68 lines
No EOL
1.8 KiB
TeX
68 lines
No EOL
1.8 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, 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, n = 227 (prime3)
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\end{verbatim}
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\begin{align}
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a = g^{x}\ (mod\ n) = 9^{2} (mod\ 227) = 81\ (public\ a) \\
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b = g^{y}\ (mod\ n) = 9^{3} (mod\ 227) = 48\ (public\ b) \\
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k_{1} = b^{x}\ (mod\ n) = 48^{2}\ (mod\ 227) = 34\ (private) \\
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k_{2} = a^{y}\ (mod\ n) = 81^{3}\ (mod\ 227) = 34\ (private) \\
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k = k_{1} = k_{2} = 34\ (private)
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\end{align}
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\newpage
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\subsection{Fragen und Antworten}
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1. What attack is the Diffie-Hellman key exchange vulnerable to?
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\begin{list}{-}{}
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\item Man in the Middle
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\end{list}
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2. What measures can be taken to prevent this type of attack?
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\begin{list}{-}{}
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\item Encrypting exchange (VPN)
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\item Signature verification
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\item Combine with RSA/AES
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\item Authentication at Server-Level over QR code or 2Factor-Authentication
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\end{list}
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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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\begin{list}{-}{}
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\item A generator is a number that will be the base of the calculation and is shared between the 2 parties
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\item G is a small prime number.
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\end{list}
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\begin{align}
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g^{a}\ (mod\ n) \neq g^{b}\ (mod\ n) \\
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g^{(a\ *\ b)}\ (mod\ n) = g^{(b\ *\ a)}\ (mod\ n)
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\end{align}
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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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\begin{align}
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d = e^{-1}\ mod\ ((p1-1)(p2-1)) \\
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d = 60^{-1}\ mod\ ((61-1)(23-1)) = 60^{-1} mod\ 1320
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\end{align} |