Guide to Elliptic Curve Cryptography

  • Darrel Hankerson
  • Scott Vanstone
  • Alfred Menezes

Part of the Springer Professional Computing book series (SPC)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Pages 153-204
  3. Pages 205-256
  4. Back Matter
    Pages 257-311

About this book



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.


*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



-- Security / Cryptography

-- Beginning / Intermediate Level


Crib Elliptic Curve Cryptography Network security Public-key systems Signatur algorithms cryptographic protocol cryptography cryptosystems data security digital signature encryption error-correcting code finite field

Authors and affiliations

  • Darrel Hankerson
    • 1
  • Scott Vanstone
    • 2
  • Alfred Menezes
    • 2
  1. 1.Department of MathematicsAuburn UniversityAuburnUSA
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

Bibliographic information