Introduction to Cryptography with Mathematical Foundations and Computer Implementations: (Discrete Mathematics and Its Applications)

From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in cryptography, it delineates cryptographic concepts in chronological order, developing the mathematics as needed. Written in an engaging yet rigorous style, each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with "Exercises for the Reader;" complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter, and detailed solutions to most odd-numbered exercises can be found in a designated appendix. The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platform-independent applet pages for some core programs and algorithms. As the reliance on cryptography by business, government, and industry continues and new technologies for transferring data become available, cryptography plays a permanent, important role in day-to-day operations. This self-contained sophomore-level text traces the evolution of the field, from its origins through present-day cryptosystems, including public key cryptography and elliptic curve cryptography.

Table of Contents:
An Overview of the Subject. Divisibility and Modular Arithmetic. The Evolution of Codemaking until the Computer Era. Matrices and the Hill Cryptosystem. The Evolution of Codebreaking until the Computer Era. Representation and Arithmetic of Integers in Different Bases. Block Cryptosystems and the Data Encryption Standard (DES). Some Number Theory and Algorithms. Public Key Cryptography. Finite Fields in General and GF(28) in Particular. The Advanced Encryption Standard (AES) Protocol. Elliptic Curve Cryptography. Appendices. References.

About the Author :
Alexander Stanoyevitch is a professor at California State University--Dominguez Hills. He completed his doctorate in mathematical analysis at the University of Michigan, Ann Arbor, and has held academic positions at the University of Hawaii and the University of Guam. Dr. Stanoyevitch has taught many upper-level classes to mathematics and computer science students, has published several articles in leading mathematical journals, and has been an invited speaker at numerous lectures and conferences in the United States, Europe, and Asia. His research interests include areas of both pure and applied mathematics.

Review :
This book is a very comprehensible introduction to cryptography. It will be very suitable for undergraduate students. There is adequate material in the book for teaching one or two courses on cryptography. The author has provided many mathematically oriented as well as computer-based exercises. I strongly recommend this book as an introductory book on cryptography for undergraduates. --IACR Book Reviews, April 2011 ! a particularly good entry in a crowded field. ! As someone who has taught cryptography courses in the past, I was particularly impressed with the scaled-down versions of DES and AES that the author describes ! . Stanoyevitch's writing style is clear and engaging, and the book has many examples illustrating the mathematical concepts throughout. ! One of the many smart decisions that the author made was to also include many computer implementations and exercises at the end of each chapter. ! It is also worth noting that he has many MATLAB implementations on his website. ! It is clear that Stanoyevitch designed this book to be used by students and that he has taught this type of student many times before. The book feels carefully structured in a way that builds nicely ! it is definitely a solid choice and will be on the short list of books that I would recommend to a student wanting to learn about the field. --MAA Reviews, May 2011 I perused the structure, the writing, the pedagogical approach/layout: I can recognize a labor of pedagogical love when I see one. Certainly, the colloquial but still rigorous approach makes the concepts accessible, and the worked out solutions for the student, the much-needed and appreciated chapter on finite fields, and the division of problems into theory and programming are sensible. But it is the little thoughtful touches that make the book truly shine: the position of the notation index right on the front cover; the historical excursions as mental relief to keep students' interest peaked; judicious use of accessible examples plus step-by-step worked out math to illustrate concepts; and whitespace in the margin for notes, the text layout with breathing room to offset the inevitable terseness of mathematical cryptology. It is apparent that Prof. Stanoyevitch put a lot of pedagogical and intellectual effort into making a textbook -- a book aimed at students that makes life easier for the instructor. In addition, the book's companion site features short MATLAB m-files and applets for quick demos. The Index of Algorithms is useful. In short, this is a very well done, thoughtful introduction to cryptography. --Daniel Bilar, Department of Computer Science, University of New Orleans, Louisiana, USA