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@ -115,7 +115,7 @@ Similarly derive the formula $p_nq_{n-2}-p_{n-2}q_n = (-1)^{n-2}a_n$.
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\problem{}<diff>
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Recall $C_n=p_n/q_n$.
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Show that $C_n-C_{n-1}=\frac{(-1)^{n-1}}{q_{n-1}q_n}$
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and $C_n-C_{n-2}=\frac{(-1)^{n-2}a_n}{q_{n-2}q_n}$.
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and $C_n-C_{n-2}=\frac{(-1)^{n-2}a_n}{q_{n-2}q_n}$. \par
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\hint{Use \ref{form1} and $p_nq_{n-2}-p_{n-2}q_n = (-1)^{n-2}a_n$ respectively}
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In \ref{sqrt5}, the value $\alpha-C_n$ alternated between negative and positive
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@ -93,7 +93,7 @@ What is their shared secret?
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\problem{}
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Let $p = 11$, $g = 2$, $a = 9$, and $b = 4$. \par
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Run the algorithm. What is the resultingw shared secret?
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Run the algorithm. What is the resulting shared secret?
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\begin{solution}
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$g^b = 5$\par
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@ -117,9 +117,9 @@ Also, say Eve knows the value of $m_1 - m_2$. How can Eve find $m_1$ and $m_2$?\
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\note[Note]{If Bob doesn't change his key, Eve will also be able to decrypt future messages.}
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\begin{solution}
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$c_2 - d_2 = (m_1 - m_2)A^k$. \par
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So, $(c_2 - d_2)(m_1 - m_2)^{-1} = A^k$.\par
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Now that we have $A^k$, we can compute $m_1 = c_2 \times A^{-k}$.
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$c_2 - d_2 = (m_1 - m_2)A^k$ \par
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So, $(c_2 - d_2)(m_1 - m_2)^{-1} = A^k$\par
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Now that we have $A^k$, we can compute $m_1 = c_2 \times A^{-k}$
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\end{solution}
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\vfill
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