Hardware Implementation of Finite-Field Arithmetic

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Hardware Implementation of Finite-Field Arithmetic

Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. This is an essential guide for hardware engineers involved in the development of embedded systems.

List Price $115.00
Website Price $103.50

Author: Jean-Pierre Deschamps PhD, José Luis Imaña PhD, Gustavo D Sutter PhD
Format: Hardcover
Copyright: 2009
Pages: 360

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Description

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 ring Zp[x]/f(x.
Operations over the binary field GF(2m) using normal, polynomial, dual, and triangular.

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.

About the Authors
Jean-Pierre Deschamps PhD is a professor at the University Rovira i Virgili in Tarragona, Spain.
José Luis Imaña PhD is a professor at Complutense University of Madrid, Spain.
Gustavo D Sutter PhD is a professor at the Autonomous University of Madrid, Spain.

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