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\begin{center} {\large \textbf{Math 437 -- Homework 7}} \smallskip \\ 
Due 10:15am on Thursday, March 2, 2017  \\ \ \\
 \end{center}

Please indicate any sources you used for a given problem on the solution to that problem. 
For example, if you worked with another student to get the solution to a problem, please indicate who.
You are welcome to work together in small groups, but please try the problems on your own first and write up 
your own solutions. \\ \medskip 


\begin{prob} Ch. 8 \#7 (on page 304)
\end{prob}\ \\


\begin{prob} Ch. 8 \#19 (on page 306)
\end{prob}\ \\


\begin{prob}
Alice wins a trip to meet a certain celebrity, and she wants to tell Bob the good news
privately.  The public part of Bob's RSA key is $n =308911$ (which factors as $541 \cdot 571$).  \\ 

\item[(a)] Alice and Bob want to agree on a secret RSA exponent using Diffie-Hellman key exchange.
 Bob chooses $k = 13$ and $r = 13$ and sends $k$ and $k^r ({\rm mod \ } n)$ to Alice.  He receives back $k^s \equiv 39584 ({\rm mod \ }n)$. 
 What secret exponent $a$ will Alice and Bob use?  \\

\item[(b)]
Alice uses the exponent $a$ to encrypt the zip code where she is going and sends Bob the encrypted message $164103$.
What is the zip code and who is she meeting? 
\end{prob}\ \\





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