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Solutions Manual Applied Algebra

Codes, Ciphers and Discrete Algorithms, Second Edition
2009
Chapman & Hall/CRC (Hersteller)
978-1-4398-2497-9 (ISBN)
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Using mathematical tools from number theory and finite fields, this text presents practical methods for solving problems in data security and data integrity. It covers many algorithms that arise in cryptography and error-control codes. It includes an appendix that reviews prerequisite topics in algebra and number theory.
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents 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








A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook (R), 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. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups.


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


Carol L. Walker is 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.

Colorado State University, Fort Collins, USA Florida Atlantic University, Boca Raton, USA New Mexico State University, Las Cruces, USA Monmouth University, Middletown, New Jersey, USA

Preface


Integers and Computer Algebra


Integers


Computer Algebra vs. Numerical Analysis


Sums and Products


Mathematical Induction


Codes


Binary and Hexadecimal Codes


ASCII Code


Morse Code


Braille


Two-out-of-Five Code


Hollerith Codes


Euclidean Algorithm


The Mod Function


Greatest Common Divisors


Extended Euclidean Algorithm


The Fundamental Theorem of Arithmetic


Modular Arithmetic


Ciphers


Cryptography


Cryptanalysis


Substitution and Permutation Ciphers


Block Ciphers


The Playfair Cipher


Unbreakable Ciphers


Enigma Machine


Error-Control Codes


Weights and Hamming Distance


Bar Codes Based on Two-out-of-Five Code


Other Commercial Codes


Hamming (7, 4) Code


Chinese Remainder Theorem


Systems of Linear Equations Modulo n


Chinese Remainder Theorem


Extended Precision Arithmetic


Greatest Common Divisor of Polynomials


Hilbert Matrix


Theorems of Fermat and Euler


Wilson's Theorem


Powers Modulo n


Fermat's Little Theorem


Rabin's Probabilistic Primality Test


Exponential Ciphers


Euler's Theorem


Public Key Ciphers


The Rivest-Shamir-Adleman Cipher System


Electronic Signatures


A System for Exchanging Messages


Knapsack Ciphers


Digital Signature Standard


Finite Fields


The Galois Field GFp


The Ring GFp[x] of Polynomials


The Galois Field GF4


The Galois Fields GF8 and GF16


The Galois Field GFpn


The Multiplicative Group of GFpn


Random Number Generators


Error-Correcting Codes


BCH Codes


A BCH Decoder


Reed-Solomon Codes


Advanced Encryption Standard


Data Encryption Standard


The Galois Field GF256


The Rijndael Block Cipher


Polynomial Algorithms and Fast Fourier Transforms


Lagrange Interpolation Formula


Kronecker's Algorithm


Neville's Iterated Interpolation Algorithm


Secure Multiparty Protocols


Discrete Fourier Transforms


Fast Fourier Interpolation


Appendix A: Topics in Algebra and Number Theory


Number Theory


Groups


Rings and Polynomials


Fields


Linear Algebra and Matrices


Solutions to Odd Problems


Bibliography


Notation


Algorithms


Figures


Tables


Index

Erscheint lt. Verlag 26.10.2009
Zusatzinfo 43 Tables, black and white
Sprache englisch
Maße 216 x 279 mm
Gewicht 635 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Graphentheorie
Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 1-4398-2497-5 / 1439824975
ISBN-13 978-1-4398-2497-9 / 9781439824979
Zustand Neuware
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