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<!DOCTYPE html>
<html>
<head>
<title>Crypto Exercises</title>
<link rel="stylesheet" href="./cryptoexercises-stylesheet.css" />
</head>
<!----------------------------------------------------------------------------->
<header>
<table class="headerTable" cellspacing="0">
<tr>
<td class="left">
<img class="bannerImage" src="./LLCipher_logo.png" alt="Llcipher logo" />
</td>
<td class="middle">
<p>Cryptography Challenges</p>
</td>
<td class="right">
<img class="lincolnLogo" src="./lincoln_logo.png" alt="Lincoln logo" />
</td>
</tr>
</table>
</header>
<!----------------------------------------------------------------------------->
<nav>
<ul>
<li><a href="./index.html">Home</a></li>
</ul>
<br />
<ul>
<li class="title">Background</li>
<li><a href="./el_gamal_encryption.html">El Gamal Encryption</a>
<li><a href="./rsa_encryption.html">RSA Encryption</a>
</ul>
<br />
<ul>
<li class="title">Challenges</li>
<li><a href="./classical_crypto.html">Classical Crypto</a></li>
<li><a href="./exercise_one.html">RSA Challenge One</a></li>
<li><a href="./exercise_two.html">RSA Challenge Two</a></li>
<li><a href="./exercise_three.html">RSA Challenge Three</a></li>
<li><a href="./exercise_three_a.html">RSA Challenge Three (a)</a></li>
<li><a href="./exercise_four.html">RSA Challenge Four</a></li>
<li><a href="./exercise_five.html">El Gamal Challenge</a></li>
</ul>
<br />
<ul>
<li class="title">Other Stuff</li>
<li><a href="./references.html">References</a></li>
<li><a href="./credits.html">Credits</a></li>
</ul>
</nav>
<!----------------------------------------------------------------------------->
<article>
<table class="exerciseLayoutTable" cellspacing="0">
<tr>
<h1>Welcome</h1>
<p>This webapp offers a number of challenges in attacking the RSA and El Gamal cryptosystems.
Each attack is meant to illustrate a way to <i>misuse</i> RSA or El Gamal; when they are used correctly, they are not vulnerable to any of these attacks.</p>
<table class="homeTable" cellspacing="0">
<tr class="headerRow">
<!--
<td class="exerciseId">Challenge</td>
-->
<td class="exerciseName" colspan="2">Challenge Name</td>
<td class="exerciseDescription">Challenge Description</td>
</tr>
<tr class="oddRow">
<!--
<td class="exerciseId">1</td>
-->
<td class="exerciseName"><b>RSA Challenge One</b></td>
<td class="exerciseName">Small Message Space Attack</td>
<td class="exerciseDescription">Given an RSA ciphertext encrypting one of several messages, recover the message.</td>
</tr>
<tr class="evenRow">
<!--
<td class="exerciseId">2</td>
-->
<td class="exerciseName"><b>RSA Challenge Two</b></td>
<td class="exerciseName">Small Plaintext and Encryption Exponent Attack</td>
<td class="exerciseDescription">Given an RSA ciphertext encrypting a small message with a small public key (e.g. e = 5), recover the message.</td>
</tr>
<tr class="oddRow">
<!--
<td class="exerciseId">3</td>
-->
<td class="exerciseName"><b>RSA Challenge Three</b></td>
<td class="exerciseName">Broadcast Attack</td>
<td class="exerciseDescription">Given RSA ciphertexts with different moduli but the same low encryption exponent, recover the message.</td>
</tr>
<tr class="evenRow">
<!--
<td class="exerciseId">4</td>
-->
<td class="exerciseName"><b>RSA Challenge Four</b></td>
<td class="exerciseName">Modulus Reuse Attack</td>
<td class="exerciseDescription">Given an encryption key, a decryption key and a modulus, recover the decryption key corresponding to a different encryption key but the same modulus.</td>
</tr>
<tr class="oddRow">
<!--
<td class="exerciseId">5</td>
-->
<td class="exerciseName"><b>El Gamal Challenge</b></td>
<td class="exerciseName">Randomness Reuse Attack</td>
<td class="exerciseDescription">Given an encryption key, two ciphertexts which use the same random exponent y and the plaintext corresponding to one of those ciphertexts, recover the second plaintext.</td>
</tr>
</table>
<small>
This material is based upon work supported under Air Force Contract No. FA8721-05-C-0002 and/or FA8702-15-D-0001.
Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. Air Force.
</small>
</table>
</tr>
</table>
</article>
<!----------------------------------------------------------------------------->
<footer>
<small>
© 2016, by Uri Blumenthal, Jeff Diewald, and Sophia Yakoubov, and 2024, by David Wilson and Nick Cunningham.
</small>
</footer>
</body>
</html>