add exercise 3a

mit-ll · Aug 7, 2024 · 2fba3e3 · 2fba3e3
1 parent dbe4cef
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diff --git a/classical_crypto.html b/classical_crypto.html
@@ -38,6 +38,7 @@
     <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>

diff --git a/credits.html b/credits.html
@@ -38,6 +38,7 @@
     <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>

diff --git a/el_gamal_encryption.html b/el_gamal_encryption.html
@@ -41,6 +41,7 @@
     <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>

diff --git a/exercise_five.html b/exercise_five.html
@@ -41,6 +41,7 @@
     <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>

diff --git a/exercise_four.html b/exercise_four.html
@@ -41,6 +41,7 @@
     <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>

diff --git a/exercise_one.html b/exercise_one.html
@@ -41,6 +41,7 @@
     <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>

diff --git a/exercise_three.html b/exercise_three.html
@@ -41,6 +41,7 @@
     <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>

diff --git a/exercise_three_a.html b/exercise_three_a.html
@@ -0,0 +1,184 @@
+<!DOCTYPE html>
+<html>
+<head>
+  <title>Crypto Exercises</title>
+  <link rel="stylesheet" href="./cryptoexercises-stylesheet.css" />
+  <script src="./sjcl/sjcl.js"></script>
+  <script src="./functions.js"></script>
+</head>
+<body onload="loadProblem()">
+<!----------------------------------------------------------------------------->
+<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>
+    <td class="exerciseDetails">
+      <h1>RSA Challenge Three (a): RSA Modulus Reuse</h1>
+<div class="exerciseDescription">
+  <p><b>The Problem:</b> Given two RSA ciphertexts of the same message encrypted with the same modulus but different public keys, recover the plaintext.</p>
+</div>
+<div class="problemStatement">
+  <p>
+    Awfulland and Badland keep making strange choices with their keys - both of them are using the same modulus, even though their public keys are different.
+    Horridland has formed a new attack plan, and is sending an encrypted copy of the plan to Awfulland and Badland.
+    You've gotten a copy of both encrypted messages:
+  </p>
+  <ul>
+    <li>Awfulland's message, encrypted as c<sub>A</sub> =
+    m<sup>e<sub>A</sub></sup> mod N (using Awfulland's public exponent
+    e<sub>A</sub>), and</li>
+    <li>Badland's message, encrypted as c<sub>B</sub> = m<sup>e<sub>B</sub></sup>
+    mod N (using Badland's public exponent e<sub>B</sub>).</li>
+  </ul> 
+  <p>Use the fact that both copies of the message are encrypted using the
+  same modulus to figure out what the evil plot is.</p> 
+
+  <p>For this exercise, use the following values:</p>
+<table class="exerciseValuesTable" cellspacing="0">
+  <tr class="headerRow">
+    <td class="name">Name</td>
+    <td class="value">Value</td>
+  </tr>
+    <tr class="oddRow">
+      <td class="name">Common modulus:</td>
+      <td class="value"><div id="modulus">153380639740849</div></td>
+    </tr>
+    <tr class="evenRow">
+      <td class="name">Ciphertext #1</td>
+      <td class="value"><div id="ciphertext_1">106230071531067</div></td>
+    </tr>
+    <tr class="oddRow">
+      <td class="name">Exponent #1</td>
+      <td class="value"><div id="exponent_1">1745</div></td>
+    </tr>
+    <tr class="evenRow">
+      <td class="name">Ciphertext #2</td>
+      <td class="value"><div id="ciphertext_2">51206346831694</div></td>
+    </tr>
+    <tr class="oddRow">
+      <td class="name">Exponent #2</td>
+      <td class="value"><div id="exponent_2">57</div></td>
+    </tr>
+</table>
+
+<form class="new_exercise">
+  <table class="answerFormTable" cellspacing="0">
+    <tr>
+      <td>
+        <!--
+        # The size of this text area is probably much smaller, but may
+        # also vary from exercise to exercise. The right answer is 
+        # probably to see if this value can be moved into CSS, and
+        # then change the class name based on the exercise.
+        -->
+        <label class="answer" for="exercise_answer">Your Answer:</label>
+        <textarea class="answer" name="exercise[answer]" id="exercise_answer" cols="100" rows="20">
+</textarea>
+      </td>
+    </tr>
+    <tr>
+      <td>
+           <!-- 
+           # Save the answer hash
+           -->
+           <input value="" type="hidden" id="ans_hash" />
+        <input type="submit" name="commit" value="Check Your Answer" onclick="checkAnswer(); return false;" />
+        <div id="anscheck_result"></div>
+      </td>
+    </tr>
+  </table>
+</form>
+</div>
+<!-- Create and check problems -->
+<script>
+function loadProblem() {
+  // if you're still checking, please don't cheat
+  let answerhash = sjcl.hash.sha256.hash("Candy");
+  document.getElementById('ans_hash').value = answerhash;
+  return false;
+}
+
+function checkAnswer() {
+  let ans = document.getElementById('exercise_answer').value;
+  let anshash = sjcl.hash.sha256.hash(ans);
+  let realanshash = document.getElementById('ans_hash').value;
+  if (anshash == realanshash) {
+    document.getElementById('anscheck_result').innerHTML = "Correct!";
+  }
+  else {
+    document.getElementById('anscheck_result').innerHTML = "Incorrect";
+  }
+  return false;
+}
+</script>
+
+    </td>
+    <!-- start tool panel -->
+    <td class="cryptoToolkit"> 
+      <iframe
+      src="./toolpanel.html"
+      frameborder="0"
+      scrolling="yes"
+      seamless="seamless"
+      style="display:block;
+      width:100%;
+      height:85vh;"
+      >
+      </iframe>
+    </td>
+    <!-- end tool panel -->
+  </tr>
+</table>  
+</article>
+<!----------------------------------------------------------------------------->
+<footer>
+<small>
+&copy; 2016, by Uri Blumenthal, Jeff Diewald, and Sophia Yakoubov, and 2024, by David Wilson and Nick Cunningham.
+</small>
+</footer>
+</body>
+</html>
diff --git a/exercise_two.html b/exercise_two.html
@@ -42,6 +42,7 @@
     <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>

diff --git a/index.html b/index.html
@@ -38,6 +38,7 @@
     <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>

diff --git a/references.html b/references.html
@@ -38,6 +38,7 @@
     <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>

diff --git a/rsa_encryption.html b/rsa_encryption.html
@@ -38,6 +38,7 @@
     <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>