Hardware Implementation of Finite-Field Arithmetic

by Jean-Pierre Deschamps

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(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:	9780071545822
Publisher:	McGraw Hill LLC
Publication date:	01/14/2009
Sold by:	Barnes & Noble
Format:	eBook
Pages:	368
File size:	11 MB
Note:	This product may take a few minutes to download.

About the Author

Jean-Pierre Deschamps (Tarragone, Spain) received an MS degree in electrical engineering from the University of Louvain, Belgium, in 1967, the PhD in computer science from the Autonomous University of Barcelona, Spain, in 1983, and a PhD degree in electrical engineering from the Polytechnic School of Lausanne, Switzerland, in 1984. He is currently a professor at the University Rovira i Virgili, Tarragona, Spain. His research interests include ASIC and FPGA design, digital arithmetic and cryptography. He is the author of seven books and about a hundred international papers.

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