algebraic curves in cryptography

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Algebraic Curves And Cryptography

Author : V. Kumar Murty
ISBN : 9780821871607
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File Size : 51. 15 MB
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Algebraic Curves In Cryptography

Author : San Ling
ISBN : 9781420079470
Genre : Mathematics
File Size : 29. 9 MB
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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 sharing, frameproof codes, and broadcast encryption. Suitable for researchers and graduate students in mathematics and computer science, this self-contained book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected topic in cryptography (other than elliptic curve cryptography). The topics covered include secret sharing schemes, authentication codes, frameproof codes, key distribution schemes, broadcast encryption, and sequences. Chapters begin with introductory material before featuring the application of algebraic curves.

Applications Of Algebraic Curves To Cryptography

Author : Seung Kook Park
ISBN : 9780549344209
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File Size : 56. 9 MB
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In this thesis we study two different applications of algebraic curves to cryptography.

Algebraic Curves And Finite Fields

Author : Harald Niederreiter
ISBN : 9783110379556
Genre : Mathematics
File Size : 51. 81 MB
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This book collects the results of the workshops on Applications of Algebraic Curves and Applications of Finite Fields at the RICAM in 2013. These workshops brought together the most prominet researchers in the area of finite fields and their applications around the world, addressing old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

Algebraic Geometry In Coding Theory And Cryptography

Author : Harald Niederreiter
ISBN : 9781400831302
Genre : Mathematics
File Size : 62. 8 MB
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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

Families Of Algebraic Curves With Application In Coding Theory And Cryptography

Author : Maria Petkova
ISBN : OCLC:624534893
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File Size : 26. 91 MB
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Introduction To Plane Algebraic Curves

Author : Ernst Kunz
ISBN : 9780817644437
Genre : Mathematics
File Size : 68. 35 MB
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* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook

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