algebraic curves in cryptography discrete mathematics and its applications

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Algebraic Curves In Cryptography

Author : San Ling
ISBN : 9781420079470
Genre : Mathematics
File Size : 52. 67 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.

Algebraic Curves And Finite Fields

Author : Harald Niederreiter
ISBN : 9783110379556
Genre : Mathematics
File Size : 38. 77 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.

Introduction To Coding Theory Second Edition

Author : Jurgen Bierbrauer
ISBN : 9781482299816
Genre : Computers
File Size : 28. 51 MB
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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.

Progress In Cryptology Africacrypt 2014

Author : David Pointcheval
ISBN : 9783319067346
Genre : Computers
File Size : 48. 39 MB
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This book constitutes the refereed proceedings of the 7th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICA CRYPT 2014, held in Marrakesh, Morocco in May 2014. The 26 papers presented together with 1 invited talk were carefully reviewed and selected from 83 submissions. The aim of Africa crypt 2014 is to provide an international forum for practitioners and researchers from industry, academia and government from all over the world for a wide ranging discussion of all forms of cryptography and its applications as follows: Public-Key Cryptography, Hash Functions, Secret-Key Cryptanalysis, Number Theory, Hardware Implementation, Protocols and Lattice-based Cryptography.

Elliptic Curves And Their Applications To Cryptography

Author : Andreas Enge
ISBN : 9781461552079
Genre : Computers
File Size : 82. 99 MB
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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 And Algorithmic Problems In Finite Fields

Author : Igor Shparlinski
ISBN : 9789401118064
Genre : Mathematics
File Size : 67. 35 MB
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Algebraic Geometry And Its Applications

Author : Jean Chaumine
ISBN : 9789812793430
Genre : Electronic books
File Size : 45. 1 MB
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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. Sample Chapter(s). Chapter 1: Fast addition on non-hyperelliptic genus 3 curves (424 KB). Contents: Symmetric Cryptography and Algebraic Curves (F Voloch); Galois Invariant Smoothness Basis (J-M Couveignes & R Lercier); Fuzzy Pairing-Based CL-PKC (M Kiviharju); On the Semiprimitivity of Cyclic Codes (Y Aubry & P Langevin); Decoding of Scroll Codes (G H Hitching & T Johnsen); An Optimal Unramified Tower of Function Fields (K Brander); On the Number of Resilient Boolean Functions (S Mesnager); On Quadratic Extensions of Cyclic Projective Planes (H F Law & P P W Wong); Partitions of Vector Spaces over Finite Fields (Y Zelenyuk); and other papers. Readership: Mathematicians, researchers in mathematics (academic and industry R&D).

Elliptic Curves

Author : Lawrence C. Washington
ISBN : 1420071475
Genre : Mathematics
File Size : 85. 8 MB
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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.

Handbook Of Elliptic And Hyperelliptic Curve Cryptography

Author : Henri Cohen
ISBN : 1420034987
Genre : Mathematics
File Size : 74. 57 MB
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The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.

Finite Fields With Applications To Coding Theory Cryptography And Related Areas

Author : Gary L. Mullen
ISBN : 9783642594359
Genre : Mathematics
File Size : 46. 7 MB
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