diff --git a/Advanced/Continued Fractions/parts/02 part B.tex b/Advanced/Continued Fractions/parts/02 part B.tex index 22fdd67..f492086 100644 --- a/Advanced/Continued Fractions/parts/02 part B.tex +++ b/Advanced/Continued Fractions/parts/02 part B.tex @@ -115,7 +115,7 @@ Similarly derive the formula $p_nq_{n-2}-p_{n-2}q_n = (-1)^{n-2}a_n$. \problem{} Recall $C_n=p_n/q_n$. Show that $C_n-C_{n-1}=\frac{(-1)^{n-1}}{q_{n-1}q_n}$ -and $C_n-C_{n-2}=\frac{(-1)^{n-2}a_n}{q_{n-2}q_n}$. +and $C_n-C_{n-2}=\frac{(-1)^{n-2}a_n}{q_{n-2}q_n}$. \par \hint{Use \ref{form1} and $p_nq_{n-2}-p_{n-2}q_n = (-1)^{n-2}a_n$ respectively} In \ref{sqrt5}, the value $\alpha-C_n$ alternated between negative and positive diff --git a/Advanced/Cryptography/parts/4 DiffieHellman.tex b/Advanced/Cryptography/parts/4 DiffieHellman.tex index 16cca29..5c2cf12 100755 --- a/Advanced/Cryptography/parts/4 DiffieHellman.tex +++ b/Advanced/Cryptography/parts/4 DiffieHellman.tex @@ -93,7 +93,7 @@ What is their shared secret? \problem{} Let $p = 11$, $g = 2$, $a = 9$, and $b = 4$. \par -Run the algorithm. What is the resultingw shared secret? +Run the algorithm. What is the resulting shared secret? \begin{solution} $g^b = 5$\par diff --git a/Advanced/Cryptography/parts/5 Elgamal.tex b/Advanced/Cryptography/parts/5 Elgamal.tex index 6998a06..fe6eced 100755 --- a/Advanced/Cryptography/parts/5 Elgamal.tex +++ b/Advanced/Cryptography/parts/5 Elgamal.tex @@ -117,9 +117,9 @@ Also, say Eve knows the value of $m_1 - m_2$. How can Eve find $m_1$ and $m_2$?\ \note[Note]{If Bob doesn't change his key, Eve will also be able to decrypt future messages.} \begin{solution} - $c_2 - d_2 = (m_1 - m_2)A^k$. \par - So, $(c_2 - d_2)(m_1 - m_2)^{-1} = A^k$.\par - Now that we have $A^k$, we can compute $m_1 = c_2 \times A^{-k}$. + $c_2 - d_2 = (m_1 - m_2)A^k$ \par + So, $(c_2 - d_2)(m_1 - m_2)^{-1} = A^k$\par + Now that we have $A^k$, we can compute $m_1 = c_2 \times A^{-k}$ \end{solution} \vfill