xii PREFACE
The first issue is the most obvious. You need to authorize your credit
card company or bank to transfer funds to the merchant; however, you’re not
face-to-face with the seller, and you have to send your information through a
probably very insecure channel. It’s imperative that no one is able to obtain
your personal information and pretend to be you in future transactions!
There are, however, two other very important items. The process must
be fast; people aren’t willing to wait minutes to make sure an order has been
confirmed. Also, there’s always the problem of a message being corrupted.
What if some of the message is mistransmitted or misread by the party on
the other end? These questions lead us to the study of efficient algorithms
and error detection and correction codes. These have found a wealth of ap-
plications not just in cryptography, but also in areas where the information
is not secret.
Two great examples are streaming video and Universal Product Codes
(UPC). In streaming video the information (everything from sports high-
lights to CSPAN debates) is often unprotected and deliberately meant to
be freely available to all; what matters is being able to transmit it quickly
and play it correctly on the other end. Fruits and vegetables are some of
the few remaining items to resist getting a UPC barcode; these black and
white patterns are on almost all products. It may shock you to realize how
these are used. It’s far more than helping the cashier charge you the proper
amount; they’re also used to help stores update their inventory in real time
as well as correlate and analyze your purchases to better target you in the
future! These are both wonderful examples of the need to detect and correct
errors.
These examples illustrate that problems and solutions arising from cryp-
tography often have applications in other disciplines. That’s why we didn’t
title this book as an introduction to cryptography, but rather to encryption.
Cryptography is of course important in the development of the field, but it’s
not the entire story.
The purpose of this book is to introduce just enough mathematics to
explore these topics and to familiarize you with the issues and challenges
of the field. Fortunately, basic algebra and some elementary number the-
ory is enough to describe the systems and methods. This means you can
read this book without knowing calculus or linear algebra; however, it’s im-
portant to understand what “elementary” means. While we don’t need to
use powerful theorems from advanced mathematics, we do need to be very
clever in combining our tools from algebra. Fortunately we’re following the
paths of giants, who have had numerous “aha moments” and have seen sub-
tle connections between seemingly disparate subjects. We leisurely explore
these paths, emphasizing the thought processes that led to these remarkable
advances.
Below is a quick summary of what is covered in this book, which we
follow with outlines for semester-long courses. Each chapter ends with a
collection of problems. Some problems are straightforward applications of
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