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| Author | : Everett W. Howe |
| Publisher | : Springer |
| Total Pages | : 150 |
| Release | : 2017-11-15 |
| Genre | : Mathematics |
| ISBN | : 3319639315 |
Download Algebraic Geometry for Coding Theory and Cryptography Book in PDF, ePub and Kindle
Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference’s goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.
| Author | : Harald Niederreiter |
| Publisher | : Princeton University Press |
| Total Pages | : 272 |
| Release | : 2009-09-21 |
| Genre | : Mathematics |
| ISBN | : 140083130X |
Download Algebraic Geometry in Coding Theory and Cryptography Book in PDF, ePub and Kindle
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books
| Author | : Ruud Pellikaan |
| Publisher | : Cambridge University Press |
| Total Pages | : 612 |
| Release | : 2017-11-02 |
| Genre | : Mathematics |
| ISBN | : 1108547826 |
Download Codes, Cryptology and Curves with Computer Algebra Book in PDF, ePub and Kindle
This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.
| Author | : Arnaldo Garcia |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 212 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 1402053347 |
Download Topics in Geometry, Coding Theory and Cryptography Book in PDF, ePub and Kindle
The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.
| Author | : N.E. Hurt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 368 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 9401702519 |
Download Many Rational Points Book in PDF, ePub and Kindle
This volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators." "The book will be of use to mathematicians, physicists and engineers interested in the mathematical methods of algebraic geometry as they apply to coding theory and cryptography."--Jacket
| Author | : Henning Stichtenoth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : 9783540564898 |
Download Algebraic Function Book in PDF, ePub and Kindle
This book has two objectives. The first is to fill a void in the existing mathematical literature by providing a modern, self-contained and in-depth exposition of the theory of algebraic function fields. Topics include the Riemann-Roch theorem, algebraic extensions of function fields, ramifications theory and differentials. Particular emphasis is placed on function fields over a finite constant field, leading into zeta functions and the Hasse-Weil theorem. Numerous examples illustrate the general theory. Error-correcting codes are in widespread use for the reliable transmission of information. Perhaps the most fascinating of all the ties that link the theory of these codes to mathematics is the construction by V.D. Goppa, of powerful codes using techniques borrowed from algebraic geometry. Algebraic function fields provide the most elementary approach to Goppa's ideas, and the second objective of this book is to provide an introduction to Goppa's algebraic-geometric codes along these lines. The codes, their parameters and links with traditional codes such as classical Goppa, Peed-Solomon and BCH codes are treated at an early stage of the book. Subsequent chapters include a decoding algorithm for these codes as well as a discussion of their subfield subcodes and trace codes. Stichtenoth's book will be very useful to students and researchers in algebraic geometry and coding theory and to computer scientists and engineers interested in information transmission.
| Author | : Stéphane Ballet |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 303 |
| Release | : 2021-07-01 |
| Genre | : Education |
| ISBN | : 1470454262 |
Download Arithmetic, Geometry, Cryptography and Coding Theory Book in PDF, ePub and Kindle
This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10–14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series. Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.
| Author | : J. van Lint |
| Publisher | : Birkhäuser |
| Total Pages | : 82 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034892861 |
Download Introduction to Coding Theory and Algebraic Geometry Book in PDF, ePub and Kindle
These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
| Author | : Edgar Martinez-moro |
| Publisher | : World Scientific |
| Total Pages | : 334 |
| Release | : 2012-12-18 |
| Genre | : Mathematics |
| ISBN | : 9814483826 |
Download Algebraic Geometry Modeling In Information Theory Book in PDF, ePub and Kindle
Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.
| Author | : Gilles Lachaud |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 219 |
| Release | : 2009-06-11 |
| Genre | : Mathematics |
| ISBN | : 0821847163 |
Download Arithmetic, Geometry, Cryptography and Coding Theory Book in PDF, ePub and Kindle
This volume contains the proceedings of the 11th conference on $\mathrm{AGC^{2}T}$, held in Marseille, France in November 2007. There are 12 original research articles covering asymptotic properties of global fields, arithmetic properties of curves and higher dimensional varieties, and applications to codes and cryptography. This volume also contains a survey article on applications of finite fields by J.-P. Serre. $\mathrm{AGC^{2}T}$ conferences take place in Marseille, France every 2 years. These international conferences have been a major event in the area of applied arithmetic geometry for more than 20 years.
