Update part5.tex

Lab04/documentation/part5/part5.tex

@@ -13,8 +13,8 @@ prime1 = 211, prime2 = 223, prime3 = 227, e=11
 \subsection{Berechnungen}
 
 \begin{align}
-d = e^{-1} mod ((prime1-1)(prime2-1)) \\
-d = 11^{-1} mod ((211-1)(223-1)) = 21191
+    d = e^{-1}\ mod\ ((prime1-1)(prime2-1)) \\
+    d = 11^{-1}\ mod\ ((211-1)(223-1)) = 21191
 \end{align}
 
 \begin{verbatim}
@@ -22,24 +22,28 @@ g = 9, x = 2, y = 3
 \end{verbatim}
 
 \begin{align}
-    a = g^{x} (mod\ prime3) = 9^{2} (mod\ 227) = 81 \\
-    b = g^{y} (mod\ prime3) = 9^{3} (mod\ 227) = 48 \\
-    k_{1} = b^{x}(mod\ prime3) = 48^{2}(mod\ 227) = 34 \\
-    k_{2} = a^{y}(mod\ prime3) = 81^{3}(mod\ 227) = 34 \\
+    a = g^{x}\ (mod\ prime3) = 9^{2} (mod\ 227) = 81 \\
+    b = g^{y}\ (mod\ prime3) = 9^{3} (mod\ 227) = 48 \\
+    k_{1} = b^{x}\ (mod\ prime3) = 48^{2}\ (mod\ 227) = 34 \\
+    k_{2} = a^{y}\ (mod\ prime3) = 81^{3}\ (mod\ 227) = 34 \\
     k = k_{1} = k_{2} = 34
 \end{align}
 
-\subsection{Fragen}
+\subsection{Fragen und Antworten}
 
 1. What attack is the Diffie-Hellman key exchange vulnerable to?
 
-Man in the Middle attacks
+Man in the Middle
 
 2. What measures can be taken to prevent this type of attack?
 
-RSA Encryption
+Encryption, Authentication over QR code or 2Factor-Authentication
 
 3. For the Diffie-Hellman, a generator g is used. Explain what a generator is and how can it be found
 
 4. Show why for the primes 61,23 and the public key e=60 no private key d can be found
 
+\begin{align}
+    d = e^{-1}\ mod\ ((p1-1)(p2-1)) \\
+    d = 60^{-1}\ mod\ ((61-1)(23-1)) = 60^{-1} mod\ 1320
+\end{align}