Springer Professional Computing

By: Darrel Hankerson, Alfred J. Menezes, Scott Vanstone

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Hardcover | 8 January 2004

At a Glance

Hardcover
336 Pages

Dimensions(cm)
24.13 x 17.78 x 1.91

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$279.75

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After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism.

Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application.

Features & Benefits:

* Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems

* Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology

* Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic

* Distills complex mathematics and algorithms for easy understanding

* Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software tools

This comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

Industry Reviews

From the reviews:

"It is the first book to give a comprehensive and careful presentation of all the implementation issues involved with ECC. ... The book contains chapters on implementing finite field arithmetic ... . There is also an extensive chapter on engineering considerations ... . is very clearly written and numerous algorithms are presented in a format suitable for easy implementations. The book will be useful for engineers and computer scientists who want to know about the important issues in implementing ECC." (Steven D. Galbraith, Mathematical Reviews, 2005)

"This book is entirely dedicated to elliptic curve cryptography. It starts - after a short overview - with finite field arithmetic ... . The book is a guide for security professionals and developers ... . It is very carefully written and may serve as a reference book for mathematicians as well." (J. Schoissengeier, Monatshefte fuer Mathematik, Vol. 144 (1), 2005)

"This is a very useful handbook for anybody who is or must be interested in practical elliptic curve cryptography and its applications. ... is presented in a rather non-theoretical way and at a beginner to intermediate level. On the other hand, researchers should find the book useful because of the extensive survey of the related literature (each chapter ends with notes and further references, the bibliography containing almost 500 items)." (EMS Newsletter, September, 2005)

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You Can Find This Book In

Non-Fiction Reference, Information & Interdisciplinary Subjects Interdisciplinary Studies Communication Studies Computing & I.T.Computer Security Data Encryption Computer Science Privacy & Data Protection Research & Information Coding Theory & Cryptology Information theory

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Paperback

Published: 1st December 2010

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List of Algorithms	p. ix
List of Tables	p. xiv
List of Figures	p. xvi
Acronyms	p. xvii
Preface	p. xix
Introduction and Overview	p. 1
Cryptography basics	p. 2
Public-key cryptography	p. 6
RSA systems	p. 6
Discrete logarithm systems	p. 8
Elliptic curve systems	p. 11
Why elliptic curve cryptography?	p. 15
Roadmap	p. 19
Notes and further references	p. 21
Finite Field Arithmetic	p. 25
Introduction to finite fields	p. 25
Prime field arithmetic	p. 29
Addition and subtraction	p. 30
Integer multiplication	p. 31
Integer squaring	p. 34
Reduction	p. 35
Inversion	p. 39
NIST primes	p. 44
Binary field arithmetic	p. 47
Addition	p. 47
Multiplication	p. 48
Polynomial multiplication	p. 48
Polynomial squaring	p. 52
Reduction	p. 53
Inversion and division	p. 57
Optimal extension field arithmetic	p. 62
Addition and subtraction	p. 63
Multiplication and reduction	p. 63
Inversion	p. 67
Notes and further references	p. 69
Elliptic Curve Arithmetic	p. 75
Introduction to elliptic curves	p. 76
Simplified Weierstrass equations	p. 78
Group law	p. 79
Group order	p. 82
Group structure	p. 83
Isomorphism classes	p. 84
Point representation and the group law	p. 86
Projective coordinates	p. 86
The elliptic curve y[superscript 2] = x[superscript 3] + ax + b	p. 89
The elliptic curve y[superscript 2] + xy = x[superscript 3] + ax[superscript 2] + b	p. 93
Point multiplication	p. 95
Unknown point	p. 96
Fixed point	p. 103
Multiple point multiplication	p. 109
Koblitz curves	p. 114
The Frobenius map and the ring Z[tau]	p. 114
Point multiplication	p. 119
Curves with efficiently computable endomorphisms	p. 123
Point multiplication using halving	p. 129
Point halving	p. 130
Performing point halving efficiently	p. 132
Point multiplication	p. 137
Point multiplication costs	p. 141
Notes and further references	p. 147
Cryptographic Protocols	p. 153
The elliptic curve discrete logarithm problem	p. 153
Pohlig-Hellman attack	p. 155
Pollard's rho attack	p. 157
Index-calculus attacks	p. 165
Isomorphism attacks	p. 168
Related problems	p. 171
Domain parameters	p. 172
Domain parameter generation and validation	p. 173
Generating elliptic curves verifiably at random	p. 175
Determining the number of points on an elliptic curve	p. 179
Key pairs	p. 180
Signature schemes	p. 183
ECDSA	p. 184
EC-KCDSA	p. 186
Public-key encryption	p. 188
ECIES	p. 189
PSEC	p. 191
Key establishment	p. 192
Station-to-station	p. 193
ECMQV	p. 195
Notes and further references	p. 196
Implementation Issues	p. 205
Software implementation	p. 206
Integer arithmetic	p. 206
Floating-point arithmetic	p. 209
SIMD and field arithmetic	p. 213
Platform miscellany	p. 215
Timings	p. 219
Hardware implementation	p. 224
Design criteria	p. 226
Field arithmetic processors	p. 229
Secure implementation	p. 238
Power analysis attacks	p. 239
Electromagnetic analysis attacks	p. 244
Error message analysis	p. 244
Fault analysis attacks	p. 248
Timing attacks	p. 250
Notes and further references	p. 250
Sample Parameters	p. 257
Irreducible polynomials	p. 257
Elliptic curves	p. 261
Random elliptic curves over F[subscript p]	p. 261
Random elliptic curves over F[subscript 2 superscript m]	p. 263
Koblitz elliptic curves over F[subscript 2 superscript m]	p. 263
ECC Standards	p. 267
Software Tools	p. 271
General-purpose tools	p. 271
Libraries	p. 273
Bibliography	p. 277
Index	p. 305
Table of Contents provided by Ingram. All Rights Reserved.

Springer Professional Computing

At a Glance

Hardcover

Industry Reviews

Shipping

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Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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