Introduction to Cryptography with Coding Theory [Hardcover]

Features and Benefits

Assumes a math background of calculus and linear algebra. This background is needed more for 'math sophistication' than for actual content.
Flexible organization-Each chapter is modular and can be covered in any order.
Computer examples included in Appendix-Using Mathematica, Maple, MATLAB, these examples explain how to do computation and demonstrate important concepts. They can also be downloaded from the companion website.
Full chapter on error correcting codes-Allows professors to introduce the basic elements of coding theory.

This book is based on a course in cryptography at the upper level undergraduate and beginning graduate level that has been given at the University of Maryland since 1997. When designing the course, we decided on the following requirements.

• The course should be up-to-date and cover a broad selection of topics from a mathematical point of view.
• The material should be accessible to mathematically mature students having little background in number theory and computer programming.
• There should be examples involving numbers large enough to demonstrate how the algorithms really work.

We wanted to avoid concentrating solely on RSA and discrete logarithms, which would have made the course mostly a number theory course. We also did not want to teach a course on protocols and how to hack into friends' computers. That would have made the course less mathematical than desired.

There are numerous topics in cryptology that can be discussed in an introductory course. We have tried to include many of them. The chapters represent, for the most part, topics that were covered during the different semesters we taught the course. There is certainly more material here than could be treated in most one-semester courses. The first eight chapters represent the core of the material. The choice of which of the remaining chapters are used depends on the level of the students.

The chapters are numbered, thus giving them an ordering. However, except for Chapter 3 on number theory, which pervades the subject, the chapters are fairly independent of each other and can be covered in almost any reasonable order. Although we don't recommend doing so, a daring reader could possibly read Chapters 4 through 17 in reverse order, with only having to look ahead/behind a few times.

The chapters on Information Theory, Elliptic Curves, (quantum Methods, and Error Correcting Codes are somewhat more mathematical than the others. The chapter on Error Correcting Codes was included, at the suggestion of several reviewers, because courses that include introductions to both cryptology and coding theory are fairly common.

Computer examples. Suppose you want to give an example for RSA. You could choose two one-digit primes and pretend to be working with fifty-digit primes, or you could use your favorite software package to do an actual example with large primes. Or perhaps you are working with shift ciphers and are trying to decrypt a message by trying all 26 shifts of the ciphertext. This should also be done on a computer. At the end of the book are appendices containing Computer Examples written in each of Mathematica®, Maple®, and MATLAB® that show how to do such calculations. These languages were chosen because they are user friendly and do not require prior programming experience. Although the course has been taught successfully without computers, these examples are an integral part of the book and should be studied, if at all possible. Not only do they contain numerical examples of how to do certain computations but also they demonstrate important ideas and issues that arise. They were placed at the end of the book because of the logistic and aesthetic problems of including extensive computer examples in three languages at the ends of chapters.Homework problems (the Computer Problems in various chapters) based on the software allow students to play with examples individually. Of course, students having more programming background could write their own programs instead.