Mathematical Ciphers: From Caesar to RSA (Mathematical World)

Features

• Cover Type: Paperback with 159 pages
• Published by: American Mathematical Society August 24, 2006
• Written in: English
• ISBN 10 Number: 0821837303
• ISBN 13 Number: 978-0821837306
• Book Dimensions: 9.8 x 6.8 x 0.4 inches
• Weighs: 11.2 ounces

Product Description
A cipher is a scheme for creating coded messages for the secure exchange of information. Throughout history, many different coding schemes have been devised. One of the oldest and simplest mathematical systems was used by Julius Caesar. This is where Mathematical Ciphers begins. Building on that simple system, Young moves on to more complicated schemes, ultimately ending with the RSA cipher, which is used to provide security for the Internet. This book is structured differently from most mathematics texts. It does not begin with a mathematical topic, but rather with a cipher. The mathematics is developed as it is needed; the applications motivate the mathematics. As is typical in mathematics textbooks, most chapters end with exercises. Many of these problems are similar to solved examples and are designed to assist the reader in mastering the basic material. A few of the exercises are one-of-a-kind, intended to challenge the interested reader. Implementing encryption schemes is considerably easier with the use of the computer. For all the ciphers introduced in this book, JavaScript programs are available from the Web. In addition to developing various encryption schemes, this book also introduces the reader to number theory. Here, the study of integers and their properties is placed in the exciting and modern context of cryptology. Mathematical Ciphers can be used as a textbook for an introductory course in mathematics for all majors. The only prerequisite is high school mathematics.

Reader Reviews
This book is a basic introduction to ciphers and the cover blurb is quite correct in stating that only high school mathematics is used. The ciphers examined are: *) Caesar shift cipher *) Multiplication cipher *) Multiplication-shift cipher *) Exponential cipher *) RSA cipher Each cipher type is first demonstrated in action, then the mathematics of encryption and decryption using that cipher type is explained. Modular arithmetic is the fundamental area of mathematics needed and it is covered in detail. The order of presentation is quite natural and necessary; the shift and multiplication ciphers are followed by the multiplication-shift and then the exponential. This provides a solid lead-in to the RSA cipher and I found the explanation of how digital signatures can be constructed to be the clearest I have ever read. There are many encryption books on the market today, while this one is on the lower end of difficulty, it is on the higher end of understandability. The writing is clear, well organized and at the stated target level.