Hardware Implementation of Finite-Field Arithmetic / Edition 1

Hardware Implementation of Finite-Field Arithmetic / Edition 1

by Jean-Pierre Deschamps, José Luis Imaña, Gustavo D. Sutter
     
 

ISBN-10: 0071545816

ISBN-13: 9780071545815

Pub. Date: 02/19/2009

Publisher: McGraw-Hill Professional Publishing

Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC)

Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation,

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Overview

Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC)

Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division.

This comprehensive resource begins with an overview of mathematics, covering algebra, number theory, finite fields, and cryptography. The book then presents algorithms which can be executed and verified with actual input data. Logic schemes and VHDL models are described in such a way that the corresponding circuits can be easily simulated and synthesized. The book concludes with a real-world example of a finite-field application—elliptic-curve cryptography. This is an essential guide for hardware engineers involved in the development of embedded systems.

Get detailed coverage of:

  • Modulo m reduction
  • Modulo m addition, subtraction, multiplication, and exponentiation
  • Operations over GF(p) and GF(pm)
  • Operations over the commutative ringZp[x]/f(x)
  • Operations over the binary field GF(2m) using normal, polynomial, dual, and triangular

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Product Details

ISBN-13:
9780071545815
Publisher:
McGraw-Hill Professional Publishing
Publication date:
02/19/2009
Pages:
360
Product dimensions:
6.00(w) x 9.10(h) x 1.20(d)

Table of Contents

Chapter 1. Mathematical background

Chapter 2. Mod m reduction

Chapter 3. Mod m operations

Chapter 4. Operations over GF(p)

Chapter 5. Operations over Zp [x] / f(x)

Chapter 6. Operations over GF(pn)

Chapter 7. Operations over GF(2m) - Polynomial bases

Chapter 8. Operations over GF(2m) - Normal bases

Chapter 9. Operations over GF(2m) - Other bases

Chapter 10. Elliptic curve cryptography
Appendix A. p = 2(192) - 2(64) - 1

Appendix B. Optical Extension Fields

Appendix C. Binary Fields

Appendix D. Ada versus VHDL

Index

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