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\title[Math 75 Homework \#1]{Math 75: Mathematical Cryptography \\ Homework \#1}
\date{Due Wednesday, 6 April 2016}

\maketitle

\section*{Problems}

\begin{problab}{1}
What is the message embedded in the following?

\vspace{1ex}
\begin{quote}
\begin{sffamily}
\hspace{2.5ex}Dear George,

Greetings to all at Oxford.  Many thanks for your

letter and for the Summer examination package.

All Entry Forms and Fees Forms should be ready

for final despatch to the syndicate by Friday

20th or at the very latest, I'm told, by the 21st.

Admin has improved here, though there's room

for improvement still; just give us all two or three

more years and we'll really show you!  Please

don't let these wretched 16+ proposals destroy

your basic O and A pattern.  Certainly this

sort of change, if implemented immediately,

would bring chaos.
\end{sffamily}
\end{quote}
\end{problab}

\begin{problab}{2}
In one of Dorothy Sayers' mysteries, Lord Peter is confronted with the following message:

\vspace{1ex}

\begin{verbatim}
I thought to see the fairies in the fields, but I saw only the evil
elephants with their black backs.  Woe! how that sight awed me!  The
elves danced all around and about while I heard voices calling clearly.
Ah! how I tried to see--throw off the ugly cloud--but no blind eye of a
mortal was permitted to spy them.  So then came minstrels, having gold
trumpets, harps and drums.  These played very loudly beside me,
breaking that spell.  So the dream vanished, whereat I thanked Heaven.  I
shed many tears before the thin moon rose up, frail and faint as a sickle of
straw.  Now though the Enchanter gnash his teeth vainly, yet shall he
return as the spring returns.  Oh, wretched man!  Hell gapes, Erebus now
lies open.  The mouths of Death wait on thy end.
\end{verbatim}
\vspace{1ex}

He also discovers the key to the message, which is a sequence of integers:
\[ \text{\textup{\texttt{7876565434321123434565678788787656543432112343456567878878765654433211234}}} \]

Decrypt the message.  \textup{\emph{[Hint: What is the largest integer value?]}}
\end{problab}

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\begin{problab}{3}
The message 
\begin{center}
\texttt{jajsymtzlmnbfqpymwtzlmymjafqqjdtkymjxmfitbtkijfymnkjfwstjanq}
\end{center}
was encrypted using a shift cipher.  Decrypt the message.
\end{problab}

\begin{problab}{4}
For fun, take a stab at this problem.  In one of his cases, Sherlock Holmes was confronted with the following message:

\begin{center}
\textnormal{534 C2 13 127 36 31 4 7 21 41}

\textnormal{DOUGLAS 109 293 5 37 BIRLSTONE}

\textnormal{26 BIRLSTONE 9 127 171}
\end{center}
Although Watson was puzzled, Holmes was able immediately to deduce the type of cipher.  Can you?
\end{problab}

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