Handbook Of Elliptic And Hyperelliptic Curve Cryptography

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Handbook of Elliptic and Hyperelliptic Curve Cryptography

Author : Henri Cohen
Publisher : CRC Press
ISBN 13 : 1420034987
Total Pages : 842 pages
Book Rating : 4.4/5 (2 download)

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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 842 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.

Handbook of Elliptic and Hyperelliptic Curve Cryptography

Author :
Publisher :
ISBN 13 : 9780367801625
Total Pages : 808 pages
Book Rating : 4.8/5 (16 download)

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Book Synopsis Handbook of Elliptic and Hyperelliptic Curve Cryptography by :

Download or read book Handbook of Elliptic and Hyperelliptic Curve Cryptography written by and published by . This book was released on 2006 with total page 808 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.

Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition

Author : Henri Cohen
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781439840009
Total Pages : 1024 pages
Book Rating : 4.8/5 (4 download)

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Book Synopsis Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition by : Henri Cohen

Download or read book Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition written by Henri Cohen and published by Chapman and Hall/CRC. This book was released on 2016-03-26 with total page 1024 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook provides a complete reference on elliptic and hyperelliptic curve cryptography. Addressing every aspect of the field, the book contains all of the background necessary to understand the theory and security of cryptosystems as well as the algorithms that can be used to implement them. This second edition features the latest developments on pairing-based cryptography, new ideas on index-calculus attacks, improved algorithms for genus-2 arithmetic, and a number of other new additions. It also includes many new applications and provides better explanations on some of the more mathematical presentations.

Guide to Elliptic Curve Cryptography

Author : Darrel Hankerson
Publisher : Springer Science & Business Media
ISBN 13 : 0387218467
Total Pages : 312 pages
Book Rating : 4.3/5 (872 download)

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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 312 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.

Elliptic Curves and Their Applications to Cryptography

Author : Andreas Enge
Publisher : Springer Science & Business Media
ISBN 13 : 1461552079
Total Pages : 175 pages
Book Rating : 4.4/5 (615 download)

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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 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.

Elliptic Curves

Author : Lawrence C. Washington
Publisher : CRC Press
ISBN 13 : 1420071475
Total Pages : 533 pages
Book Rating : 4.4/5 (2 download)

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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

Regularity Results for Nonlinear Elliptic Systems and Applications

Author : Alain Bensoussan
Publisher : Springer Science & Business Media
ISBN 13 : 3662129051
Total Pages : 450 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Regularity Results for Nonlinear Elliptic Systems and Applications by : Alain Bensoussan

Download or read book Regularity Results for Nonlinear Elliptic Systems and Applications written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.

Modern Cryptography and Elliptic Curves: A Beginner’s Guide

Author : Thomas R. Shemanske
Publisher : American Mathematical Soc.
ISBN 13 : 1470435829
Total Pages : 252 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Modern Cryptography and Elliptic Curves: A Beginner’s Guide by : Thomas R. Shemanske

Download or read book Modern Cryptography and Elliptic Curves: A Beginner’s Guide written by Thomas R. Shemanske and published by American Mathematical Soc.. This book was released on 2017-07-31 with total page 252 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.

Handbook of Financial Cryptography and Security

Author : Burton Rosenberg
Publisher : CRC Press
ISBN 13 : 1420059823
Total Pages : 631 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Financial Cryptography and Security by : Burton Rosenberg

Download or read book Handbook of Financial Cryptography and Security written by Burton Rosenberg and published by CRC Press. This book was released on 2010-08-02 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Cryptography and Security elucidates the theory and techniques of cryptography and illustrates how to establish and maintain security under the framework of financial cryptography. It applies various cryptographic techniques to auctions, electronic voting, micropayment systems, digital rights, financial portfolios, routing

Algorithmic Cryptanalysis

Author : Antoine Joux
Publisher : CRC Press
ISBN 13 : 1420070037
Total Pages : 516 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Algorithmic Cryptanalysis by : Antoine Joux

Download or read book Algorithmic Cryptanalysis written by Antoine Joux and published by CRC Press. This book was released on 2009-06-15 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a

Cryptanalysis of Number Theoretic Ciphers

Author : Samuel S. Wagstaff, Jr.
Publisher : CRC Press
ISBN 13 : 1351991949
Total Pages : 340 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Cryptanalysis of Number Theoretic Ciphers by : Samuel S. Wagstaff, Jr.

Download or read book Cryptanalysis of Number Theoretic Ciphers written by Samuel S. Wagstaff, Jr. and published by CRC Press. This book was released on 2019-08-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

Pairing-Based Cryptography - Pairing 2009

Author : Hovav Shacham
Publisher : Springer Science & Business Media
ISBN 13 : 3642032974
Total Pages : 275 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Pairing-Based Cryptography - Pairing 2009 by : Hovav Shacham

Download or read book Pairing-Based Cryptography - Pairing 2009 written by Hovav Shacham and published by Springer Science & Business Media. This book was released on 2009-07-20 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Pairing-Based Cryptography, Pairing 2009, held in Palo Alto, CA, USA, in August 2009. The 16 full papers presented were carefully reviewed and selected from 38 submissions. The papers are organized in topical sections on signature security, curves, pairing computation, non-interactive zero-knowledge systems and applications, group signatures, and protocols.

Strongly Elliptic Systems and Boundary Integral Equations

Author : William Charles Hector McLean
Publisher : Cambridge University Press
ISBN 13 : 9780521663755
Total Pages : 376 pages
Book Rating : 4.6/5 (637 download)

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Book Synopsis Strongly Elliptic Systems and Boundary Integral Equations by : William Charles Hector McLean

Download or read book Strongly Elliptic Systems and Boundary Integral Equations written by William Charles Hector McLean and published by Cambridge University Press. This book was released on 2000-01-28 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2000 book provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains.

Finite Automata and Application to Cryptography

Author : Renji Tao
Publisher : Springer Science & Business Media
ISBN 13 : 3540782575
Total Pages : 411 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Finite Automata and Application to Cryptography by : Renji Tao

Download or read book Finite Automata and Application to Cryptography written by Renji Tao and published by Springer Science & Business Media. This book was released on 2009-03-08 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Automata and Application to Cryptography mainly deals with the invertibility theory of finite automata and its application to cryptography. In addition, autonomous finite automata and Latin arrays, which are relative to the canonical form for one-key cryptosystems based on finite automata, are also discussed. Finite automata are regarded as a natural model for ciphers. The Ra Rb transformation method is introduced to deal with the structure problem of such automata; then public key cryptosystems based on finite automata and a canonical form for one-key ciphers implementable by finite automata with bounded-error-propagation and without data expansion are proposed. The book may be used as a reference for computer science and mathematics majors, including seniors and graduate students. Renji Tao is a Professor at the Institute of Software, Chinese Academy of Sciences, Beijing.

Advances in Elliptic Curve Cryptography

Author : Ian F. Blake
Publisher : Cambridge University Press
ISBN 13 : 9781139441223
Total Pages : 308 pages
Book Rating : 4.4/5 (412 download)

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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.

An Introduction to Cryptography

Author : Richard A. Mollin
Publisher : CRC Press
ISBN 13 : 1420011243
Total Pages : 413 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis An Introduction to Cryptography by : Richard A. Mollin

Download or read book An Introduction to Cryptography written by Richard A. Mollin and published by CRC Press. This book was released on 2006-09-18 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field. With numerous additions and restructured material, this edition

Functional Encryption

Author : Khairol Amali Bin Ahmad
Publisher : Springer Nature
ISBN 13 : 3030608905
Total Pages : 311 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Functional Encryption by : Khairol Amali Bin Ahmad

Download or read book Functional Encryption written by Khairol Amali Bin Ahmad and published by Springer Nature. This book was released on 2021-06-12 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides awareness of methods used for functional encryption in the academic and professional communities. The book covers functional encryption algorithms and its modern applications in developing secure systems via entity authentication, message authentication, software security, cyber security, hardware security, Internet of Thing (IoT), cloud security, smart card technology, CAPTCHA, digital signature, and digital watermarking. This book is organized into fifteen chapters; topics include foundations of functional encryption, impact of group theory in cryptosystems, elliptic curve cryptography, XTR algorithm, pairing based cryptography, NTRU algorithms, ring units, cocks IBE schemes, Boneh-Franklin IBE, Sakai-Kasahara IBE, hierarchical identity based encryption, attribute based Encryption, extensions of IBE and related primitives, and digital signatures. Explains the latest functional encryption algorithms in a simple way with examples; Includes applications of functional encryption in information security, application security, and network security; Relevant to academics, research scholars, software developers, etc.