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\noindent \textbf{Math 314 - Fall 2016 \hfill 
Name:} 
\hspace{2in} %Replace this line with your name!

\noindent \textbf{Mission 1} \hfill Due September 6, 2016 \vspace{-4mm}\\

\small \textit{I must study politics and war that my sons may have liberty to study mathematics and philosophy.}\\\vspace{1mm} \hfill---John Adams

\vspace{-5mm}
\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 and attach it with the assignment.  
	\item Either print out this assignment and write your answers on it, or download the latex source and type your answers in the document.  Make sure you still show your work!
	\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 (T\&W 2.13 \# 3)  Encrypt \texttt{howareyou} using the affine function $5x+7 \pmod{26}$.  What is the decryption function? Check that it works.
	\begin{framed} 
	\vspace{4.23in}
	%Type your answer here!
	
	\end{framed}
	\item (T\&W 2.13 \# 4)  Consider an affine cipher$\pmod{26}$.  You do a chosen plaintext attack using \texttt{hahaha}.  The ciphertext is \texttt{NONONO}.  Determine the encryption function. \begin{framed} 
	\vspace{3in}
	%Type your answer here!
	
	\end{framed}
	\item This problem involves the Dancing Men code from a Sherlock Holmes story.
		\begin{enumerate}[a.]
			\item Read Section 2.5 (Sherlock Holmes), and describe (in a paragraph) how Sherlock figures out which dancing man represents the letter \texttt{e} as well as the letter \texttt{r}.\\ 
			\begin{framed}
			\vspace{2in}
			%Type your answer here!
			
			\end{framed}
			\item Explain in one sentence what the little flags mean.\\
			\begin{framed}
			\vspace{1in}
			%Type your answer here!
			
			\end{framed}
		\end{enumerate}
    \pagebreak
	\item (T\&W 2.14 \# 6)  Suppose you encrypt using an affine cipher, then encrypt the encryption using another affine cipher (both are working$\mod{26}$).  Is there any advantage to doing this rather than using a single affine cipher? Why or why not?\\ 
	\begin{framed}
	\vspace{3in}
	%Type your answer here!
	
	\end{framed}

\end{enumerate}

\section{Recommended Exercises}
\noindent These will not be graded but are recommended if you need more practice.
\begin{itemize}
	\item Section 2.13: \# 1, 5, 7
\end{itemize}
	
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