Mathbook XML text for the exploration of mathematics in cryptology
I have been teaching cryptology to undergraduates for a number of years now an feel that they could benefit from a hands on text which walks them through the history and techniques of cryptology. I also want to ensure that the text is as historically accurate as possible by using original sources (or their translations) whenever possible.
Goals and Aims of the text:
\begin{itemize}
\item Present a \textit{brief} overview of the history of cryptology
\item Present the cryptology as it was not with significantly newer or older concepts
\item Exception to the previous statement will be the use of some modern terminology where appropriate
\item Present a variety of mathematical topics: Statistical analysis, Linear Algebra, Number Theory, Group Theory
\item Present the material from an inquiry based perspective when possible
\item Present the text as a battle back and forth between making and breaking codes
\end{itemize}
What should be covered in terms of content can be summarized by the list:
\begin{itemize}
\item 500 B.C.E. (and before): Atabash, Scytale, Demaratus, Histiaeus
\item 50 B.C.E.: Caesar
\item 700-1000: Arab Cryptology*
\item 1400-1850: Foiling Frequencies*: Alberti's, Vigen\'{e}re's , Jefferson's, and Playfair's Ciphers
\item 1846: Babbage / Kasiski Test*
\item 1914-1918: World War I: Zimmermann's Telegram, ADFGVX Cipher, etc.
\item 1919: One Time Pad*
\item 1929: Hill's Cipher*
\item 1934: Enigma* in the service of the German military
\item 1978: RSA*
\item 1991: Zimmermann and PGP
\item 2000: Quantum Cryptology
\end{itemize}