In one sentence, cryptography is the science of transmitting information secretly. It includes studying methods to do such secret transmission and methods for breaking the secret. When we talk about a method in cryptography, we wish to see some serious numerical examples and some reasonable computations with computers. The book under review fulfills this requirement, introducing fundamental concepts of cryptography and examining almost all of them with Maple.
As the table of contents shows, the book covers introductory and fundamental topics of cryptography. The language of the book is elementary, making it accessible to any person with some undergraduate knowledge in science or engineering. To understand the computational parts, the reader should be familiar with Maple and Maple programming. The choice of Maple was prompted by the fact that it is the computer algebra system used in the courses which provided the initial motivation for the book. Hence, many other programming systems can be used perfectly well instead of Maple.
The book is useful for a wide range of audiences. It can be used in an introductory course in cryptography for mathematics, computer science and engineering students. It includes some parts of algorithmic number theory, and it covers elementary concepts of number theory and algebra. It is full of meaningful examples of algorithms and the corresponding Maple code for various topics of cryptography and fundamental number theory. Moreover, the book can be considered as a complement for any on Maple software, and indeed it gives some very good examples of Maple programming with details, including their complexity analysis.
Exercises appear frequently in the body of the book; mainly they ask the reader to analyze complexity of a method, or to write a Maple program for a function. Indeed, the book focuses on the computational side of the story. For beginners in cryptography the instructor will probably want to introduce some additional exercises.
Mehdi Hassani is a faculty member at the Department of Mathematics, Zanjan University, Iran. His field of interest is Elementary, Analytic and Probabilistic Number Theory.