MTU Library Catalogue

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Applied algebra : codes, ciphers, and discrete algorithms / Darel W. Hardy, Fred Richman and Carol L. Walker.

By: Hardy, Darel W.
Contributor(s): Walker, Carol L, 1935- | Richman, Fred, 1938-.
Material type: materialTypeLabelBookSeries: Discrete mathematics and its applications.Publisher: London : Chapman & Hall, 2009Edition: Second edition.Description: 410 p. : ill. ; 24 cm.ISBN: 9781420071429 ; 1420071424 .Subject(s): Coding theory | Computer security -- MathematicsDDC classification: 003.54
Contents:
Integers and computer algebra -- Codes -- Euclidean algorithm -- Ciphers -- Error-control codes -- Chinese remainder theorem -- Theorems of Fermat and Euler -- Public key ciphers -- Finite fields -- Error-correcting codes -- Advanced encryption standard -- Polynomial algorithms and fast Fourier transforms.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 003.54 (Browse shelf(Opens below)) 1 Available 00114552
General lending MTU Bishopstown Library Store 003.54 (Browse shelf(Opens below)) 1 Available 00113468
Total holds: 0

Enhanced descriptions from Syndetics:

Using mathematical tools from number theory and finite fields,Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Editionpresents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes.

New to the Second Edition

Downloadable resources containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises

Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems.

About the Authors
Darel W. Hardyis Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups.

Fred Richmanis a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics.

Carol L. Walkeris Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.

Bibliography: (pages 395-396) and index.

Integers and computer algebra -- Codes -- Euclidean algorithm -- Ciphers -- Error-control codes -- Chinese remainder theorem -- Theorems of Fermat and Euler -- Public key ciphers -- Finite fields -- Error-correcting codes -- Advanced encryption standard -- Polynomial algorithms and fast Fourier transforms.

Table of contents provided by Syndetics

  • Preface
  • 1 Integers and Computer Algebra (p. 1)
  • 1.1 Integers (p. 1)
  • 1.2 Computer Algebra vs. Numerical Analysis (p. 4)
  • 1.3 Sums and Products (p. 6)
  • 1.4 Mathematical Induction (p. 8)
  • 2 Codes (p. 15)
  • 2.1 Binary and Hexadecimal Codes (p. 15)
  • 2.2 ASCII Code (p. 22)
  • 2.3 Morse Code (p. 24)
  • 2.4 Braille (p. 27)
  • 2.5 Two-out-of-Five Code (p. 32)
  • 2.6 Hollerith Codes (p. 34)
  • 3 Euclidean Algorithm (p. 39)
  • 3.1 The Mod Function (p. 39)
  • 3.2 Greatest Common Divisors (p. 42)
  • 3.3 Extended Euclidean Algorithm (p. 47)
  • 3.4 The Fundamental Theorem of Arithmetic (p. 52)
  • 3.5 Modular Arithmetic (p. 55)
  • 4 Ciphers (p. 61)
  • 4.1 Cryptography (p. 61)
  • 4.2 Cryptanalysis (p. 68)
  • 4.3 Substitution and Permutation Ciphers (p. 75)
  • 4.4 Block Ciphers (p. 82)
  • 4.5 The Playfair Cipher (p. 88)
  • 4.6 Unbreakable Ciphers (p. 92)
  • 4.7 Enigma Machine (p. 95)
  • 5 Error-Control Codes (p. 101)
  • 5.1 Weights and Hamming Distance (p. 101)
  • 5.2 Bar Codes Based on Two-out-of-Five Code (p. 106)
  • 5.3 Other Commercial Codes (p. 112)
  • 5.4 Hamming (7, 4) Code (p. 120)
  • 6 Chinese Remainder Theorem (p. 127)
  • 6.1 Systems of Linear Equations Modulo n (p. 127)
  • 6.2 Chinese Remainder Theorem (p. 132)
  • 6.3 Extended Precision Arithmetic (p. 137)
  • 6.4 Greatest Common Divisor of Polynomials (p. 141)
  • 6.5 Hilbert Matrix (p. 147)
  • 7 Theorems of Fermat and Euler (p. 153)
  • 7.1 Wilson's Theorem (p. 153)
  • 7.2 Powers Modulo n (p. 155)
  • 7.3 Fermat's Little Theorem (p. 158)
  • 7.4 Rabin's Probabilistic Primality Test (p. 163)
  • 7.5 Exponential Ciphers (p. 168)
  • 7.6 Euler's Theorem (p. 171)
  • 8 Public Key Ciphers (p. 177)
  • 8.1 The Rivest-Shamir-Adleman Cipher System (p. 177)
  • 8.2 Electronic Signatures (p. 183)
  • 8.3 A System for Exchanging Messages (p. 185)
  • 8.4 Knapsack Ciphers (p. 190)
  • 8.5 Digital Signature Standard (p. 194)
  • 9 Finite Fields (p. 199)
  • 9.1 The Galois Field GFp (p. 199)
  • 9.2 The Ring GFp[x] of Polynomials (p. 204)
  • 9.3 The Galois Field GF4 (p. 212)
  • 9.4 The Galois Fields GF8 and GF16 (p. 217)
  • 9.5 The Galois Field GFpn (p. 225)
  • 9.6 The Multiplicative Group of GFpn (p. 229)
  • 9.7 Random Number Generators (p. 235)
  • 10 Error-Correcting Codes (p. 241)
  • 10.1 BCH Codes (p. 242)
  • 10.2 A BCH Decoder (p. 249)
  • 10.3 Reed-Solomon Codes (p. 258)
  • 11 Advanced Encryption Standard (p. 261)
  • 11.1 Data Encryption Standard (p. 262)
  • 11.2 The Galois Field GF256 (p. 265)
  • 11.3 The Rijndael Block Cipher (p. 270)
  • 12 Polynomial Algorithms and Fast Fourier Transforms (p. 277)
  • 12.1 Lagrange Interpolation Formula (p. 277)
  • 12.2 Kronecker's Algorithm (p. 282)
  • 12.3 Neville's Iterated Interpolation Algorithm (p. 285)
  • 12.4 Secure Multiparty Protocols (p. 290)
  • 12.5 Discrete Fourier Transforms (p. 292)
  • 12.6 Fast Fourier Interpolation (p. 301)
  • Appendix A Topics in Algebra and Number Theory (p. 307)
  • A.1 Number Theory (p. 307)
  • A.2 Groups (p. 308)
  • A.3 Rings and Polynomials (p. 310)
  • A.4 Fields (p. 311)
  • A.5 Linear Algebra and Matrices (p. 312)
  • Solutions to Odd Problems (p. 317)
  • Bibliography (p. 395)
  • Notation (p. 397)
  • Algorithms (p. 399)
  • Figures (p. 401)
  • Tables (p. 403)
  • Index (p. 405)

Author notes provided by Syndetics

Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University.
Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University.
Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University.