Error Correcting Codes Finite Geometries And Cryptography

Author : Aiden A. Bruen,David L. Wehlau
Publisher : American Mathematical Soc.
Page : 255 pages
File Size : 43,5 Mb
Release : 2010-09-03
Category : Mathematics
ISBN : 9780821849569

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Error-Correcting Codes, Finite Geometries and Cryptography by Aiden A. Bruen,David L. Wehlau Pdf

This interdisciplinary volume contains papers from both a conference and special session on Error-Control Codes, Information Theory and Applied Cryptography. The conference was held at the Fields Institute in Toronto, On, Canada from December 5-6, 2007, and the special session was held at the Canadian Mathematical Society's winter meeting in London, ON, Canada from December 8-10, 2007. The volume features cutting-edge theoretical results on the Reed-Muller and Reed-Solomon codes, classical linear codes, codes from nets and block designs, LDPC codes, perfect quantum and orthogonal codes, iterative decoding, magnetic storage and digital memory devices, and MIMO channels. There are new contributions on privacy reconciliation, resilient functions, cryptographic hash functions, and new work on quantum coins. Related original work in finite geometries concerns two-weight codes coming from partial spreads, (0, 1) matrices with forbidden configurations, Andre embeddings, and representations of projective spaces in affine planes. Great care has been taken to ensure that high expository standards are met by the papers in this volume. Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interst and of benefit both to the experienced and to newcomers alike.

Author : G. Longo,M. Marchi,A. Sgarro
Publisher : Springer
Page : 230 pages
File Size : 43,7 Mb
Release : 2014-05-04
Category : Computers
ISBN : 9783709128381

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Geometries, Codes and Cryptography by G. Longo,M. Marchi,A. Sgarro Pdf

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 topics as 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.

Author : Simeon Ball
Publisher : Springer Nature
Page : 185 pages
File Size : 43,5 Mb
Release : 2020-05-08
Category : Mathematics
ISBN : 9783030411534

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A Course in Algebraic Error-Correcting Codes by Simeon Ball Pdf

This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

Author : Ruud Pellikaan,Xin-Wen Wu,Stanislav Bulygin,Relinde Jurrius
Publisher : Cambridge University Press
Page : 611 pages
File Size : 40,9 Mb
Release : 2017-11-02
Category : Language Arts & Disciplines
ISBN : 9780521817110

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Codes, Cryptology and Curves with Computer Algebra by Ruud Pellikaan,Xin-Wen Wu,Stanislav Bulygin,Relinde Jurrius Pdf

Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.

Author : Aiden A. Bruen,Mario A. Forcinito,James M. McQuillan
Publisher : John Wiley & Sons
Page : 690 pages
File Size : 43,9 Mb
Release : 2021-07-21
Category : Computers
ISBN : 9781119582427

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Cryptography, Information Theory, and Error-Correction by Aiden A. Bruen,Mario A. Forcinito,James M. McQuillan Pdf

CRYPTOGRAPHY, INFORMATION THEORY, AND ERROR-CORRECTION A rich examination of the technologies supporting secure digital information transfers from respected leaders in the field As technology continues to evolve Cryptography, Information Theory, and Error-Correction: A Handbook for the 21ST Century is an indispensable resource for anyone interested in the secure exchange of financial information. Identity theft, cybercrime, and other security issues have taken center stage as information becomes easier to access. Three disciplines offer solutions to these digital challenges: cryptography, information theory, and error-correction, all of which are addressed in this book. This book is geared toward a broad audience. It is an excellent reference for both graduate and undergraduate students of mathematics, computer science, cybersecurity, and engineering. It is also an authoritative overview for professionals working at financial institutions, law firms, and governments who need up-to-date information to make critical decisions. The book’s discussions will be of interest to those involved in blockchains as well as those working in companies developing and applying security for new products, like self-driving cars. With its reader-friendly style and interdisciplinary emphasis this book serves as both an ideal teaching text and a tool for self-learning for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, and entrepreneurs. Six new chapters cover current topics like Internet of Things security, new identities in information theory, blockchains, cryptocurrency, compression, cloud computing and storage. Increased security and applicable research in elliptic curve cryptography are also featured. The book also: Shares vital, new research in the field of information theory Provides quantum cryptography updates Includes over 350 worked examples and problems for greater understanding of ideas. Cryptography, Information Theory, and Error-Correction guides readers in their understanding of reliable tools that can be used to store or transmit digital information safely.

Author : Jiri Adamek
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 41,8 Mb
Release : 2011-02-14
Category : Computers
ISBN : 9781118031513

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Foundations of Coding by Jiri Adamek Pdf

Although devoted to constructions of good codes for error control, secrecy or data compression, the emphasis is on the first direction. Introduces a number of important classes of error-detecting and error-correcting codes as well as their decoding methods. Background material on modern algebra is presented where required. The role of error-correcting codes in modern cryptography is treated as are data compression and other topics related to information theory. The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.

Author : David R. Kohel,Robert Rolland
Publisher : American Mathematical Soc.
Page : 166 pages
File Size : 46,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849552

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Arithmetic, Geometry, Cryptography, and Coding Theory 2009 by David R. Kohel,Robert Rolland Pdf

This volume contains the proceedings of the 12th conference on Arithmetic, Geometry, cryptography and coding Theory, held in Marseille, France from March 30 to April 3, 2009, as well as the first Geocrypt conference, held in pointe-a-pitre, guadeloupe, from April 27 to may 1, 2009, and the European science Foundation exploratory workshop on curves, coding Theory, and Cryptography, held in Marseille, France from March 25 to 29, 2009. The articles Contained in this volume come from three related symposia organized by the group Arithmetique et Theorie de I' Information in Marseille. The topics cover arithmetic properties of curves and higher dimensional varieties with applications to codes and cryptography.

Author : Harald Niederreiter,Chaoping Xing
Publisher : Princeton University Press
Page : 272 pages
File Size : 42,9 Mb
Release : 2009-09-21
Category : Mathematics
ISBN : 9781400831302

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Algebraic Geometry in Coding Theory and Cryptography by Harald Niederreiter,Chaoping Xing Pdf

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 : Alp Bassa,Alain Couvreur,David Kohel
Publisher : American Mathematical Soc.
Page : 199 pages
File Size : 52,8 Mb
Release : 2017-03-27
Category : Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Finite ground fields
ISBN : 9781470428105

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Arithmetic, Geometry, Cryptography and Coding Theory by Alp Bassa,Alain Couvreur,David Kohel Pdf

This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 537 pages
File Size : 50,9 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9781108715775

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Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Author : Stéphane Ballet,Gaetan Bisson,Irene Bouw
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 54,5 Mb
Release : 2021-07-01
Category : Education
ISBN : 9781470454265

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Arithmetic, Geometry, Cryptography and Coding Theory by Stéphane Ballet,Gaetan Bisson,Irene Bouw Pdf

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 : W. Cary Huffman,Jon-Lark Kim,Patrick Solé
Publisher : CRC Press
Page : 998 pages
File Size : 40,8 Mb
Release : 2021-03-26
Category : Computers
ISBN : 9781351375108

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Concise Encyclopedia of Coding Theory by W. Cary Huffman,Jon-Lark Kim,Patrick Solé Pdf

Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

Author : Michael Huber
Publisher : Now Publishers Inc
Page : 107 pages
File Size : 41,8 Mb
Release : 2010
Category : Computers
ISBN : 9781601983589

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Combinatorial Designs for Authentication and Secrecy Codes by Michael Huber Pdf

Combinatorial Designs for Authentication and Secrecy Codes is a succinct in-depth review and tutorial of a subject that promises to lead to major advances in computer and communication security. This monograph provides a tutorial on combinatorial designs, which gives an overview of the theory. Furthermore, the application of combinatorial designs to authentication and secrecy codes is described in depth. This close relationship of designs with cryptography and information security was first revealed in Shannon's seminal paper on secrecy systems. We bring together in one source foundational and current contributions concerning design-theoretic constructions and characterizations of authentication and secrecy codes.

Author : Ricardo Castaño-Bernard,Yan S. Soibelman,Ilia Zharkov
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 52,6 Mb
Release : 2010
Category : Algebraic varieties
ISBN : 9780821848845

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Mirror Symmetry and Tropical Geometry by Ricardo Castaño-Bernard,Yan S. Soibelman,Ilia Zharkov Pdf

This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. --

Author : Henry Berthold Mann
Publisher : John Wiley & Sons
Page : 268 pages
File Size : 46,8 Mb
Release : 1968
Category : Computers
ISBN : UOM:39015002075367

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Error Correcting Codes by Henry Berthold Mann Pdf