diff --git a/Lab04/documentation/part5/part5.tex b/Lab04/documentation/part5/part5.tex index 117a4c0..1f75989 100644 --- a/Lab04/documentation/part5/part5.tex +++ b/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} \ No newline at end of file