Algebraic Geometry For Coding Theory And Cryptography
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Algebraic Geometry For Coding Theory And Cryptography
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Author : Everett W. Howe
language : en
Publisher: Springer
Release Date : 2017-11-15
Algebraic Geometry For Coding Theory And Cryptography written by Everett W. Howe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.
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.
Algebraic Geometry In Coding Theory And Cryptography
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Author : Harald Niederreiter
language : en
Publisher: Princeton University Press
Release Date : 2009-09-21
Algebraic Geometry In Coding Theory And Cryptography written by Harald Niederreiter and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-21 with Mathematics categories.
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
Topics In Geometry Coding Theory And Cryptography
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Author : Arnaldo Garcia
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-15
Topics In Geometry Coding Theory And Cryptography written by Arnaldo Garcia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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, such as coding theory, sphere packings and lattices, sequence design, and cryptography. The use of function fields often led to better results than those of classical approaches. This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance. The topics focus on material which has not yet been presented in other books or survey articles. Wherever applications are pointed out, a special effort has been made to present some background concerning their use.
Algebraic Geometry In Coding Theory
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Author : Harald Niederreiter
language : en
Publisher:
Release Date : 2008-09-01
Algebraic Geometry In Coding Theory written by Harald Niederreiter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-01 with categories.
"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
Algebraic Geometry Modeling In Information Theory
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Author : Edgar Martinez-moro
language : en
Publisher: World Scientific
Release Date : 2012-12-18
Algebraic Geometry Modeling In Information Theory written by Edgar Martinez-moro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-18 with Mathematics categories.
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.
Coding Theory And Cryptology
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Author : Harald Niederreiter
language : en
Publisher: World Scientific
Release Date : 2002
Coding Theory And Cryptology written by Harald Niederreiter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security.
Codes Cryptology And Curves With Computer Algebra
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Author : Ruud Pellikaan
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-02
Codes Cryptology And Curves With Computer Algebra written by Ruud Pellikaan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-02 with Computers categories.
Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.
Arithmetic Geometry And Coding Theory
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Author : R. Pellikaan
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-20
Arithmetic Geometry And Coding Theory written by R. Pellikaan and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-20 with Mathematics categories.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Geometries Codes And Cryptography
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Author : G. Longo
language : en
Publisher: Springer
Release Date : 2014-05-04
Geometries Codes And Cryptography written by G. Longo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Computers categories.
The general problem studied by information theory is the reliable transmission of information through unreliable channels. Channels can be unreliable either because they are disturbed by noise or because unauthorized receivers intercept the information transmitted. In the first case, the theory of error-control codes provides techniques for correcting at least part of the errors caused by noise. In the second case cryptography offers the most suitable methods for coping with the many problems linked with secrecy and authentication. Now, both error-control and cryptography schemes can be studied, to a large extent, by suitable geometric models, belonging to the important field of finite geometries. This book provides an update survey of the state of the art of finite geometries and their applications to channel coding against noise and deliberate tampering. The book is divided into two sections, "Geometries and Codes" and "Geometries and Cryptography". The first part covers such topicsas Galois geometries, Steiner systems, Circle geometry and applications to algebraic coding theory. The second part deals with unconditional secrecy and authentication, geometric threshold schemes and applications of finite geometry to cryptography. This volume recommends itself to engineers dealing with communication problems, to mathematicians and to research workers in the fields of algebraic coding theory, cryptography and information theory.
Algebraic Function Fields And Codes
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Author : Henning Stichtenoth
language : en
Publisher: Springer
Release Date : 2009-08-29
Algebraic Function Fields And Codes written by Henning Stichtenoth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Mathematics categories.
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.