Invitation to Cryptography

In 1994, my colleague Terri Lindquester had a pedagogical inspiration: to teach cryptology. The lack of unified resources to teach an introductory course with mathematical themes, historical content, and current cryptographic relevance required her to piece together material from various sources. She had considerable success with The Science of Secret Writing: more students requested it at registration time than could be accommodated, her own insights and teaching abilities made the course itself lively and appealing to the students enrolled, and students from a wide range of academic disciplines learned some mathematics and cryptology. The experience convinced her that there was a genuine need for an up-to-date introductory cryptology text, and this prompted her to seek National Science Foundation (NSF) funding to develop materials for such a course. A guiding principle was to introduce mathematics in the context of cryptology. This book is the result of Terri's application for that funding, of the foundation's awarding it, and of a great deal of work, teaching, and writing in the interim. Unfortunately for those who use this text, very little of it is Terri's writing. Almost coincident with the awarding of funding for the project, Terri was called to serve in an administrative capacity at Rhodes College. The demands of this post were such that it would be extraordinarily difficult for her to work on the cryptology project, and indeed its fate was, for a time, in question. In 1997, through conversations with and encouragement from Terri, I embarked on the project: teaching the second offering of Secret Writing, doing research, and writing materials based on her course notes from the first offering of Secret Writing. I became "Chief Staff Mathematician" on the project. With her continuing consultation and reviewing of early drafts, the book has evolved into its present form. This book is directed toward those whose mathematical background includes college-preparatory courses such as high school algebra and geometry. In earlier drafts, I have used it as the basis for a course for which there were no formal mathematical prerequisites at the college level. Students majoring in areas ranging from Art History to Zoology took the course. Many had not taken mathematics in four or five years. The purpose of the book is to introduce students to segments of history and current cryptological practice that have mathematical content or underpinnings. This is not a mathematics text in the strictest sense because it does not begin with a few definitions and axioms and build up a mathematical edifice on that. However, a variety of mathematical topics are developed here: modular arithmetic, probability and statistics, matrix arithmetic, Boolean functions, complexity theory, and number theory. In each case, the topic is germane to cryptology. The concepts introduced in this book may also be a springboard for those who may not be drawn into technical careers but who instead may be headed toward careers in public service or industry where important policy or strategic decisions regarding information security will be made. The more technical background the policymakers and managers have, the better. With any luck, these pages may provide some of that background. The treatment here is not comprehensive, but the concepts discussed cover a number of the current uses of cryptographic methods. The mathematical basis of cryptography has been a theme throughout this exposition, and what is here can provide an entree to a range of mathematical areas. Readers may find their way into the general mathematical literature as well by following the links provided in the mathematical references in this book. The academic and popular literature on cryptology is large and growing rapidly. It represents a considerable body of general knowledge about cryptology and specific information on implementations in hardware and software. In tBarr, Thomas H. is the author of 'Invitation to Cryptography', published 2001 under ISBN 9780130889768 and ISBN 0130889768.