Gröbner Bases, Coding, and Cryptography
Gröbner Bases, Coding, and Cryptography

Author: Massimiliano Sala

Publisher: Springer Science & Business Media

Published: 2009-05-28

Total Pages: 428

ISBN-13: 3540938060

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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.

Gröbner Bases and Applications
Gröbner Bases and Applications

Author: Bruno Buchberger

Publisher: Cambridge University Press

Published: 1998-02-26

Total Pages: 566

ISBN-13: 9780521632980

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Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.

Boolean Gröbner Bases
Boolean Gröbner Bases

Author: Michael Brickenstein

Publisher: Logos Verlag Berlin GmbH

Published: 2010

Total Pages: 158

ISBN-13: 3832525971

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There exist very few concepts in computational algebra which are as central to theory and applications as Grobner bases. This thesis describes theory, algorithms and applications for the special case of Boolean polynomials. These parts form the mathematical foundations of the PolyBoRi framework (developed by the author together with Alexander Dreyer). The PolyBoRi framework has applications spread over a large number of domains ranging from formal verification, computational biology to cryptanalysis and many more. It is emerged to a worldwide audience by the Sage computational algebra system.

Coding and Cryptography
Coding and Cryptography

Author: Øyvind Ytrehus

Publisher: Springer Science & Business Media

Published: 2006-07-06

Total Pages: 452

ISBN-13: 3540354816

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This book constitutes the thoroughly refereed post-proceedings of the International Workshop on Coding and Cryptography, WCC 2005, held in Bergen, Norway, in March 2005. The 33 revised full papers were carefully reviewed and selected during two rounds of review. The papers address all aspects of coding theory, cryptography and related areas, theoretical or applied.

Codes, Cryptology and Curves with Computer Algebra
Codes, Cryptology and Curves with Computer Algebra

Author: Ruud Pellikaan

Publisher: Cambridge University Press

Published: 2017-11-02

Total Pages: 612

ISBN-13: 1108547826

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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.

Codes and Algebraic Curves
Codes and Algebraic Curves

Author: Oliver Pretzel

Publisher: Clarendon Press

Published: 1998-01-08

Total Pages: 209

ISBN-13: 0191589047

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The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is an updated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, and applications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author: Maria Bras-Amorós

Publisher: Springer Science & Business Media

Published: 2009-05-25

Total Pages: 253

ISBN-13: 3642021808

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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.

Public Key Cryptography -- PKC 2012
Public Key Cryptography -- PKC 2012

Author: Marc Fischlin

Publisher: Springer

Published: 2012-05-19

Total Pages: 746

ISBN-13: 364230057X

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This book constitutes the refereed proceedings of the 15th International Conference on Practice and Theory in Public Key Cryptography, PKC 2012, held in Darmstadt, Germany, in May 2012. The 41 papers presented were carefully reviewed and selected from 188 submissions. The book also contains one invited talk. The papers are organized in the following topical sections: homomorphic encryption and LWE, signature schemes, code-based and multivariate crypto, public key encryption: special properties, identity-based encryption, public-key encryption: constructions, secure two-party and multi-party computations, key exchange and secure sessions, public-key encryption: relationships, DL, DDH, and more number theory, and beyond ordinary signature schemes.

Fast Software Encryption
Fast Software Encryption

Author: Anne Canteaut

Publisher: Springer

Published: 2012-09-10

Total Pages: 471

ISBN-13: 3642340474

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This book constitutes the thoroughly refereed post-conference proceedings of the 19th International Workshop on Fast Software Encryption, held in Washington, DC, USA, in March 2012. The 24 revised full papers presented together with 1 invited talk were carefully reviewed and selected from 89 initial submissions. The papers are organized in topical sections on block ciphers, differential cryptanalysis, hash functions, modes of operation, new tools for cryptanalysis, new designs and Keccak.

Algorithmic Cryptanalysis
Algorithmic Cryptanalysis

Author: Antoine Joux

Publisher: CRC Press

Published: 2009-06-15

Total Pages: 516

ISBN-13: 1420070037

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Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a