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Applied algebra. Codes, ciphers and discrete algorithms. With CD-ROM. 2nd ed. (English) Zbl 1158.94002

Discrete Mathematics and its Applications. Boca Raton, FL: CRC Press (ISBN 978-1-4200-7142-9/hbk). x, 410 p. (2009).
A feature, common to some recent books, is to present the two topics of Cryptography and Error-Correcting Codes together with a certain amount of other algebraic and arithmetic materials.
The present title, “designed for a course in applied algebra for juniors and seniors majoring in mathematics and computer sciences”, follows these steps and seeks to provide an introduction to those two main topics but inserting additional chapters covering the necessary mathematical tools.
The book is divided in 12 Chapters and a final Appendix collecting definitions and basic results on Algebra and Number Theory. Chapters 1, 3, 6 and 7 cover the Elementary Number Theory’s tools while Chapter 9 gives an introduction on Finite Fields and Chapter 12 is devoted to Polynomial Algorithms and Fast Fourier Transforms. Chapter 2 discusses methods to represent the information (ASCII, Morse, Braille, etc.). Chapters 4 (Ciphers), 8 (Public key) and 11 (AES) cover the topic of Cryptography while Chapters 5 and 10 deal with Error-Correcting Codes.
The book is clearly written and quite detailed and with many examples, figures and tables included through the text. A list of problems is provided at the end of each Section (with solutions to the odd ones at the end of the book).
This second edition (the first appeared in 2003, cf. Zbl 1156.94300) includes a CD-Rom with an interactive version powered by the software package Scientific Notebook.

MSC:

94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
11Axx Elementary number theory
94A60 Cryptography
14G50 Applications to coding theory and cryptography of arithmetic geometry
94Bxx Theory of error-correcting codes and error-detecting codes
12E20 Finite fields (field-theoretic aspects)

Citations:

Zbl 1156.94300
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