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Update part5.tex

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Florian Hoss 2022-05-30 21:30:19 +02:00
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1 changed files with 13 additions and 9 deletions
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Lab04/documentation/part5/part5.tex
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@ -13,8 +13,8 @@ prime1 = 211, prime2 = 223, prime3 = 227, e=11
\subsection{Berechnungen} \subsection{Berechnungen}
\begin{align} \begin{align}
d = e^{-1} mod ((prime1-1)(prime2-1)) \\ d = e^{-1}\ mod\ ((prime1-1)(prime2-1)) \\
d = 11^{-1} mod ((211-1)(223-1)) = 21191 d = 11^{-1}\ mod\ ((211-1)(223-1)) = 21191
\end{align} \end{align}
\begin{verbatim} \begin{verbatim}
@ -22,24 +22,28 @@ g = 9, x = 2, y = 3
\end{verbatim} \end{verbatim}
\begin{align} \begin{align}
a = g^{x} (mod\ prime3) = 9^{2} (mod\ 227) = 81 \\ a = g^{x}\ (mod\ prime3) = 9^{2} (mod\ 227) = 81 \\
b = g^{y} (mod\ prime3) = 9^{3} (mod\ 227) = 48 \\ b = g^{y}\ (mod\ prime3) = 9^{3} (mod\ 227) = 48 \\
k_{1} = b^{x}(mod\ prime3) = 48^{2}(mod\ 227) = 34 \\ k_{1} = b^{x}\ (mod\ prime3) = 48^{2}\ (mod\ 227) = 34 \\
k_{2} = a^{y}(mod\ prime3) = 81^{3}(mod\ 227) = 34 \\ k_{2} = a^{y}\ (mod\ prime3) = 81^{3}\ (mod\ 227) = 34 \\
k = k_{1} = k_{2} = 34 k = k_{1} = k_{2} = 34
\end{align} \end{align}
\subsection{Fragen} \subsection{Fragen und Antworten}
1. What attack is the Diffie-Hellman key exchange vulnerable to? 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? 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 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 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}