Guide to Elliptic Curve Cryptography
Description
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.
Reviews / Votes
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)
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Content
Before implementing an elliptic curve system, several selections have to be made concerning the finite field, elliptic curve, and cryptographic protocol:
1. a finite field, a representation for the field elements, and algorithms for performing field arithmetic;
2. an elliptic curve, a representation for the elliptic curve points, and algorithms for performing elliptic curve arithmetic; and
3. a protocol, and algorithms for performing protocol arithmetic.
There are many factors that can infiuence the choices made. All of these must be considered simultaneously in order to arrive at the best solution for a particular application. Relevant factors include security considerations, application platform (software or hardware), constraints of the particular computing environment (e.g., processing speed, code size (ROM), memory size (RAM), gate count, power consumption), and constraints of the particular communications environment (e.g., bandwidth, response time).
Not surprisingly, it is difficult, if not impossible, to decide on a single "best" set of choices. For example, the optimal choices for a workstation application can be quite different from the optimal choices for a smart card application. The purpose of this book is to provide security practitioners with a comprehensive account of the various implementation and security considerations for elliptic curve cryptography, so that informed decisions of the most suitable options can be made for particular applications. The remainder of the book is organized as follows.
Chapter 2 gives a brief introduction to finite fields. It then presents algorithms that are well-suited for software implementation of the arithmetic operations in three kinds of finite fields-prime fields, binary fields and optimal extension fields.
Chapter 3 provides a brief introduction to elliptic curves, and presents different methods for representing points and for performing elliptic curve arithmetic. Also considered are techniques for accelerating the arithmetic on Koblitz curves and other elliptic curves admitting efficiently-computable endomorphisms.
Chapter 4 describes elliptic curve protocols for digital signatures, public-key encryption and key establishment, and considers the generation and validation of domain parameters and key pairs. The state-of-the-art in algorithms for solving the elliptic curve discrete logarithm problem are surveyed.
Chapter 5 considers selected engineering aspects of implementing elliptic curve cryptography in software and hardware. Also examined are side-channel attacks where an adversary exploits information leaked by cryptographic devices, including electromagnetic radiation, power consumption, and error messages.
The appendices present some information that may be useful to implementors. Appendix A presents specific examples of elliptic curve domain parameters that are suitable for cryptographic use. Appendix B summarizes the important standards that describe elliptic curve mechanisms. Appendix C lists selected software tools that are available for performing relevant number-theoretic calculations.
