Codes. The Guide to Secrecy From Ancient to Modern Times

700 Pages·2005·12.73 MB·English

by  Richard A. Mollin

Codes
The Guide to Secrecy
from Ancient
to Modern Times
DISCRETE
MATHEMATICS
and
ITS APPLICATIONS
Series Editor
Kenneth H. Rosen, Ph.D.
Juergen Bierbrauer, Introduction to Coding Theory
Kun-Mao Chao and Bang Ye Wu, Spanning Trees and Optimization Problems
Charalambos A. Charalambides, Enumerative Combinatorics
Charles J. Colbourn and Jeffrey H. Dinitz, The CRC Handbook of Combinatorial Designs
Steven Furino, Ying Miao, and Jianxing Yin, Frames and Resolvable Designs: Uses,
Constructions, and Existence
Randy Goldberg and Lance Riek, A Practical Handbook of Speech Coders
Jacob E. Goodman and Joseph O’Rourke, Handbook of Discrete and Computational Geometry,
Second Edition
Jonathan Gross and Jay Yellen, Graph Theory and Its Applications
Jonathan Gross and Jay Yellen, Handbook of Graph Theory
Darrel R. Hankerson, Greg A. Harris, and Peter D. Johnson, Introduction to Information
Theory and Data Compression, Second Edition
Daryl D. Harms, Miroslav Kraetzl, Charles J. Colbourn, and John S. Devitt, Network Reliability:
Experiments with a Symbolic Algebra Environment
Derek F. Holt with Bettina Eick and Eamonn A. O’Brien, Handbook of Computational Group Theory
David M. Jackson and Terry I. Visentin, An Atlas of Smaller Maps in Orientable and
Nonorientable Surfaces
Richard E. Klima, Ernest Stitzinger, and Neil P. Sigmon, Abstract Algebra Applications
with Maple
Patrick Knupp and Kambiz Salari, Verification of Computer Codes in Computational Science
and Engineering
William Kocay and Donald L. Kreher, Graphs, Algorithms, and Optimization
Donald L. Kreher and Douglas R. Stinson, Combinatorial Algorithms: Generation Enumeration
and Search
Charles C. Lindner and Christopher A. Rodgers, Design Theory
Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone, Handbook of Applied
Cryptography
Continued Titles
Richard A. Mollin, Algebraic Number Theory
Richard A. Mollin, Codes: The Guide to Secrecy from Ancient to Modern Times
Richard A. Mollin, Fundamental Number Theory with Applications
Richard A. Mollin, An Introduction to Cryptography
Richard A. Mollin, Quadratics Richard A. Mollin, RSA and Public-Key Cryptography
Kenneth H. Rosen, Handbook of Discrete and Combinatorial Mathematics
Douglas R. Shier and K.T. Wallenius, Applied Mathematical Modeling: A Multidisciplinary
Approach
Jörn Steuding, Diophantine Analysis
Douglas R. Stinson, Cryptography: Theory and Practice, Second Edition
Roberto Togneri and Christopher J. deSilva, Fundamentals of Information Theory and
Coding Design
Lawrence C. Washington, Elliptic Curves: Number Theory and Cryptography

DISCRETE MATHEMATICS AND ITS APPLICATIONS
Series Editor KENNETH H. ROSEN
Codes
The Guide to Secrecy
from Ancient
to Modern Times
Richard A. Mollin
Boca Raton London New York Singapore
C4703_Discl.fm Page 1 Friday, April 8, 2005 1:36 PM
Published in 2005 by
Chapman & Hall/CRC
Taylor & Francis Group
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© 2005 by Taylor & Francis Group, LLC
Chapman & Hall/CRC is an imprint of Taylor & Francis Group
No claim to original U.S. Government works
Printed in the United States of America on acid-free paper
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International Standard Book Number-10: 1-58488-470-3 (Hardcover)
International Standard Book Number-13: 978-1-58488-470-5 (Hardcover)
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Library of Congress Cataloging-in-Publication Data
Mollin, Richard A., 1947-
Codes: the guide to secrecy from ancient to modern times / Richard A. Mollin.
p. cm.
Includes bibliographical references and index.
ISBN 1-58488-470-3 (alk. paper)
1. Computer security. 2. Data encryption (Computer science) I. Title.
QA76.9.A25M67 2005
005.8'2--dc22 2005041403
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Preface
Thisbookhasbeenwrittenwithabroadspectrumofreadersinmind,which
includes anyone interested in secrecy and related issues. Thus, this is a tome
for the merely curious, as well as history-minded readers, amateur mathemati-
cians, engineers, bankers, academics, students, those practitioners working in
cryptography, specialists in the field, and instructors wanting to use the book
for a text in a course on a variety of topics related to codes. We will look at
thistopicfromallaspectsincludingnotonlythoserelatedtocryptography(the
study of methods for sending messages in secret), but also the notion of codes
as removal of noise from telephone channels, satellite signals, CDs and the like.
The uninitiated reader may consider the following. Imagine a world where
you can send a secret message to someone, and describe to anyone listening
in precise detail how you disguised the message. Yet that person could not
remove the disguise from that message no matter how much time or how many
resources are available. Well, that world exists in the here and now, and the
methodology is called public-key cryptography. It permeates our lives, from the
use of a bank card at an automated teller machine ATM to the buying of items
or bank transactions over the Internet. You can even purchase items over the
Internet and do so anonymously, as you would using hard cash. In this book,
you will find out how this is done.
Doyoueverwonderhowsecureyourprivateconversationisoveracellphone?
In general, they are not secure at all. In this book, you will find out how they
can be made secure. And those transactions over the Internet, just how secure
are they? Can these methods be trusted? In this text, you will learn which
methodologies are secure and which are not. Here is an excerpt from the end
of Chapter 2 that is apt. “What made all of the above not just possible, but
rather a necessity — that good old mother of invention — was the advent of
the Internet. While information secrecy, as we have seen throughout history,
was strictly the purview of governments and their agents, the Internet, and its
associated e-mail and e-commerce activities, demanded a mechanism for the
ordinarycitizentohavetheir privacyconcernsaddressed. ... Fewofusactually
understand the mechanisms behind all of these protocols that we use every
day (although this book will foster that understanding), yet cryptography has
becomeeverybody’sbusiness,henceeverybody’sconcern. Thereforeitisalmost
a personal duty that each of us learn as much as possible about the underlying
mechanisms that affect our security, our privacy, and therefore our well-being.”
What are smart cards and how do they affect your life? This book reveals
the answers. What are biometrics and how do they affect you? Several of your
identitycharacteristicssuchasfingerprints,retinaldata,voiceprints,andfacial
geometry, to mention a few, can be embedded in smart cards to identify you
to a bank, for instance. Perhaps you have allergies to some medicines, such as
penicillin, and this information can be embedded in a medical smart card so
that in the event of an accident, appropriate measures can be taken that may
save your life. Read this book to find out how this is done.
vii
viii
How did all this begin and where is it headed? Read Chapter 1 to learn
about the rumblings of the art of secrecy carved in stone almost four millennia
ago and how it evolved to the present where it permeates nearly every aspect
of your life.
(cid:2) Features of This Text
• The text is accessible to virtually anyone who wishes to learn the issues
surrounding secrecy. To this end, Appendix A contains all necessary mathe-
matical facts for the novice, or as a fingertip reference for the initiated. Other
appendices, such as Appendix E, contain the requisite probability theory for
background needed to understand Information and Coding Theory in Chapter
11, for instance. Moreover, the main text is geared to gently introduce the
necessary concepts as they arise. The more difficult or advanced topics are
marked with the pointing hand symbol (cid:3) for the more advanced (or adventur-
ous) reader.
• There are nearly 200 examples, diagrams, figures, and tables throughout
the text to illustrate the history and concepts presented.
•Morethan200 footnotes pepperthetextasfurtherroutesforinformation-
gathering. Think of these as analogues of hyperlinks in the Internet (see page
328), where you can click on a highlighted portion to get further information
about a given topic, or ignore it if you already have this knowledge or are not
interested. These links provide avenues to pursue information about related
topics that might be of separate interest to a wide variety of readers.
• There are more than 80 mini bibliographies throughout the text of those
whohelpedtodeveloptheconceptssurroundingcodes,aswellashistoricaldata
in general to provide the human side of the concepts introduced.
•Therearejustunder300references forfurtherreadinginthebibliography.
This provides further pointers for the reader interested in pursuing topics of
interestrelatedtowhatispresentedherein. Moreover,itprovidesthefoundation
for the facts presented.
• The index has nearly 5000 entries, and has been devised in such a way to
ensure that there is maximum ease in getting information from the text.
• To the instructor who wishes to give a course from this text: There are
morethan370exercisesinAppendixG separatedaccordingtochapterandeven
the appendices A–F. (Some are marked with a ✰ symbol for those particularly
challenging problems.) The wealth of material in this book allows for more
than one course to be given on various aspects of secrecy and even a mini-
course in coding and information theory (see Chapter 11). With nearly 50
Theorems, Propositions, and related material, and more than 60 equations, the
background is amply covered. Moreover, this text is self-contained so that no
other reference is needed since the aforementioned appendices have all possible
background and advanced material covered in detail (see the Table of Contents
for the information covered in each appendix).
• The webpage cited below will contain a file for updates. Furthermore,
comments via the e-mail address below are also welcome.
ix
(cid:2) Acknowledgments: The author is grateful to various people for their
timeinproofreadingvariousaspectsofthisproject. ThanksgotoProfessorJohn
Brillhart, who received portions pertaining to his expertise, and as a pioneer
in computational number theory with his seminal work in primality testing
and factoring, it is an honour to have had him on board. I am grateful to
my American colleague Jacek Fabrykowski, a mathematician who devoted his
time to looking at the material. A special thanks to my former student (now
working cryptographer), Thomas Zaplachinski, whose invaluable expertise in
the field helped to keep the material current and accurate. A nonspecialist,
Michael Kozielec, assisted greatly in giving me the valuable perspective of the
uninitiated for this project which was highly beneficial in setting the proper
tone for the book. Thanks go to Ken Rosen, the series editor, who always
works diligently to promote the books in the series, and another special thanks
to Bob Stern, my senior editor, who makes the transition from copy to finished
product a seamless task. For specific information, especially on fine-tuning of
details on MULTICS, and related information, thanks go to Brian Kernighan
for providing background data.
Richard Mollin, Calgary
website: http://www.math.ucalgary.ca/˜ramollin/
e-mail: [email protected]