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| 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 | : Everett W. Howe |
| Publisher | : Springer |
| Total Pages | : 160 |
| 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 | : 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 | : 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 | : 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 | : Ruud Pellikaan |
| Publisher | : Cambridge University Press |
| Total Pages | : 611 |
| Release | : 2017-11-02 |
| Genre | : Computers |
| ISBN | : 0521817110 |
Download Codes, Cryptology and Curves with Computer Algebra Book in PDF, ePub and Kindle
Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.
| Author | : Edgar Martinez-Moro |
| Publisher | : World Scientific |
| Total Pages | : 334 |
| Release | : 2013 |
| Genre | : Computers |
| ISBN | : 9814335754 |
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 | : Harald Niederreiter |
| Publisher | : |
| Total Pages | : |
| Release | : 2008-09-01 |
| Genre | : |
| ISBN | : 9780691102894 |
Download Algebraic Geometry in Coding Theory Book in PDF, ePub and Kindle
"This is a beautifully written volume that gives the necessary background to read the research literature on coding and cryptography based on concepts from curves in algebraic geometries. Both of the authors are outstanding researchers, well known for the clarity and depth of their contributions. This work is a valuable and welcome addition to the literature on coding and cryptography."--Ian F. Blake, University of British Columbia
| Author | : Henning Stichtenoth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 2009-02-11 |
| Genre | : Mathematics |
| ISBN | : 3540768785 |
Download Algebraic Function Fields and Codes Book in PDF, ePub and Kindle
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
| 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.
