Finish lab

Lab04/documentation/part5/part5.tex

@@ -7,7 +7,7 @@ openssl prime -generate -bits 8
 \end{verbatim}
 
 \begin{verbatim}
-prime1 = 211, prime2 = 223, prime3 = 227, e=11
+prime1 = 211, prime2 = 223, e=11
 \end{verbatim}
 
 \subsection{Berechnungen}
@@ -18,29 +18,36 @@ prime1 = 211, prime2 = 223, prime3 = 227, e=11
 \end{align}
 
 \begin{verbatim}
-g = 9, x = 2, y = 3
+g = 9, x = 2, y = 3, n = 227 (prime3)
 \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 \\
-    k = k_{1} = k_{2} = 34
+    a = g^{x}\ (mod\ n) = 9^{2} (mod\ 227) = 81\ (public\ a) \\
+    b = g^{y}\ (mod\ n) = 9^{3} (mod\ 227) = 48\ (public\ b) \\
+    k_{1} = b^{x}\ (mod\ n) = 48^{2}\ (mod\ 227) = 34\ (private) \\
+    k_{2} = a^{y}\ (mod\ n) = 81^{3}\ (mod\ 227) = 34\ (private) \\
+    k = k_{1} = k_{2} = 34\ (private)
 \end{align}
 
 \subsection{Fragen und Antworten}
 
 1. What attack is the Diffie-Hellman key exchange vulnerable to?
 
-Man in the Middle
+- Man in the Middle
 
 2. What measures can be taken to prevent this type of attack?
 
-Encryption, Authentication over QR code or 2Factor-Authentication
+- 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
 
+- A generator is a number that will be the base of the calculation and is shared between the 2 parties. G is a small prime number.
+
+\begin{align}
+    g^{a}\ (mod\ n) \neq g^{b}\ (mod\ n) \\
+    g^{(a\ *\ b)}\ (mod\ n) = g^{(b\ *\ a)}\ (mod\ n)
+\end{align}
+
 4. Show why for the primes 61,23 and the public key e=60 no private key d can be found
 
 \begin{align}