RSA

TheUnlimited64 · Oct 28, 2019 · 54051fa · 54051fa
1 parent 0bc6769
commit 54051fa
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Showing 2 changed files with 68 additions and 7 deletions.
diff --git a/Verschlüsselung.html b/Verschlüsselung.html
@@ -188,9 +188,19 @@
               <li>Teilerfremde Zahl zu &phi;(N) finden. Bedingung: 1&lt;e&lt;&phi;(N)</li>
               <li>e*d mod(&phi;(N))=1 (d wird gesucht)</li>
             </ol>
-          </div>
+          </div><br>
           Private Key:(N;d)<br>
-          Public Key: (N;e)<br>
+          Public Key: (N;e)<br><br>
+          Verschlüsselt wird durch (m= Nachricht,c=Verschlüsselt)<br>
+          <div class="code-block">
+            c = m<sup>e</sup> mod(N)
+          </div>
+          Entschlüsselt wird mit<br>
+          <div class="code-block">
+            m = c<sup>d</sup> mod(N)
+          </div><br>
+          Anmerkung: Aufgrund von einem datatype Overflows und fehlender Präzision der Verwendeten Datentypen wurde eine
+          Funktion zum verschlüsseln verwendet, die höhere Mathematik verwendet um die Zahlen kleiner zu halten.
         </div>
         <div class="card-footer">
           <a href="https://de.wikipedia.org/wiki/RSA-Kryptosystem">Wikipedia</a> + Student
@@ -202,6 +212,7 @@
     </div>
   </div>
 </body>
+
 <body>
   <div class="modal fade" id="RSAModal">
     <div class="modal-dialog modal-xl">
@@ -223,19 +234,19 @@ <h4>RSA-Algorithmus</h4>
             </div>
             <div class="col-md-2">
               <label for="componentN">N:</label>
-              <input class="form-control" id="componentN" readonly />
+              <input class="form-control" id="componentN" />
             </div>
             <div class="col-md-2">
               <label for="componentphiN">&phi;(N):</label>
               <input class="form-control" id="componentphiN" readonly />
             </div>
             <div class="col-md-2">
               <label for="componente">e:</label>
-              <input class="form-control" id="componente" readonly />
+              <input class="form-control" id="componente" />
             </div>
             <div class="col-md-2">
               <label for="componente">d:</label>
-              <input class="form-control" id="componentd" readonly />
+              <input class="form-control" id="componentd" />
             </div>
           </div>
           <div class="row">
@@ -282,13 +293,15 @@ <h4>RSA-Algorithmus</h4>
     fürs Design verwendet.
   </div>
 </footer>
+
 </html>
 
 <script type="text/javascript">
   $('#generateRSA').on("click", function () {
     KeyGen();
+    encrypt();
   });
-  $('#text').on('input',function(){
+  $('#text').on('input', function () {
     encrypt();
   });
   $("#CäsarCodieren").on("click", function () {

diff --git a/scripts/RSA.js b/scripts/RSA.js
@@ -105,15 +105,63 @@ function KeyGen() {
 }
 
 function encrypt() {
+    if($('#text').val()){
     var N = $('#componentN').val();
+    N = parseInt(N);
     var e = $('#componente').val();
+    e = parseInt(e);
     var text = $('#text').val();
     var Output = "";
     for (var i in text) {
         var KeyCode = text.charCodeAt(i);
 
-        KeyCode = Math.pow(KeyCode, e) % N;
+        KeyCode = powFun(KeyCode,e,N)
         Output += KeyCode;
+        Output+=" ";
     }
     $('#encrypted').val(Output);
+
+
+
+
+
+}
+}
+/* Encrypt function https://stackoverflow.com/questions/30630603/javascript-self-made-pow-with-modulo */
+function addmod(x, y, n)
+{
+    // Precondition: x<n, y<n
+    // If it will overflow, use alternative calculation
+    if (x + y <= x) x = x - (n - y) % n;
+    else x = (x + y) % n;
+    return x;
+}
+
+function sqrmod(a, n)
+{
+    var b;
+    var sum = 0;
+
+    // Make sure original number is less than n
+    a = a % n;
+
+    // Use double and add algorithm to calculate a*a mod n
+    for (b = a; b != 0; b >>= 1) {
+        if (b & 1) {
+            sum = addmod(sum, a, n);
+        }
+        a = addmod(a, a, n);
+    }
+    return sum;
+}
+
+function powFun(base, ex, mo) {
+    var r;
+    if(ex === 0) 
+        return 1;
+    else if(ex % 2 === 0) {
+        r = powFun(base, ex/2, mo) % mo ;
+        // return (r * r) % mo;
+        return sqrmod(r, mo);
+    }else  return (base * powFun(base, ex - 1, mo)) % mo;
 }