Algebraic Geometry In Coding Theory And Cryptography

Author by : Harald Niederreiter
Languange : en
Publisher by : Princeton University Press
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Total Read : 51
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Description : 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


Algebraic Geometry For Coding Theory And Cryptography

Author by : Everett W. Howe
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 13
Total Download : 371
File Size : 42,6 Mb
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Description : 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 For Coding Theory And Cryptography

Author by : Everett W. Howe
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 97
Total Download : 503
File Size : 40,7 Mb
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Description : 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.


Topics In Geometry Coding Theory And Cryptography

Author by : Arnaldo Garcia
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 26
Total Download : 458
File Size : 55,6 Mb
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Description : 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.


Algebraic Geometry Modeling In Information Theory

Author by : Edgar Martínez-Moro
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 76
Total Download : 709
File Size : 40,5 Mb
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Description : 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.


Algebraic Geometry In Coding Theory

Author by : Harald Niederreiter
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 88
Total Download : 176
File Size : 41,8 Mb
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Description : "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


Gr Bner Bases Coding And Cryptography

Author by : Massimiliano Sala
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 87
Total Download : 928
File Size : 53,9 Mb
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Description : Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations. This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.


Geometries Codes And Cryptography

Author by : G. Longo
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 46
Total Download : 604
File Size : 49,8 Mb
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Description : 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.


Coding Theory And Cryptology

Author by : Harald Niederreiter
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 29
Total Download : 227
File Size : 48,6 Mb
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Description : 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.


Finite Fields With Applications To Coding Theory Cryptography And Related Areas

Author by : Gary L. Mullen
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 62
Total Download : 809
File Size : 45,9 Mb
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Description : The Sixth International Conference on Finite Fields and Applications, Fq6, held in the city of Oaxaca, Mexico, from May 21-25, 2001, continued a series of biennial international conferences on finite fields. This volume documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.


Many Rational Points

Author by : N.E. Hurt
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 19
Total Download : 171
File Size : 40,9 Mb
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Description : 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.


Arithmetic Geometry And Coding Theory

Author by : Yves Aubry
Languange : en
Publisher by : SMF
Format Available : PDF, ePub, Mobi
Total Read : 82
Total Download : 422
File Size : 50,8 Mb
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Description : In May 2003, two events were held in the CIRM (Marseille-Luminy) devoted to arithmetic, geometry and their applications in coding theory and cryptography: a European school ``Algebraic Geometry and Information Theory'' and the 9th international conference ``Arithmetic, Geometry and Coding Theory''. Some of the courses of the conferences are published in this volume. Topics covered include: Abelian varieties, function fields and curves over finite fields, Galois group of pro-$p$-extensions, Dedekind zeta functions of number fields, numerical semigroups, Waring numbers, bilinear complexity of the multiplication in finite fields and class number problems.


Codes Cryptology And Curves With Computer Algebra

Author by : Ruud Pellikaan
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 82
Total Download : 301
File Size : 40,6 Mb
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Description : Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.


Advances In Algebraic Geometry Codes

Author by : Edgar Martinez-Moro
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 624
File Size : 41,6 Mb
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Description : Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.


Algorithmic Arithmetic Geometry And Coding Theory

Author by : Stéphane Ballet
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 94
Total Download : 921
File Size : 43,8 Mb
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Description : This volume contains the proceedings of the 14th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held June 3-7, 2013, at CIRM, Marseille, France. These international conferences, held every two years, have been a major event in the area of algorithmic and applied arithmetic geometry for more than 20 years. This volume contains 13 original research articles covering geometric error correcting codes, and algorithmic and explicit arithmetic geometry of curves and higher dimensional varieties. Tools used in these articles include classical algebraic geometry of curves, varieties and Jacobians, Suslin homology, Monsky-Washnitzer cohomology, and -functions of modular forms.


Algebraic Function Fields And Codes

Author by : Henning Stichtenoth
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 27
Total Download : 869
File Size : 55,7 Mb
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Description : 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.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Stéphane Ballet
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 81
Total Download : 993
File Size : 54,7 Mb
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Description : 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.


Gr Bner Bases Coding And Cryptography

Author by : Massimiliano Sala
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 79
Total Download : 301
File Size : 55,6 Mb
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Description : Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations. This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.


Gr Bner Bases Coding And Cryptography

Author by : Massimiliano Sala
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 83
Total Download : 933
File Size : 51,9 Mb
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Description : Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations. This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.


Coding Theory And Applications

Author by : Ángela I. Barbero
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 43
Total Download : 203
File Size : 51,5 Mb
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Description : This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017. The 24 full papers presented were carefully reviewed and selected for inclusion in this volume. The papers cover relevant research areas in modern coding theory, including codes and combinatorial structures, algebraic geometric codes, group codes, convolutional codes, network coding, other applications to communications, and applications of coding theory in cryptography.


Concise Encyclopedia Of Coding Theory

Author by : W. Cary Huffman
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 94
Total Download : 157
File Size : 47,9 Mb
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Description : 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


Codes And Rings

Author by : Minjia Shi
Languange : en
Publisher by : Academic Press
Format Available : PDF, ePub, Mobi
Total Read : 17
Total Download : 839
File Size : 48,9 Mb
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Description : Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory. New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area. Consolidates 20+ years of research in one volume, helping researchers save time in the evaluation of disparate literature Discusses duality formulas in the context of Frobenius rings Reviews decomposition of quasi-cyclic codes under ring action Evaluates the ideal and modular structure of skew-cyclic codes Supports applications in data compression, distributed storage, network coding, cryptography and across error-correction


Algebraic Aspects Of Digital Communications

Author by : Tanush Shaska
Languange : en
Publisher by : IOS Press
Format Available : PDF, ePub, Mobi
Total Read : 71
Total Download : 575
File Size : 53,8 Mb
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Description : Developments of the last few decades in digital communications have created a close link between mathematics and areas of computer science and electrical engineering. A collaboration between such areas now seems very natural, due to problems which require deep knowledge and expertise in each area. Algebra and some of its branches, such as algebraic geometry, computational algebra, group theory, etc., have played a special role in such collaboration.


Integrable Systems And Algebraic Geometry

Author by : Ron Donagi
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 14
Total Download : 425
File Size : 40,8 Mb
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Description : Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.


Groups Matrices And Vector Spaces

Author by : James B. Carrell
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 51
Total Download : 394
File Size : 55,6 Mb
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Description : This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.