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Codes: An Introduction to Information Communication and Cryptography

Norman L. Biggs (Autor)

Buch | Softcover

274 Seiten

2008
Springer London Ltd (Verlag)
978-1-84800-272-2 (ISBN)

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Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.

Coding and its uses.- Prefix free codes.- Economical coding.- Data compression.- Noisy channels.- The problem of reliable communication.- The noisy coding theorems.- Linear codes.- Algebraic coding theory.- Coding natural languages.- The development of cryptography.- Cryptography in theory and practice.- The RSA cryptosystem.- Cryptography and calculation.- Elliptic curve cryptography.

Erscheint lt. Verlag	25.8.2008
Reihe/Serie	Springer Undergraduate Mathematics Series
Zusatzinfo	36 Illustrations, black and white; X, 274 p. 36 illus.
Verlagsort	England
Sprache	englisch
Maße	178 x 235 mm
Themenwelt	Informatik ► Theorie / Studium ► Kryptologie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-84800-272-6 / 1848002726
ISBN-13	978-1-84800-272-2 / 9781848002722
Zustand	Neuware