Description
Taylor & Francis Ltd Applied Algebracodes Ciphers And Discrete Algorithms Second Edition 2009 Edition by Darel W. Hardy, Fred Richman
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 EditionA 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 systemNew appendix that reviews prerequisite topics in algebra and number theoryDouble the number of exercisesInstead 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 AuthorsDarel 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. PrefaceIntegers and Computer AlgebraIntegers Computer Algebra vs. Numerical Analysis Sums and Products Mathematical InductionCodesBinary and Hexadecimal Codes ASCII Code Morse Code Braille Two-out-of-Five Code Hollerith CodesEuclidean AlgorithmThe Mod Function Greatest Common Divisors Extended Euclidean Algorithm The Fundamental Theorem of Arithmetic Modular ArithmeticCiphersCryptography Cryptanalysis Substitution and Permutation Ciphers Block Ciphers The Playfair Cipher Unbreakable Ciphers Enigma MachineError-Control CodesWeights and Hamming Distance Bar Codes Based on Two-out-of-Five CodeOther Commercial Codes Hamming (7, 4) CodeChinese Remainder TheoremSystems of Linear Equations Modulo n Chinese Remainder Theorem Extended Precision Arithmetic Greatest Common Divisor of Polynomials Hilbert MatrixTheorems of Fermat and EulerWilson's Theorem Powers Modulo n Fermat's Little Theorem Rabin's Probabilistic Primality Test Exponential Ciphers Euler's TheoremPublic Key CiphersThe Rivest-Shamir-Adleman Cipher System Electronic Signatures A System for Exchanging Messages Knapsack Ciphers Digital Signature StandardFinite FieldsThe 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 GeneratorsError-Correcting CodesBCH Codes A BCH Decoder Reed-Solomon CodesAdvanced Encryption StandardData Encryption Standard The Galois Field GF256 The Rijndael Block CipherPolynomial Algorithms and Fast Fourier TransformsLagrange Interpolation Formula Kronecker's Algorithm Neville's Iterated Interpolation Algorithm Secure Multiparty Protocols Discrete Fourier Transforms Fast Fourier InterpolationAppendix A: Topics in Algebra and Number Theory Number Theory Groups Rings and Polynomials Fields Linear Algebra and MatricesSolutions to Odd ProblemsBibliography Notation Algorithms Figures Tables Index