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fix spelling
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Andre Henriques 2023-11-07 21:42:49 +00:00
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cw/cw.tex
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@ -223,7 +223,7 @@
in this case $r_a$ from alice cancels $r_b$ from alice, and $r_a$ from bob cancels $r_b$ from bob in this case $r_a$ from alice cancels $r_b$ from alice, and $r_a$ from bob cancels $r_b$ from bob
\subsubsection*{6.3.2} \subsubsection*{6.3.2}
To send an encrypted message using this system: To send an encrypted message using this system between 2 people, i.e. Alice and Bob:
\begin{enumerate} \begin{enumerate}
\item Bob and Alice choose a prime $p$ \item Bob and Alice choose a prime $p$
\item The sender, let's say Alice, selects $m$ and two random values $r_{a1}$ and $r_{a2}$ such that $(m^{r_{a1}})^{r_{a2}} = m (\text{mod } p)$ \item The sender, let's say Alice, selects $m$ and two random values $r_{a1}$ and $r_{a2}$ such that $(m^{r_{a1}})^{r_{a2}} = m (\text{mod } p)$
@ -234,10 +234,13 @@
\item Bob then calculates $m = t3^{r_{b2}} (\text{mod } p)$, this undoes step 5 \item Bob then calculates $m = t3^{r_{b2}} (\text{mod } p)$, this undoes step 5
\end{enumerate} \end{enumerate}
\subsubsection*{6.3.3} \subsubsection*{6.3.3}
Bob and Alice exchange information 4 times, they choose the primes and then 3 exchanges during the encryption process. Information is exchanged 4 times with this crypto system, they choose the primes and then 3 exchanges happen during the encryption process.
While for ElGamal you need to exchange information only twice, once to exchange public keys and the second to exchange the encrypted message While for ElGamal you need to exchange information only twice, once to exchange public keys and the second to exchange the encrypted message
\subsubsection*{6.3.4} \subsubsection*{6.3.4}
If the discrite logarithm problem is easy to solve then Elgamal is also easy to solve. While for this case the being able to solve the discrite logarithm problem does not help an attacker with breaking the algorithm because the attacker only knows the result of the exponenciation and does not know the value of the base which is publicly known with Elgamal.
The Diffle-Hellman problem also does not apply since that problem rellies on. if we know $g^x$ and $g^y$ being able to figure out $g^{xy}$ but on this case the problem is slightly different. Is being able to figure out $g^x^y$.
Therefore this problem does not depend on the discrite logarithm problem
\section*{7} \section*{7}
\subsection*{7.1} \subsection*{7.1}