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Cryptography edits

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mark
2023-08-30 15:27:07 -07:00
parent bc43a4ecce
commit 366f79f3d4
3 changed files with 22 additions and 7 deletions
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7
Advanced/Cryptography/parts/1 mod.tex
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@ -4,11 +4,11 @@
$\mathbb{Z}_n$ is the set of integers mod $n$. For example, $\mathbb{Z}_5 = \{0, 1, 2, 3, 4\}$. \par
\problem{}
Create a multiplication addition table for $\mathbb{Z}_4$:
Create a multiplication table for $\mathbb{Z}_4$:
\begin{center}
\begin{tabular}{c | c c c c}
+ & 0 & 1 & 2 & 3 \\
\times & 0 & 1 & 2 & 3 \\
\hline
0 & ? & ? & ? & ? \\
1 & ? & ? & ? & ? \\
@ -36,8 +36,7 @@ $a$ has an inverse in $\mathbb{Z}_n$ iff $\gcd(a, n) = 1$ \par
\problem{}
Find the inverse of $3$ in $\mathbb{Z}_4$, if one exists. \par
Find the inverse of $20$ in $\mathbb{Z}_{14}$, if one exists. \par
Find the inverse of $2$ in $\mathbb{Z}_5$, if one exists.
%$34^\star \equiv -175 \equiv 366 \pmod{541}$.
Find the inverse of $4$ in $\mathbb{Z}_7$, if one exists.
\vfill