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Algebra Codes And Cryptology
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Book Synopsis Algebra, Codes and Cryptology by : Cheikh Thiecoumba Gueye
Download or read book Algebra, Codes and Cryptology written by Cheikh Thiecoumba Gueye and published by Springer Nature. This book was released on 2019-11-28 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.
Book Synopsis Algebra, Codes and Cryptology by : Cheikh Thiecoumba Gueye
Download or read book Algebra, Codes and Cryptology written by Cheikh Thiecoumba Gueye and published by . This book was released on 2019 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Algebra written by Darel W. Hardy and published by CRC Press. This book was released on 2011-08-10 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.
Book Synopsis Coding Theory and Cryptography by : D.C. Hankerson
Download or read book Coding Theory and Cryptography written by D.C. Hankerson and published by CRC Press. This book was released on 2000-08-04 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing data on number theory, encryption schemes, and cyclic codes, this highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an "easy-to-use" manner appropriate for students with only a basic background in mathematics offering revised and updated material on the Berlekamp-Massey decoding algorithm and convolutional codes. Introducing the mathematics as it is needed and providing exercises with solutions, this edition includes an extensive section on cryptography, designed for an introductory course on the subject.
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
Book Synopsis Coding Theory and Cryptography by : David Joyner
Download or read book Coding Theory and Cryptography written by David Joyner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the Conference on Coding Theory, Cryptography, and Number Theory held at the U. S. Naval Academy during October 25-26, 1998. This book concerns elementary and advanced aspects of coding theory and cryptography. The coding theory contributions deal mostly with algebraic coding theory. Some of these papers are expository, whereas others are the result of original research. The emphasis is on geometric Goppa codes (Shokrollahi, Shokranian-Joyner), but there is also a paper on codes arising from combinatorial constructions (Michael). There are both, historical and mathematical papers on cryptography. Several of the contributions on cryptography describe the work done by the British and their allies during World War II to crack the German and Japanese ciphers (Hamer, Hilton, Tutte, Weierud, Urling). Some mathematical aspects of the Enigma rotor machine (Sherman) and more recent research on quantum cryptography (Lomonoco) are described. There are two papers concerned with the RSA cryptosystem and related number-theoretic issues (Wardlaw, Cosgrave).
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.
Book Synopsis Algebraic Coding Theory (Revised Edition) by : Elwyn R Berlekamp
Download or read book Algebraic Coding Theory (Revised Edition) written by Elwyn R Berlekamp and published by World Scientific. This book was released on 2015-03-26 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
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. This book was released on 2008-08-25 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.
Book Synopsis Algebraic and Stochastic Coding Theory by : Dave K. Kythe
Download or read book Algebraic and Stochastic Coding Theory written by Dave K. Kythe and published by CRC Press. This book was released on 2017-07-28 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.
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.
Book Synopsis Cryptology and Error Correction by : Lindsay N. Childs
Download or read book Cryptology and Error Correction written by Lindsay N. Childs and published by Springer. This book was released on 2019-04-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for understanding these methods. The objective is to provide a thorough understanding of RSA, Diffie–Hellman, and Blum–Goldwasser cryptosystems and Hamming and Reed–Solomon error correction: how they are constructed, how they are made to work efficiently, and also how they can be attacked. To reach that level of understanding requires and motivates many ideas found in a first course in abstract algebra—rings, fields, finite abelian groups, basic theory of numbers, computational number theory, homomorphisms, ideals, and cosets. Those who complete this book will have gained a solid mathematical foundation for more specialized applied courses on cryptology or error correction, and should also be well prepared, both in concepts and in motivation, to pursue more advanced study in algebra and number theory. This text is suitable for classroom or online use or for independent study. Aimed at students in mathematics, computer science, and engineering, the prerequisite includes one or two years of a standard calculus sequence. Ideally the reader will also take a concurrent course in linear algebra or elementary matrix theory. A solutions manual for the 400 exercises in the book is available to instructors who adopt the text for their course.
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.
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.
Book Synopsis The Mathematics of Encryption by : Margaret Cozzens
Download or read book The Mathematics of Encryption written by Margaret Cozzens and published by American Mathematical Soc.. This book was released on 2013-09-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.
Book Synopsis Algebraic Geometry Modeling in Information Theory by : Edgar Martinez-Moro
Download or read book Algebraic Geometry Modeling in Information Theory written by Edgar Martinez-Moro and published by World Scientific. This book was released on 2013 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
