Codes Cryptology And Curves With Computer Algebra
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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.
Singularities Algebraic Geometry Commutative Algebra And Related Topics
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Author : Gert-Martin Greuel
language : en
Publisher: Springer
Release Date : 2018-09-18
Singularities Algebraic Geometry Commutative Algebra And Related Topics written by Gert-Martin Greuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-18 with Mathematics categories.
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.
Topics In Galois Fields
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Author : Dirk Hachenberger
language : en
Publisher: Springer Nature
Release Date : 2020-09-29
Topics In Galois Fields written by Dirk Hachenberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-29 with Mathematics categories.
This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.
Rational Algebraic Curves
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Author : J. Rafael Sendra
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-10
Rational Algebraic Curves written by J. Rafael Sendra 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 2007-12-10 with Mathematics categories.
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.
Algebra Codes And Cryptology
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Author : Cheikh Thiecoumba Gueye
language : en
Publisher: Springer Nature
Release Date : 2019-11-28
Algebra Codes And Cryptology written by Cheikh Thiecoumba Gueye and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-28 with Computers categories.
This book presents refereed proceedings of the First International Conference on Algebra, Codes and Cryptology, A2C 2019, held in Dakar, Senegal, in December 2019. The 14 full papers were carefully reviewed and selected from 35 submissions. The papers are organized in topical sections on non-associative and non-commutative algebra; code, cryptology and information security.
Modern Computer Algebra
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Author : Joachim von zur Gathen
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-25
Modern Computer Algebra written by Joachim von zur Gathen 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 2013-04-25 with Computers categories.
Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.
Information Security And Privacy
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Author : Yi Mu
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-24
Information Security And Privacy written by Yi Mu 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 2008-06-24 with Business & Economics categories.
This book constitutes the refereed proceedings of the 13th Australasian Conference on Information Security and Privacy, ACISP 2008, held in Wollongong, Australia, in July 2008. The 33 revised full papers presented were carefully reviewed and selected from 111 submissions. The papers cover a range of topics in information security, including authentication, key management, public key cryptography, privacy, anonymity, secure communication, ciphers, network security, elliptic curves, hash functions, and database security.
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
Applied Algebra Algebraic Algorithms And Error Correcting Codes
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Author : Maria Bras-Amorós
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-25
Applied Algebra Algebraic Algorithms And Error Correcting Codes written by Maria Bras-Amorós 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 2009-05-25 with Computers categories.
This book constitutes the refereed proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-18, held in Tarragona, Spain, in June 2009. The 22 revised full papers presented together with 7 extended absstracts were carefully reviewed and selected from 50 submissions. Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.
Finite Fields Theory And Computation
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Author : Igor Shparlinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Finite Fields Theory And Computation written by Igor Shparlinski 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 2013-03-09 with Mathematics categories.
This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.