, the security of this scheme depends on the hash function chosen, the block cipher, and the length of $n$.

What other considerations can be made?

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Given a MAC scheme as $\text{MAC}(k,m) = E_{h(m)}(k)$

  • take the message $m$ and hash it, these are public knowledge for the security game of MACs
  • Now use the decryption of the Encryption function, what do you get?
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