Guide to Elliptic Curve Cryptography

ISBN-13: 9781441929297 / Angielski / Miękka / 2010 / 312 str.

Darrel Hankerson; Alfred J. Menezes; Scott Vanstone

Opis

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.

Recenzje

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 für 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)

Spis treści

Contents List of Algorithms List of Tables List of Figures Acronyms Preface 1 Introduction and Overview 1.1 Cryptography basics 1.2 Public-key cryptography 1.2.1 RSAsystems 1.2.2 Discrete logarithmsystems 1.2.3 Elliptic curve systems 1.3 Why elliptic curve cryptography? 1.4 Roadmap 1.5 Notes and further references 2 Finite Field Arithmetic 2.1 Introduction to finite fields 2.2 Primefieldarithmetic 2.2.1 Addition and subtraction 2.2.2 Integer multiplication 2.2.3 Integer squaring 2.2.4 Reduction 2.2.5 Inversion 2.2.6 NISTprimes 2.3 Binary field arithmetic 2.3.1 Addition 2.3.2 Multiplication 2.3.3 Polynomial multiplication 2.3.4 Polynomial squaring 2.3.5 Reduction 2.3.6 Inversion and division 2.4 Optimal extension field arithmetic 2.4.1 Addition and subtraction 2.4.2 Multiplication and reduction 2.4.3 Inversion 2.5 Notes andfurther references 3 Elliptic Curve Arithmetic 3.1 Introduction to elliptic curves 3.1.1 Simplified Weierstrass equations 3.1.2 Group law 3.1.3 Group order 3.1.4 Group structure 3.1.5 Isomorphism classes 3.2 Point representation and the group law 3.2.1 Projective coordinates 3.2.2 The elliptic curve y2 = x3 +ax +b 3.2.3 The elliptic curve y2 +xy = x3 +ax2 +b 3.3 Point multiplication 3.3.1 Unknown point 3.3.2 Fixed point 3.3.3 Multiple point multiplication 3.4 Koblitz curves 3.4.1 The Frobenius map and the ring Z[ô] 3.4.2 Point multiplication 3.5 Curves with efficiently computable endomorphisms 3.6 Point multiplication using halving 3.6.1 Point halving 3.6.2 Performing point halving efficiently 3.6.3 Point multiplication 3.7 Point multiplication costs 3.8 Notes andfurther references 4 Cryptographic Protocols 4.1 The elliptic curve discrete logarithm problem 4.1.1 Pohlig-Hellmanattack 4.1.2 Pollard’s rho attack 4.1.3 Index-calculus attacks 4.1.4 Isomorphism attacks 4.1.5 Related problems 4.2 Domain parameters 4.2.1 Domain parameter generation and validation 4.2.2 Generating elliptic curves verifiably at random 4.2.3 Determining the number of points on an elliptic curve 4.3 Keypairs 4.4 Signature schemes 4.4.1 ECDSA 4.4.2 EC-KCDSA 4.5 Public-key encryption 4.5.1 ECIES 4.5.2 PSEC 4.6 Keyestablishment 4.6.1 Station-to-station 4.6.2 ECMQV 4.7 Notes and further references 5 Implementation Issues 5.1 Software implementation 5.1.1 Integer arithmetic 5.1.2 Floating-point arithmetic 5.1.3 SIMD and field arithmetic 5.1.4 Platform miscellany 5.1.5 Timings 5.2 Hardware implementation 5.2.1 Design criteria 5.2.2 Field arithmetic processors 5.3 Secure implementation 5.3.1 Power analysis attacks 5.3.2 Electromagnetic analysis attacks 5.3.3 Error message analysis 5.3.4 Fault analysis attacks 5.3.5 Timing attacks 5.4 Notes and further references A Sample Parameters A.1 Irreducible polynomials A.2 Elliptic curves A.2.1 Random elliptic curves over Fp A.2.2 Random elliptic curves over F2m A.2.3 Koblitz elliptic curves over F2m B ECC Standards C Software Tools C.1 General-purpose tools C.2 Libraries Bibliography Index

O autorze

After 18 years of research and development, elliptic curve cryptography has gained widespread exposure and acceptance in the commercial world. Industry, banking, and government standards have been drafted to facilitate widespread deployment.
This book is the first to provide a comprehensive treatment of the practical aspects of elliptic curve cryptography. It explains the basic mathematics, provides detailed descriptions of state-in-the-art in methods for efficient implementation, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. Also considered are some issues that arise in software and hardware implementation, side-channel attacks and countermeasures, and efficient parameter generation.
Written by professors who have extensive experience studying the security of elliptic curve cryptography, its implementation, and industrial applications, this book is an important resource for security professionals, developers, and implementers.
A broad overview and guide to one of the most widely used cryptosystems in wireless devices and smartcards today. The authors are some of the key researchers and developers of the EEC standards technology. Essential reference for any practitioners or professionals incomputer science, computer engineering, network design, and network/data security.

Blurb

 

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, 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, side-channel attacks and countermeasures, and efficient parameter generation. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge on efficient application.

Features:

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

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

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

*Distills complex mathematics and algorithms for easy understanding, yet total subject integration

*Includes useful literature references in each chapter, as well as a list of algorithms and appendixes on sample parameters, ECC standards, and software tools

This all-embracing and highly focused reference offers a unique overview and strategic viewpoint for one of the most widely used cryptosystems in wireless devices and smart cards today. It is an indispensable resource for any practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

Darrel Hankerson is an industry consultant and author of books on cryptography and data compression.

Alfred Menezes is co-director of the University of Waterloo’s Center for Applied Cryptographic Research, leader of an ECC algorithm standardization committee, and author of books on cryptography and cryptosystems.

Scott Vanstone coauthored an applied cryptography handbook with A. Menezes and is founder of Certicom Corp. (Canada), a leading ECC company.

 

 

 

Key topics:

>> Public-key cryptography

>> Cryptographic protocols

>> Attacks and secure implementation

>> Domain parameters

>> Signature schemes

>> Key establishment

>> ECC standards

>> Finite- and binary-field arithmetic

 

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-- Security / Cryptography

-- Beginning / Intermediate Level