Hardware Implementation of Finite-Field Arithmetic

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

Overview

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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(p^m)
• Operations over the commutative ring Z_p[x]/f(x)
  
• Operations over the binary field GF(2^m) using normal, polynomial, dual, and triangular
  

Product Details

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

About the Author

Jean-Pierre Deschamps, Ph.D., is a professor atthe University Rovira i Virgili in Tarragona, Spain.

José Luis Imaña, Ph.D., is a professor at ComplutenseUniversity of Madrid, Spain.

Gustavo D. Sutter, Ph.D., is a professor at theAutonomous University of Madrid, Spain.

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 cryptographyAppendix A. p = 2(192) - 2(64) - 1
Appendix B. Optical Extension Fields
Appendix C. Binary Fields
Appendix D. Ada versus VHDL
Index