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\begin{slide}{Beispiel}

\begin{itemize}
\item 
  Empfänger wählt Parameter:
  $p=5, q=11, n=55$.

  $\phi(n)=(p-1)(q-1)=40$

  $d=7, e = -17 \equiv 23 \bmod 40$

  öffentlicher Schlüssel $(d,n) = (7,55)$, \\
  geheimer Schlüssel $e = 23$
\item
  Nachricht (Klartext) $x = 14$, 

  verschlüsselt $y  = x^e = 14 ^ 7 \equiv 105413504  \equiv 9 \bmod 55$
\item
  Entschlüsselung 

  $y^e = 9 ^ {23} = 8862938119652501095929 \equiv 14 \bmod 55$.
\end{itemize}

\end{slide}

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