index.html

---
layout: default
title: CPA
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<div class="section" id="cpa">
<h2>CPA (Chosen-Plaintext Attack) Security Game</h2>

<p>
  <code>E</code> is the encryption function of a candidate symmetric cryptosystem <code>{E, D}</code>
</p>
<br><br>

<table>
<tbody class="normal" title="The challenger sets their binary &quot;world bit&quot; b depending on they are in world 0 or world 1 (also called &quot;experiment 0/1&quot;).">
<tr>
  <td class="meta"></td>
  <td class="challenger-0"><span class="set-var">b</span> = 0</td>
  <td class="challenger-1"><span class="set-var">b</span> = 1</td>
  <td class="communication"></td>
  <td class="adversary">Adversary</td>
</tr>
</tbody>

<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" colspan="2"><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 submits pairs of messages, and always receives the one corresponding to the bit b.">
<tr>
  <td class="meta" rowspan="2"><i class="fa fa-retweet"></i></td>
  <td class="challenger-both receive-from-right" colspan="2"><span class="set-var">m<sub>0</sub></span>, <span class="set-var">m<sub>1</sub></span></td>
  <td class="communication send-left">&larr;</td>
  <td class="adversary"><span class="set-var">m<sub>0</sub></span>, <span class="set-var">m<sub>1</sub></span> &isin; Inputs: |m<sub>0</sub>| == |m<sub>1</sub>|</td>
</tr>
<tr>
  <td class="challenger-0"><span class="set-var">c</span> = E(k, m<sub>0</sub>)</td>
  <td class="challenger-1"><span class="set-var">c</span> = E(k, m<sub>1</sub>)</td>
  <td class="communication send-right">&rarr;</td>
  <td class="adversary"><span class="set-var">c</span></td>
</tr>
</tbody>

<tbody class="normal" title="Given all the available information, the adversary selects a guess for the world bit b.">
<tr>
  <td class="meta"></td>
  <td class="challenger-0"></td>
  <td class="challenger-1"></td>
  <td class="communication"></td>
  <td class="adversary"><span class="set-var">b<sub>guess</sub></span> &isin; {0, 1}</td>
</tr>
</tbody>

<tbody class="done" title="The adversary outputs their guess.">
<tr>
  <td class="meta"></td>
  <td class="challenger-0"></td>
  <td class="challenger-1"></td>
  <td class="communication"></td>
  <td class="adversary send-down">b<sub>guess</sub><br>&darr;</td>
</tr>
</tbody>
</table>

</div>