index.html

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layout: default
title: Message Authentication Code (MAC)
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<div class="section" id="integrity">
<h2>Message Authentication Code (MAC) Security Game</h2>

<p>
  <code>{Sign, Verify}</code> is the candidate MAC scheme.
</p>
<br><br>

<table>

<tbody class="normal" title="The adversary selects a key uniformly at random from the key space.">
<tr>
  <td class="meta"></td>
  <td class="challenger-both"><span class="set-var">k</span> = rand(Keys)</td>
  <td class="communication"></td>
  <td class="adversary"></td>
</tr>
</tbody>

<tbody class="normal loop" title="The adversary sends messages repeatedly, and receives a valid tag from the challenger each time.">
<tr>
  <td class="meta" rowspan="2"><i class="fa fa-retweet"></i><br>i++</td>
  <td class="challenger-both receive-from-right"><span class="set-var">m<sub>i</sub></span></td>
  <td class="communication send-left">&larr;</td>
  <td class="adversary"><span class="set-var">m<sub>i</sub></span> &isin; Inputs</td>
</tr>
<tr>
  <td class="challenger-both"><span class="set-var">t<sub>i</sub></span> = Sign(k, m<sub>i</sub>)</td>
  <td class="communication send-right">&rarr;</td>
  <td class="adversary"><span class="set-var">t<sub>i</sub></span></td>
</tr>
</tbody>

<tbody class="normal" title="Given all the available information, the adversary attempts to produce a forged combination of message and tag that does not match any of the message-tag pairs from the query round.">
<tr>
  <td class="meta"></td>
  <td class="challenger-both"></td>
  <td class="communication"></td>
  <td class="adversary"><span class="set-var">(m<sup>*</sup>, t<sup>*</sup>)</span> &isin; Outputs: (&#x2200; i) m<sup>*</sup> &ne; m<sub>i</sub> </td>
</tr>
</tbody>

<tbody class="done" title="The adversary outputs their attempted forgery.">
<tr>
  <td class="meta"></td>
  <td class="challenger-both"></td>
  <td class="communication"></td>
  <td class="adversary send-down">(m<sup>*</sup>, t<sup>*</sup>)<br>&darr;</td>
</tr>
</tbody>
</table>

<h2>Advantage</h2>

<ul>
<li><code>Advantage(Adversary) = Pr[Verify(k, m<sup>*</sup>, t<sup>*</sup>)</code> accepts the tag as valid<code>]</code></li>
</ul>

<br><br>
<h2>Correctness</h2>

<ul>
<li><code>(&#x2200; m) Pr[k &larr; genKeys(), Verify(k, m, Sign(k, m)) == accept ] == 1</code></li>
</ul>

</div>