46 lines
1 KiB
TeX
46 lines
1 KiB
TeX
|
\section{Part 5: Asymmetric Encryption}
|
||
|
|
|
||
|
|
\subsection{Generierte Primzahlen}
|
||
|
|
|
||
|
|
\begin{verbatim}
|
||
|
|
openssl prime -generate -bits 8
|
||
|
|
\end{verbatim}
|
||
|
|
|
||
|
|
\begin{verbatim}
|
||
|
|
prime1 = 211, prime2 = 223, prime3 = 227, e=11
|
||
|
|
\end{verbatim}
|
||
|
|
|
||
|
|
\subsection{Berechnungen}
|
||
|
|
|
||
|
|
\begin{align}
|
||
|
|
d = e^{-1} mod ((prime1-1)(prime2-1)) \\
|
||
|
|
d = 11^{-1} mod ((211-1)(223-1)) = 21191
|
||
|
|
\end{align}
|
||
|
|
|
||
|
|
\begin{verbatim}
|
||
|
|
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 \\
|
||
|
|
k = k_{1} = k_{2} = 34
|
||
|
|
\end{align}
|
||
|
|
|
||
|
|
\subsection{Fragen}
|
||
|
|
|
||
|
|
1. What attack is the Diffie-Hellman key exchange vulnerable to?
|
||
|
|
|
||
|
|
Man in the Middle attacks
|
||
|
|
|
||
|
|
2. What measures can be taken to prevent this type of attack?
|
||
|
|
|
||
|
|
RSA Encryption
|
||
|
|
|
||
|
|
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
|
||
|
|
|