Rational Points on Curves Over Finite Fields

Theory and Applications

Author: Harald Niederreiter,Chaoping Xing

Publisher: Cambridge University Press

ISBN: 9780521665438

Category: Mathematics

Page: 245

View: 571

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Discussion of theory and applications of algebraic curves over finite fields with many rational points.

Finite Fields and Applications

7th International Conference, Fq7, Toulouse, France, May 5-9, 2003, Revised Papers

Author: Gary L. Mullen,Alain Poli

Publisher: Springer Science & Business Media

ISBN: 3540213244

Category: Computers

Page: 261

View: 9501

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This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004. The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.

Algebraic Curves and Finite Fields

Cryptography and Other Applications

Author: Harald Niederreiter,Alina Ostafe,Daniel Panario,Arne Winterhof

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110379554

Category: Mathematics

Page: 251

View: 3882

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Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

Encyclopedia of Statistical Sciences

Author: Samuel Kotz

Publisher: Wiley-Interscience

ISBN: 9780471743767

Category: Mathematics

Page: 680

View: 7324

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Countless professionals and students who use statistics in their work rely on the multi-volume Encyclopedia of Statistical Sciences as a superior and unique source of information on statistical theory, methods, and applications. This new edition (available in both print and on-line versions) is designed to bring the encyclopedia in line with the latest topics and advances made in statistical science over the past decade--in areas such as computer-intensive statistical methodology, genetics, medicine, the environment, and other applications. Written by over 600 world-renowned experts (including the editors), the entries are self-contained and easily understood by readers with a limited statistical background. With the publication of this second edition in 16 printed volumes, the Encyclopedia of Statistical Sciences retains its position as a cutting-edge reference of choice for those working in statistics, biostatistics, quality control, economics, sociology, engineering, probability theory, computer science, biomedicine, psychology, and many other areas. The Encyclopedia of Statistical Sciences is also available as a 16 volume A to Z set. Volume 6: In-L.

Surveys in Combinatorics 2003

Author: C. D. Wensley

Publisher: Cambridge University Press

ISBN: 9780521540124

Category: Mathematics

Page: 378

View: 9905

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The British Combinatorial Conference attracts a large following from the U.K. and international research community. Held at the University of Wales, Bangor, in 2003, the speakers included renowned experts on topics currently attracting significant research interest, as well as less traditional areas such as the combinatorics of protecting digital content. All the contributions are survey papers presenting an overview of the state of the art in a particular area.

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

Author: Anthony Hilton,John Talbot

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

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Elliptic Curves in Cryptography

Author: I. Blake,G. Seroussi,N. Smart

Publisher: Cambridge University Press

ISBN: 9780521653749

Category: Computers

Page: 204

View: 6845

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This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

L-Functions and Galois Representations

Author: David Burns,Kevin Buzzard,Jan Nekovář

Publisher: Cambridge University Press

ISBN: 0521694159

Category: Mathematics

Page: 563

View: 9597

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This collection of survey and research articles brings together topics at the forefront of the theory of L-functions and Galois representations. Highlighting important progress in areas such as the local Langlands programme, automorphic forms and Selmer groups, this timely volume treats some of the most exciting recent developments in the field. Included are survey articles from Khare on Serre's conjecture, Yafaev on the André-Oort conjecture, Emerton on his theory of Jacquet functors, Venjakob on non-commutative Iwasawa theory and Vigneras on mod p representations of GL(2) over p-adic fields. There are also research articles by: Böckle, Buzzard, Cornut and Vatsal, Diamond, Hida, Kurihara and R. Pollack, Kisin, Nekovář, and Bertolini, Darmon and Dasgupta. Presenting the very latest research on L-functions and Galois representations, this volume is indispensable for researchers in algebraic number theory.

Arithmetic and Geometry

Author: Luis Dieulefait,Gerd Faltings,D. R. Heath-Brown,Yuri I. Manin,B. Z. Moroz,Yu. V. Manin,Jean-Pierre Wintenberger

Publisher: Cambridge University Press

ISBN: 1107462541

Category: Mathematics

Page: 550

View: 8581

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The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.

Elliptic Curves

Number Theory and Cryptography

Author: Lawrence C. Washington

Publisher: CRC Press

ISBN: 9780203484029

Category: Mathematics

Page: 440

View: 9112

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Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students. Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired. By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.

O-Minimality and Diophantine Geometry

Author: A. J. Wilkie,G. O. Jones

Publisher: Cambridge University Press

ISBN: 1107462495

Category: Mathematics

Page: 232

View: 7941

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Brings the researcher up to date with recent applications of mathematical logic to number theory.