Gröbner Bases, Coding, and Cryptography

Gröbner Bases, Coding, and Cryptography PDF Author: Massimiliano Sala
Publisher: Springer Science & Business Media
ISBN: 3540938060
Category : Mathematics
Languages : en
Pages : 428

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Book 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.

Gröbner Bases, Coding, and Cryptography

Gröbner Bases, Coding, and Cryptography PDF Author: Massimiliano Sala
Publisher: Springer Science & Business Media
ISBN: 3540938060
Category : Mathematics
Languages : en
Pages : 428

Get Book Here

Book 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.

Gröbner Bases and Applications

Gröbner Bases and Applications PDF Author: Bruno Buchberger
Publisher: Cambridge University Press
ISBN: 9780521632980
Category : Mathematics
Languages : en
Pages : 566

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

Codes, Cryptology and Curves with Computer Algebra

Codes, Cryptology and Curves with Computer Algebra PDF Author: Ruud Pellikaan
Publisher: Cambridge University Press
ISBN: 1108547826
Category : Mathematics
Languages : en
Pages : 612

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Book Description
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.

Coding and Cryptography

Coding and Cryptography PDF Author: Øyvind Ytrehus
Publisher: Springer
ISBN: 3540354824
Category : Computers
Languages : en
Pages : 452

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Book Description
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.

Boolean Gröbner Bases

Boolean Gröbner Bases PDF Author: Michael Brickenstein
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832525971
Category : Computers
Languages : en
Pages : 158

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Book Description
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.

Algorithmic Algebraic Combinatorics and Gröbner Bases

Algorithmic Algebraic Combinatorics and Gröbner Bases PDF Author: Mikhail Klin
Publisher: Springer Science & Business Media
ISBN: 3642019609
Category : Mathematics
Languages : en
Pages : 315

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Book Description
This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries. There is special emphasis on algorithmic aspects and the use of the theory of Gröbner bases.

Cryptography and Coding

Cryptography and Coding PDF Author: Jens Groth
Publisher: Springer
ISBN: 331927239X
Category : Computers
Languages : en
Pages : 325

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Book Description
This book constitutes the proceedings of the 15th IMA International Conference on Cryptography and Coding, IMACC 2015, held at Oxford, UK, in December 2015. The 18 papers presented together with 1 invited talk were carefully reviewed and selected from 36 submissions. The scope of the conference was on following topics: authentication, symmetric cryptography, 2-party computation, codes, Boolean functions, information theory, and leakage resilience.

Codes and Algebraic Curves

Codes and Algebraic Curves PDF Author: Oliver Pretzel
Publisher: Clarendon Press
ISBN: 0191589047
Category : Mathematics
Languages : en
Pages : 209

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Book Description
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.

Cryptography and Coding

Cryptography and Coding PDF Author: Steven Galbraith
Publisher: Springer
ISBN: 3540772723
Category : Computers
Languages : en
Pages : 432

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Book Description
This book constitutes the refereed proceedings of the 11th IMA International Conference on Cryptography and Coding, held in Cirencester, UK in December 2007. The 22 revised full papers presented together with two invited contributions were carefully reviewed and selected from 48 submissions. The papers are organized in topical sections on signatures, boolean functions, block cipher cryptanalysis, side channels, linear complexity, public key encryption, curves, and RSA implementation.

Algebraic Aspects of Cryptography

Algebraic Aspects of Cryptography PDF Author: Neal Koblitz
Publisher: Springer Science & Business Media
ISBN: 9783540634461
Category : Computers
Languages : en
Pages : 220

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Book Description
From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews