Cryptography in C and C (2nd ed.) [Welschenbach 2013].pdf

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Cryptography
in C and C++
MICHAEL WELSCHENBACH
Translated by DAVID KRAMER
A
press
TM
Cryptography in C and C++
c
Copyright
⃝
2005 by Michael Welschenbach
Translator and Compositor: David Kramer
Editorial Board: Steve Anglin, Dan Appleman, Ewan Buckingham, Gary Cornell,
Tony Davis, Jason Gilmore, Jonathan Hassell, Chris Mills, Dominic Shakeshaft, Jim Sumser
Assistant Publisher: Grace Wong
Copy Manager: Nicole LeClerc
Production Manager: Kari Brooks-Copony
Proofreader: Anne Friedman
TEX Support: Fred Bartlett and Arthur Ogawa
Manufacturing Manager: Tom Debolski
Cover Designer: Kurt Krames
Library of Congress Cataloging-in-Publication Data
Welschenbach, Michael.
[Kryptographie in C und C++. English]
Cryptography in C and C++ / Michael Welschenbach ; translated by David Kramer.–
2nd American ed., rev. and enl.
p. cm.
The first American edition is a translation of the second German edition, which has
been revised and expanded from the first German edition.
Includes bibliographical references and index.
ISBN 1-59059-502-5
1. Computer security. 2. Cryptography. 3. C (Computer program
language) 4. C++ (Computer program language) I. Title.
QA76.9.A25W4313 2005
005.8–dc22
2005002553
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To my family, as always
Contents
Foreword
About the Author
About the Translator
Preface to the Second American Edition
Preface to the First American Edition
Preface to the First German Edition
xiii
xv
xvi
xvii
xix
xxiii
I
Arithmetic and Number Theory in C
1
3
13
19
23
24
33
34
40
45
50
67
81
81
86
101
106
118
1 Introduction
2 Number Formats: The Representation of Large Numbers in C
3 Interface Semantics
4 The Fundamental Operations
4.1 Addition and Subtraction . . . . . . . . . . .
4.2 Multiplication . . . . . . . . . . . . . . . . .
4.2.1 The Grade School Method . . . . . .
4.2.2 Squaring Is Faster . . . . . . . . . . .
4.2.3 Do Things Go Better with Karatsuba?
4.3 Division with Remainder . . . . . . . . . . .
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5 Modular Arithmetic: Calculating with Residue Classes
6 Where All Roads Meet: Modular Exponentiation
6.1 First Approaches . . . . . . . . . . . . . . .
6.2
M
-ary Exponentiation . . . . . . . . . . . .
6.3 Addition Chains and Windows . . . . . . . .
6.4 Montgomery Reduction and Exponentiation
6.5 Cryptographic Application of Exponentiation
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