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\vspace{-5mm}\noindent \textbf{Math 314 - Spring 2018 \hfill 
Name:} 
\hspace{2in} %Replace this line with your name!

\noindent \textbf{Mission 10} \hfill Due May 16th, 2018 \vspace{-4mm}\\

\small \textit{A signature always reveals a man's character - and sometimes even his name. 
}\\
\vspace{1mm} \hfill--- Evan Esar

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\normalsize
\noindent \hrulefill

\section*{Guidelines}
\begin{itemize}
	\item All work must be shown for full credit.
	\item You can choose to use SageMath code to help you solve the problems.  If you do, print out your code (or use the same folder as the latex code on SMC).
	\item Either print out this assignment and write your answers on it, or edit the latex source on SMC and type your answers in the document.  Make sure you still show your work!
There is one point of extra credit available on this assignment if you use \LaTeX
	\item You may work with classmates, but be sure to turn in your own written solutions.  Write down the name(s) of anyone who helps you.
\item Check one:\\
%You can put an x inside the framebox to "check" the box in latex for example: \framebox(12,12){x}
\framebox(12,12){} I worked with the following classmate(s): 
\rule{7cm}{0.5pt}\\ %Replace this line with names of students.
\noindent\framebox(12,12){} I did not receive any help on this assignment.
\end{itemize}

\section{Graded Problems}

\begin{enumerate}[1.]

	\item Exercise 7.6.11
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	\vspace{2.9in}
	%Type your answer here!
	
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\pagebreak
	\item Exercise 9.6.3
\begin{framed} 
	\vspace{3.5in}
	%Type your answer here!
	
\end{framed}

	\item Exercise 8.8.2  
\begin{framed} 
	\vspace{3.5in}
	%Type your answer here!
	
\end{framed}
\pagebreak

\item Alice sets up an RSA key with the primes $p=31$ and $q=43$ and exponent $e=13$.  Determine what her signature on the message $m=100$ would be. (Use a calculator/cocalc to do the exponentiation, but explain your steps!)  Verify that the signature is valid.

\begin{framed} 
	\vspace{3in}
	%Type your answer here!
	
\end{framed}

\item Alice sets up an DSA key with the primes $p=67$, $q=11$, and the primitive root $g=2$.  Suppose she picks the secret number $a=5$.  Determine the rest of her public key, and sign the message $m=17$ (supposing she picks $k=3$.  Verify that the signature is valid.

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	%Type your answer here!
	
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\end{enumerate}

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