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Elliptic Curves And Their Cryptographic Applications
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Book Synopsis Elliptic Curves and Their Applications to Cryptography by : Andreas Enge
Download or read book Elliptic Curves and Their Applications to Cryptography written by Andreas Enge and published by Springer Science & Business Media. This book was released on 1999-08-31 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elliptic Curves by : Lawrence C. Washington
Download or read book Elliptic Curves written by Lawrence C. Washington and published by CRC Press. This book was released on 2008-04-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 application
Download or read book Elliptic Tales written by Avner Ash and published by Princeton University Press. This book was released on 2012 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the latest developments in number theory by looking at the Birch and Swinnerton-Dyer Conjecture.
Book Synopsis Implementing Elliptic Curve Cryptography by : Michael Rosing
Download or read book Implementing Elliptic Curve Cryptography written by Michael Rosing and published by Manning Publications. This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implementing Elliptic Curve Cryptography proceeds step-by- step to explain basic number theory, polynomial mathematics, normal basis mathematics and elliptic curve mathematics. With these in place, applications to cryptography are introduced. The book is filled with C code to illustrate how mathematics is put into a computer, and the last several chapters show how to implement several cryptographic protocols. The most important is a description of P1363, an IEEE draft standard for public key cryptography. The main purpose of Implementing Elliptic Curve Cryptography is to help "crypto engineers" implement functioning, state-of-the- art cryptographic algorithms in the minimum time.
Book Synopsis Guide to Elliptic Curve Cryptography by : Darrel Hankerson
Download or read book Guide to Elliptic Curve Cryptography written by Darrel Hankerson and published by Springer Science & Business Media. This book was released on 2006-06-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic * Distills complex mathematics and algorithms for easy understanding * Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software tools This comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.
Book Synopsis Elliptic Curves in Cryptography by : Ian F. Blake
Download or read book Elliptic Curves in Cryptography written by Ian F. Blake and published by Cambridge University Press. This book was released on 1999-07-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.
Book Synopsis Rational Points on Elliptic Curves by : Joseph H. Silverman
Download or read book Rational Points on Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Book Synopsis Algebraic Curves in Cryptography by : San Ling
Download or read book Algebraic Curves in Cryptography written by San Ling and published by CRC Press. This book was released on 2013-06-13 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 sh
Book Synopsis High Performance Architecture and Grid Computing by : Archana Mantri
Download or read book High Performance Architecture and Grid Computing written by Archana Mantri and published by Springer Science & Business Media. This book was released on 2011-07-05 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereeds proceedings of the International Conference on High Performance Architecture and Grid Computing, HPAGC 2011, held in Chandigarh, India, in July 2011. The 87 revised full papers presented were carefully reviewed and selected from 240 submissions. The papers are organized in topical sections on grid and cloud computing; high performance architecture; information management and network security.
Book Synopsis Handbook of Elliptic and Hyperelliptic Curve Cryptography by : Henri Cohen
Download or read book Handbook of Elliptic and Hyperelliptic Curve Cryptography written by Henri Cohen and published by CRC Press. This book was released on 2005-07-19 with total page 843 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elliptic Curves and Their Applications to Cryptography by : Andreas Enge
Download or read book Elliptic Curves and Their Applications to Cryptography written by Andreas Enge and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Cryptology - Crypto '88 by : Shafi Goldwasser
Download or read book Advances in Cryptology - Crypto '88 written by Shafi Goldwasser and published by . This book was released on 2014-01-15 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modern Cryptography and Elliptic Curves by : Thomas R. Shemanske
Download or read book Modern Cryptography and Elliptic Curves written by Thomas R. Shemanske and published by American Mathematical Soc.. This book was released on 2017-07-31 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bézout's theorem as well as the construction of projective space. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollard's method of factorization, Diffie–Hellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstra's elliptic curve factorization method and ECC. The only real prerequisite for this book is a course on one-variable calculus; other necessary mathematical topics are introduced on-the-fly. Numerous exercises further guide the exploration.
Book Synopsis Mathematics of Public Key Cryptography by : Steven D. Galbraith
Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Book Synopsis Public Key Cryptography - Pkc 2003 by : Yvo Desmedt
Download or read book Public Key Cryptography - Pkc 2003 written by Yvo Desmedt and published by . This book was released on 2014-01-15 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Elliptic Curve Cryptography by : Ian F. Blake
Download or read book Advances in Elliptic Curve Cryptography written by Ian F. Blake and published by Cambridge University Press. This book was released on 2005-04-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.
Author :Josep Domingo-Ferrer Publisher :Springer Science & Business Media ISBN 13 :9780792379539 Total Pages :406 pages Book Rating :4.3/5 (795 download)
Book Synopsis Smart Card Research and Advanced Applications by : Josep Domingo-Ferrer
Download or read book Smart Card Research and Advanced Applications written by Josep Domingo-Ferrer and published by Springer Science & Business Media. This book was released on 2000-09-30 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smart cards or IC cards offer a huge potential for information processing purposes. The portability and processing power of IC cards allow for highly secure conditional access and reliable distributed information processing. IC cards that can perform highly sophisticated cryptographic computations are already available. Their application in the financial services and telecom industries are well known. But the potential of IC cards go well beyond that. Their applicability in mainstream Information Technology and the Networked Economy is limited mainly by our imagination; the information processing power that can be gained by using IC cards remains as yet mostly untapped and is not well understood. Here lies a vast uncovered research area which we are only beginning to assess, and which will have a great impact on the eventual success of the technology. The research challenges range from electrical engineering on the hardware side to tailor-made cryptographic applications on the software side, and their synergies. This volume comprises the proceedings of the Fourth Working Conference on Smart Card Research and Advanced Applications (CARDIS 2000), which was sponsored by the International Federation for Information Processing (IFIP) and held at the Hewlett-Packard Labs in the United Kingdom in September 2000. CARDIS conferences are unique in that they bring together researchers who are active in all aspects of design of IC cards and related devices and environments, thus stimulating synergy between different research communities from both academia and industry. This volume presents the latest advances in smart card research and applications, and will be essential reading for smart card developers, smart card application developers, and computer science researchers involved in computer architecture, computer security, and cryptography.
