algebraic curves in cryptography discrete mathematics and its applications

Download Book Algebraic Curves In Cryptography Discrete Mathematics And Its Applications in PDF format. You can Read Online Algebraic Curves In Cryptography Discrete Mathematics And Its Applications here in PDF, EPUB, Mobi or Docx formats.

Algebraic Curves In Cryptography

Author : San Ling
ISBN : 9781420079470
Genre : Mathematics
File Size : 41. 56 MB
Format : PDF, Mobi
Download : 174
Read : 820

Download Now


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.

Elliptic Curves

Author : Lawrence C. Washington
ISBN : 1420071475
Genre : Mathematics
File Size : 25. 83 MB
Format : PDF, ePub
Download : 773
Read : 941

Download Now


Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition Chapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues A more complete treatment of the Weil and Tate–Lichtenbaum pairings Doud’s analytic method for computing torsion on elliptic curves over Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

Algebraic Aspects Of Cryptography

Author : Neal Koblitz
ISBN : 9783662036426
Genre : Computers
File Size : 50. 43 MB
Format : PDF, ePub
Download : 643
Read : 712

Download Now


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

Introduction To Coding Theory Second Edition

Author : Jurgen Bierbrauer
ISBN : 9781482299816
Genre : Computers
File Size : 33. 96 MB
Format : PDF, ePub, Docs
Download : 339
Read : 268

Download Now


This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.

Algebraic Curves And Finite Fields

Author : Harald Niederreiter
ISBN : 9783110317916
Genre : Mathematics
File Size : 74. 76 MB
Format : PDF, ePub, Docs
Download : 859
Read : 347

Download Now


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.

Mathematics Of Public Key Cryptography

Author : Steven D. Galbraith
ISBN : 9781107013926
Genre : Computers
File Size : 26. 92 MB
Format : PDF, ePub, Mobi
Download : 562
Read : 1322

Download Now


This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Algebraic Geometry And Its Applications

Author : Jean Chaumine
ISBN : 9789812793423
Genre : Mathematics
File Size : 63. 94 MB
Format : PDF, ePub, Docs
Download : 936
Read : 751

Download Now


This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.

Introduction To Cryptography With Open Source Software

Author : Alasdair McAndrew
ISBN : 9781439825716
Genre : Computers
File Size : 46. 34 MB
Format : PDF, ePub, Mobi
Download : 430
Read : 616

Download Now


Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experience by progressing at a gentle pace, keeping mathematics at a manageable level, and including numerous end-of-chapter exercises. Focusing on the cryptosystems themselves rather than the means of breaking them, the book first explores when and how the methods of modern cryptography can be used and misused. It then presents number theory and the algorithms and methods that make up the basis of cryptography today. After a brief review of "classical" cryptography, the book introduces information theory and examines the public-key cryptosystems of RSA and Rabin’s cryptosystem. Other public-key systems studied include the El Gamal cryptosystem, systems based on knapsack problems, and algorithms for creating digital signature schemes. The second half of the text moves on to consider bit-oriented secret-key, or symmetric, systems suitable for encrypting large amounts of data. The author describes block ciphers (including the Data Encryption Standard), cryptographic hash functions, finite fields, the Advanced Encryption Standard, cryptosystems based on elliptical curves, random number generation, and stream ciphers. The book concludes with a look at examples and applications of modern cryptographic systems, such as multi-party computation, zero-knowledge proofs, oblivious transfer, and voting protocols.

Elliptic Curves And Their Applications To Cryptography

Author : Andreas Enge
ISBN : 9781461552079
Genre : Computers
File Size : 80. 97 MB
Format : PDF, Docs
Download : 595
Read : 884

Download Now


Since their invention in the late seventies, public key cryptosystems have become an indispensable asset in establishing private and secure electronic communication, and this need, given the tremendous growth of the Internet, is likely to continue growing. Elliptic curve cryptosystems represent the state of the art for such systems. Elliptic Curves and Their Applications to Cryptography: An Introduction provides a comprehensive and self-contained introduction to elliptic curves and how they are employed to secure public key cryptosystems. Even though the elegant mathematical theory underlying cryptosystems is considerably more involved than for other systems, this text requires the reader to have only an elementary knowledge of basic algebra. The text nevertheless leads to problems at the forefront of current research, featuring chapters on point counting algorithms and security issues. The Adopted unifying approach treats with equal care elliptic curves over fields of even characteristic, which are especially suited for hardware implementations, and curves over fields of odd characteristic, which have traditionally received more attention. Elliptic Curves and Their Applications: An Introduction has been used successfully for teaching advanced undergraduate courses. It will be of greatest interest to mathematicians, computer scientists, and engineers who are curious about elliptic curve cryptography in practice, without losing the beauty of the underlying mathematics.

Computational Number Theory

Author : Abhijit Das
ISBN : 9781482205824
Genre : Computers
File Size : 82. 72 MB
Format : PDF, ePub, Mobi
Download : 578
Read : 1147

Download Now


Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry. Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. A dedicated chapter on the application of number theory in public-key cryptography incorporates recent developments in pairing-based cryptography. With an emphasis on implementation issues, the book uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.

Top Download:

Best Books