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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. While the content has been reworked and improved, this edition continues to cover many algorithms that arise 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, 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 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. Covers topics from algebra, cryptography, and number theory. Includes algorithms that offer common-sense approaches to problems, such as computing large powers. Provides complete coberage on error-correcting codes. Explains the rijndael algorithm to help readers understand the data encryption standard.