Finite Fields: Theory and Computation (Hardcover)

Igor Shparlinski

ISBN 10: 0792356624 / ISBN 13: 9780792356622

Editore: Kluwer Academic Publishers, Dordrecht, 1999

Riguardo questo articolo

Hardcover. This is a survey of achievements in the theory and applications of finite fields and in many related areas such as algebraic number theory, theoretical computer science, coding theory and cryptography. Topics treated include polynomial factorization over finite fields, the finding and distribution of irreducible primitive and other special polynomials, constructing special bases of extensions of finite fields, curves and exponential sums, and linear recurrent sequences. Besides a general overview of the area, its results and methods, it suggests a number of interesting research problems of various levels of difficulty. Provides a survey of the achievements in the theory and applications of finite fields and in many related areas such as algebraic number theory, theoretical computer science, coding theory and cryptography. This book includes topics such as polynomial factorization over finite fields and constructing special bases of extensions of finite fields. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780792356622

Dati bibliografici

• Titolo: Finite Fields: Theory and Computation (Hardcover)
• Editore: Kluwer Academic Publishers, Dordrecht
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 0792356624
• ISBN 13: 9780792356622
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in­ clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener­ ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod­ ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.

Recensione

`...the book can yet be highly recommended as encyclopaedia on these topics, in particular because many Russian papers are incorporated which are hardly accessible.'
Monatschafte für Mathematik, 132:1 (2001)