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© 2014

Algebraic Circuits

Benefits

  • First self-contained reference guide to algebraic circuits

  • Provides the readers with the necessary theoretical background for an easy understanding of algebraic circuits and for their use in practice

  • Written by leading experts in the field

Book

Part of the Intelligent Systems Reference Library book series (ISRL, volume 66)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos
    Pages 1-70
  3. Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos
    Pages 71-120
  4. Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos
    Pages 121-157
  5. Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos
    Pages 159-215
  6. Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos
    Pages 217-270
  7. Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos
    Pages 271-302
  8. Antonio Lloris Ruiz, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos
    Pages 303-316
  9. Back Matter
    Pages 317-394

About this book

Introduction

This book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata, and algebraic circuits, such as finite fields or Galois fields.

The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations, and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs and cellular automata as well as a study of circuits related to Galois fields, including two real cryptographic applications of Galois fields.

Keywords

Basic algebraic circuits Digital circuits Discrete logarithm Elliptic curve cryptosystems Finite fields Galois Fields (GF) Linear feedback shift register Multi-dimensional cellular automata One-dimensional cellular automata Residue number systems

Authors and affiliations

  1. 1.Departamento de Electrónica y Tecnología de ComputadoresUniversidad de GranadaGranadaSpain
  2. 2.Departamento de Electrónica y Tecnología de ComputadoresUniversidad de GranadaGranadaSpain
  3. 3.Departamento de Electrónica y Tecnología de ComputadoresUniversidad de GranadaGranadaSpain
  4. 4.Departamento de Electrónica y Tecnología de ComputadoresUniversidad de GranadaGranadaSpain

Bibliographic information

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Reviews

From the book reviews:

“The book is very dense in the sense that it contains lots of equations and mathematical notations. The more than 100 illustrations and more than 120 tables are therefore very helpful for understanding the subject matter. … I recommend the book to hardware and software designers, as well as to cryptographers, encoders, and engineers in signal processing, who need a good understanding of the mathematical underpinnings when implementing algebraic circuits.” (Klaus Galensa, Computing Reviews, December, 2014)