45 lines
1 KiB
TeX
45 lines
1 KiB
TeX
\section{Part 5: Asymmetric Encryption}
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\subsection{Generierte Primzahlen}
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\begin{verbatim}
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openssl prime -generate -bits 8
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\end{verbatim}
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\begin{verbatim}
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prime1 = 211, prime2 = 223, prime3 = 227, e=11
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\end{verbatim}
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\subsection{Berechnungen}
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\begin{align}
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d = e^{-1} mod ((prime1-1)(prime2-1)) \\
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d = 11^{-1} mod ((211-1)(223-1)) = 21191
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\end{align}
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\begin{verbatim}
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g = 9, x = 2, y = 3
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\end{verbatim}
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\begin{align}
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a = g^{x} (mod\ prime3) = 9^{2} (mod\ 227) = 81 \\
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b = g^{y} (mod\ prime3) = 9^{3} (mod\ 227) = 48 \\
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k_{1} = b^{x}(mod\ prime3) = 48^{2}(mod\ 227) = 34 \\
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k_{2} = a^{y}(mod\ prime3) = 81^{3}(mod\ 227) = 34 \\
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k = k_{1} = k_{2} = 34
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\end{align}
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\subsection{Fragen}
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1. What attack is the Diffie-Hellman key exchange vulnerable to?
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Man in the Middle attacks
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2. What measures can be taken to prevent this type of attack?
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RSA Encryption
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3. For the Diffie-Hellman, a generator g is used. Explain what a generator is and how can it be found
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4. Show why for the primes 61,23 and the public key e=60 no private key d can be found
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