Codes Cryptology And Curves With Computer Algebra

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Codes, Cryptology and Curves with Computer Algebra

Author : Ruud Pellikaan
Publisher : Cambridge University Press
ISBN 13 : 1108547826
Total Pages : 612 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Codes, Cryptology and Curves with Computer Algebra by : Ruud Pellikaan

Download or read book Codes, Cryptology and Curves with Computer Algebra written by Ruud Pellikaan and published by Cambridge University Press. This book was released on 2017-11-02 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Geometry in Coding Theory and Cryptography

Author : Harald Niederreiter
Publisher : Princeton University Press
ISBN 13 : 140083130X
Total Pages : 272 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Algebraic Geometry in Coding Theory and Cryptography by : Harald Niederreiter

Download or read book Algebraic Geometry in Coding Theory and Cryptography written by Harald Niederreiter and published by Princeton University Press. This book was released on 2009-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Arnaldo Garcia
Publisher : Springer Science & Business Media
ISBN 13 : 1402053347
Total Pages : 212 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Topics in Geometry, Coding Theory and Cryptography by : Arnaldo Garcia

Download or read book Topics in Geometry, Coding Theory and Cryptography written by Arnaldo Garcia and published by Springer Science & Business Media. This book was released on 2006-11-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 for Coding Theory and Cryptography

Author : Everett W. Howe
Publisher : Springer
ISBN 13 : 3319639315
Total Pages : 160 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Algebraic Geometry for Coding Theory and Cryptography by : Everett W. Howe

Download or read book Algebraic Geometry for Coding Theory and Cryptography written by Everett W. Howe and published by Springer. This book was released on 2017-11-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Curves in Cryptography

Author : San Ling
Publisher : CRC Press
ISBN 13 : 1420079476
Total Pages : 340 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Algebraic Curves in Cryptography by : San Ling

Download or read book Algebraic Curves in Cryptography written by San Ling and published by CRC Press. This book was released on 2013-06-13 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sh

Coding Theory, Cryptography and Related Areas

Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642571891
Total Pages : 269 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Coding Theory, Cryptography and Related Areas by : Johannes Buchmann

Download or read book Coding Theory, Cryptography and Related Areas written by Johannes Buchmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects. The book will be useful to students, researchers, professionals, and tutors interested in this area of research.

Elementary Number Theory, Cryptography and Codes

Author : M. Welleda Baldoni
Publisher : Springer Science & Business Media
ISBN 13 : 3540692002
Total Pages : 530 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Elementary Number Theory, Cryptography and Codes by : M. Welleda Baldoni

Download or read book Elementary Number Theory, Cryptography and Codes written by M. Welleda Baldoni and published by Springer Science & Business Media. This book was released on 2008-11-28 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.

Gröbner Bases, Coding, and Cryptography

Author : Massimiliano Sala
Publisher : Springer Science & Business Media
ISBN 13 : 3540938060
Total Pages : 428 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Gröbner Bases, Coding, and Cryptography by : Massimiliano Sala

Download or read book Gröbner Bases, Coding, and Cryptography written by Massimiliano Sala and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Codes: An Introduction to Information Communication and Cryptography

Author : Norman L. Biggs
Publisher : Springer Science & Business Media
ISBN 13 : 1848002734
Total Pages : 274 pages
Book Rating : 4.8/5 (48 download)

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Book Synopsis Codes: An Introduction to Information Communication and Cryptography by : Norman L. Biggs

Download or read book Codes: An Introduction to Information Communication and Cryptography written by Norman L. Biggs and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.

Codes on Algebraic Curves

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
ISBN 13 : 1461547857
Total Pages : 352 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Codes on Algebraic Curves by : Serguei A. Stepanov

Download or read book Codes on Algebraic Curves written by Serguei A. Stepanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author : Marc Fossorier
Publisher : Springer
ISBN 13 : 3540467963
Total Pages : 516 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Marc Fossorier

Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Marc Fossorier and published by Springer. This book was released on 2003-07-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999. The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.

Making, Breaking Codes

Author : Paul B. Garrett
Publisher : Pearson
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Making, Breaking Codes by : Paul B. Garrett

Download or read book Making, Breaking Codes written by Paul B. Garrett and published by Pearson. This book was released on 2001 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book explains the basic issues of classical and modern cryptography, and provides a self contained essential mathematical background in number theory, abstract algebra, and probability--with surveys of relevant parts of complexity theory and other things. A user-friendly, down-to-earth tone presents concretely motivated introductions to these topics. More detailed chapter topics include simple ciphers; applying ideas from probability; substitutions, transpositions, permutations; modern symmetric ciphers; the integers; prime numbers; powers and roots modulo primes; powers and roots for composite moduli; weakly multiplicative functions; quadratic symbols, quadratic reciprocity; pseudoprimes; groups; sketches of protocols; rings, fields, polynomials; cyclotomic polynomials, primitive roots; pseudo-random number generators; proofs concerning pseudoprimality; factorization attacks finite fields; and elliptic curves. For personnel in computer security, system administration, and information systems.

Algebraic Geometric Codes: Basic Notions

Author : Michael Tsfasman
Publisher : American Mathematical Society
ISBN 13 : 1470470071
Total Pages : 338 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometric Codes: Basic Notions by : Michael Tsfasman

Download or read book Algebraic Geometric Codes: Basic Notions written by Michael Tsfasman and published by American Mathematical Society. This book was released on 2022-04-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.

Coding Theory And Cryptology

Author : Harald Niederreiter
Publisher : World Scientific
ISBN 13 : 981448766X
Total Pages : 460 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Coding Theory And Cryptology by : Harald Niederreiter

Download or read book Coding Theory And Cryptology written by Harald Niederreiter and published by World Scientific. This book was released on 2002-12-03 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Rational Algebraic Curves

Author : J. Rafael Sendra
Publisher : Springer Science & Business Media
ISBN 13 : 3540737251
Total Pages : 273 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Rational Algebraic Curves by : J. Rafael Sendra

Download or read book Rational Algebraic Curves written by J. Rafael Sendra and published by Springer Science & Business Media. This book was released on 2007-12-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

Algebraic Geometry Codes: Advanced Chapters

Author : Michael Tsfasman
Publisher : American Mathematical Soc.
ISBN 13 : 1470448653
Total Pages : 453 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometry Codes: Advanced Chapters by : Michael Tsfasman

Download or read book Algebraic Geometry Codes: Advanced Chapters written by Michael Tsfasman and published by American Mathematical Soc.. This book was released on 2019-07-02 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to local_libraryBook Catalogseveral domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.

Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Author : Gert-Martin Greuel
Publisher : Springer
ISBN 13 : 3319968270
Total Pages : 604 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics by : Gert-Martin Greuel

Download or read book Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics written by Gert-Martin Greuel and published by Springer. This book was released on 2018-09-18 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.