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Textbook in PDF format

Several years ago we were invited to create a new general education math- ematics course for the Honors Academy at Radford University. Wanting to create a multidisciplinary course that would demonstrate some interesting mathematical applications and also be accessible and intriguing to students with a wide variety of interests and backgrounds, we decided on a course in cryptology. Designed for students with only a basic understanding of algebra, statistics, and number theory at the secondary level, the course has been one of the most popular offerings at the Honors Academy. When deciding on material for the course, since we expected most of our students to come from nontechnical fields, our goal was to choose topics that would be easy to understand, showed the importance of cryptology in both cultural and historical contexts, and demonstrated some stimulating but relatively simple mathematical applications. A lesser goal was for students to be motivated to study the subject further and perhaps even consider careers in mathematics or the sciences.
In order to include substantive examples of the techniques presented in the course, we incorporated the mathematics software package Maple. However, the use of Maple was met with only limited success, since students had to develop a rudimentary working knowledge of Maple syntax. For some students, especially from nontechnical fields with little or no back- ground in programming or computer syntax, this proved too daunting a task. We alleviated this problem through the use of Maplets, which employ (and need) the Maple engine, but operate exclusively within windows that are simple to use and require no background in computers. By simply typing information in textboxes and using buttons and drop-down menus in Maplet windows, our students were able to complete complicated tasks with relative ease. We produced these Maplets with written code in Maple, but because our students only needed to use the end product, they did not need to have even a rudimentary working knowledge of Maple syntax.
Our philosophy concerning Maplets in the course is that they be useful and not present new problems or frustrations. We never require our students to produce Maplets or Maple code, or do anything in Maple outside our Maplet windows. In addition, for almost every topic in the course, we completely cover the topic without using Maplets before introducing Maplets for the topic. This in part dictated the style in which we wrote this book, with all Maplet material and exercises in separate, clearly-labeled sections. More specifically, for almost every topic in the book, we completely cover the topic in one section, and then introduce one or more Maplets for the topic in the following section. This gives the book the added feature that it can easily be used for general education courses on cryptology in which advanced technology is not incorporated. The Maplet sections can be omitted without any loss of continuity, and all non-Maplet examples and exercises can be completed with at most a simple hand-held calculator.
Introduction to Cryptology
Substitution Ciphers
Transposition Ciphers
The Enigma Machine and Navajo Code
Shift and Affine Ciphers
Alberti and Vigenère Ciphers
Hill Ciphers
RSA Ciphers
El Gamal Ciphers
The Advanced Encryption Standard
Message Authentication
Hints or Answers to Selected Exercises