Guide To Elliptic Curve Cryptography

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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.

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.

Random Curves

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 3540740783
Total Pages : 393 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Random Curves by : Neal Koblitz

Download or read book Random Curves written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2009-05-03 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neal Koblitz is a co-inventor of one of the two most popular forms of encryption and digital signature, and his autobiographical memoirs are collected in this volume. Besides his own personal career in mathematics and cryptography, Koblitz details his travels to the Soviet Union, Latin America, Vietnam and elsewhere; political activism; and academic controversies relating to math education, the C. P. Snow "two-culture" problem, and mistreatment of women in academia. These engaging stories fully capture the experiences of a student and later a scientist caught up in the tumultuous events of his generation.

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

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.

Guide to Pairing-Based Cryptography

Author : Nadia El Mrabet
Publisher : CRC Press
ISBN 13 : 1498729517
Total Pages : 410 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Guide to Pairing-Based Cryptography by : Nadia El Mrabet

Download or read book Guide to Pairing-Based Cryptography written by Nadia El Mrabet and published by CRC Press. This book was released on 2017-01-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes. As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes. Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography.

Serious Cryptography

Author : Jean-Philippe Aumasson
Publisher : No Starch Press
ISBN 13 : 1593278268
Total Pages : 313 pages
Book Rating : 4.5/5 (932 download)

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Book Synopsis Serious Cryptography by : Jean-Philippe Aumasson

Download or read book Serious Cryptography written by Jean-Philippe Aumasson and published by No Starch Press. This book was released on 2017-11-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical guide to modern encryption breaks down the fundamental mathematical concepts at the heart of cryptography without shying away from meaty discussions of how they work. You’ll learn about authenticated encryption, secure randomness, hash functions, block ciphers, and public-key techniques such as RSA and elliptic curve cryptography. You’ll also learn: - Key concepts in cryptography, such as computational security, attacker models, and forward secrecy - The strengths and limitations of the TLS protocol behind HTTPS secure websites - Quantum computation and post-quantum cryptography - About various vulnerabilities by examining numerous code examples and use cases - How to choose the best algorithm or protocol and ask vendors the right questions Each chapter includes a discussion of common implementation mistakes using real-world examples and details what could go wrong and how to avoid these pitfalls. Whether you’re a seasoned practitioner or a beginner looking to dive into the field, Serious Cryptography will provide a complete survey of modern encryption and its applications.

Implementing Elliptic Curve Cryptography

Author : Michael Rosing
Publisher : Manning Publications
ISBN 13 : 9781884777691
Total Pages : 0 pages
Book Rating : 4.7/5 (776 download)

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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.

Elliptic Curves in Cryptography

Author : Ian F. Blake
Publisher : Cambridge University Press
ISBN 13 : 9780521653749
Total Pages : 228 pages
Book Rating : 4.6/5 (537 download)

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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 explains the mathematics behind practical implementations of elliptic curve systems.

Mathematics of Public Key Cryptography

Author : Steven D. Galbraith
Publisher : Cambridge University Press
ISBN 13 : 1107013925
Total Pages : 631 pages
Book Rating : 4.1/5 (7 download)

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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.

IoT Security

Author : Madhusanka Liyanage
Publisher : John Wiley & Sons
ISBN 13 : 1119527945
Total Pages : 327 pages
Book Rating : 4.1/5 (195 download)

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Book Synopsis IoT Security by : Madhusanka Liyanage

Download or read book IoT Security written by Madhusanka Liyanage and published by John Wiley & Sons. This book was released on 2019-12-24 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date guide to an overview of authentication in the Internet of Things (IoT) The Internet of things (IoT) is the network of the countless physical devices that have the possibility to connect and exchange data. Among the various security requirements, authentication to the IoT is the first step to prevent the impact of attackers. IoT Security offers an important guide into the development of the many authentication mechanisms that provide IoT authentication at various levels such as user level, device level and network level. The book covers a wide range of topics including an overview of IoT and addresses in detail the security challenges at every layer by considering both the technologies and the architecture used. The authors—noted experts on the topic—provide solutions for remediation of compromised security, as well as methods for risk mitigation, and offer suggestions for prevention and improvement. In addition, IoT Security offers a variety of illustrative use cases. This important book: Offers an authoritative reference designed for use by all IoT stakeholders Includes information for securing devices at the user, device, and network levels Contains a classification of existing vulnerabilities Written by an international group of experts on the topic Provides a guide to the most current information available on IoT security Written for network operators, cloud operators, IoT device manufacturers, IoT device users, wireless users, IoT standardization organizations, and security solution developers, IoT Security is an essential guide that contains information on security features, including underlying networks, architectures, and security requirements.

Handbook of Information and Communication Security

Author : Peter Stavroulakis
Publisher : Springer Science & Business Media
ISBN 13 : 3642041175
Total Pages : 867 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Handbook of Information and Communication Security by : Peter Stavroulakis

Download or read book Handbook of Information and Communication Security written by Peter Stavroulakis and published by Springer Science & Business Media. This book was released on 2010-02-23 with total page 867 pages. Available in PDF, EPUB and Kindle. Book excerpt: At its core, information security deals with the secure and accurate transfer of information. While information security has long been important, it was, perhaps, brought more clearly into mainstream focus with the so-called “Y2K” issue. Te Y2K scare was the fear that c- puter networks and the systems that are controlled or operated by sofware would fail with the turn of the millennium, since their clocks could lose synchronization by not recognizing a number (instruction) with three zeros. A positive outcome of this scare was the creation of several Computer Emergency Response Teams (CERTs) around the world that now work - operatively to exchange expertise and information, and to coordinate in case major problems should arise in the modern IT environment. Te terrorist attacks of 11 September 2001 raised security concerns to a new level. Te - ternational community responded on at least two fronts; one front being the transfer of reliable information via secure networks and the other being the collection of information about - tential terrorists. As a sign of this new emphasis on security, since 2001, all major academic publishers have started technical journals focused on security, and every major communi- tions conference (for example, Globecom and ICC) has organized workshops and sessions on security issues. In addition, the IEEE has created a technical committee on Communication and Information Security. Te ?rst editor was intimately involved with security for the Athens Olympic Games of 2004.

An Introduction to Mathematical Cryptography

Author : Jeffrey Hoffstein
Publisher : Springer
ISBN 13 : 1493917110
Total Pages : 538 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis An Introduction to Mathematical Cryptography by : Jeffrey Hoffstein

Download or read book An Introduction to Mathematical Cryptography written by Jeffrey Hoffstein and published by Springer. This book was released on 2014-09-11 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

Cryptography and Public Key Infrastructure on the Internet

Author : Klaus Schmeh
Publisher : John Wiley & Sons
ISBN 13 : 0470862483
Total Pages : 488 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Cryptography and Public Key Infrastructure on the Internet by : Klaus Schmeh

Download or read book Cryptography and Public Key Infrastructure on the Internet written by Klaus Schmeh and published by John Wiley & Sons. This book was released on 2006-01-04 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical guide to Cryptography and its use in the Internet and other communication networks. This overview takes the reader through basic issues and on to more advanced concepts, to cover all levels of interest. Coverage includes all key mathematical concepts, standardisation, authentication, elliptic curve cryptography, and algorithm modes and protocols (including SSL, TLS, IPSec, SMIME, & PGP protocols). * Details what the risks on the internet are and how cryptography can help * Includes a chapter on interception which is unique amongst competing books in this field * Explains Public Key Infrastructures (PKIs) - currently the most important issue when using cryptography in a large organisation * Includes up-to-date referencing of people, organisations, books and Web sites and the latest information about recent acts and standards affecting encryption practice * Tackles the practical issues such as the difference between SSL and IPSec, which companies are active on the market and where to get further information

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.

Group Theoretic Cryptography

Author : Maria Isabel Gonzalez Vasco
Publisher : CRC Press
ISBN 13 : 1584888377
Total Pages : 244 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Group Theoretic Cryptography by : Maria Isabel Gonzalez Vasco

Download or read book Group Theoretic Cryptography written by Maria Isabel Gonzalez Vasco and published by CRC Press. This book was released on 2015-04-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory appears to be a promising source of hard computational problems for deploying new cryptographic constructions. This reference focuses on the specifics of using groups, including in particular non-Abelian groups, in the field of cryptography. It provides an introduction to cryptography with emphasis on the group theoretic perspective, making it one of the first books to use this approach. The authors provide the needed cryptographic and group theoretic concepts, full proofs of essential theorems, and formal security evaluations of the cryptographic schemes presented. They also provide references for further reading and exercises at the end of each chapter.

A Classical Introduction to Cryptography

Author : Serge Vaudenay
Publisher : Springer Science & Business Media
ISBN 13 : 9780387254647
Total Pages : 370 pages
Book Rating : 4.2/5 (546 download)

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Book Synopsis A Classical Introduction to Cryptography by : Serge Vaudenay

Download or read book A Classical Introduction to Cryptography written by Serge Vaudenay and published by Springer Science & Business Media. This book was released on 2005-09-16 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Classical Introduction to Cryptography: Applications for Communications Security introduces fundamentals of information and communication security by providing appropriate mathematical concepts to prove or break the security of cryptographic schemes. This advanced-level textbook covers conventional cryptographic primitives and cryptanalysis of these primitives; basic algebra and number theory for cryptologists; public key cryptography and cryptanalysis of these schemes; and other cryptographic protocols, e.g. secret sharing, zero-knowledge proofs and undeniable signature schemes. A Classical Introduction to Cryptography: Applications for Communications Security is designed for upper-level undergraduate and graduate-level students in computer science. This book is also suitable for researchers and practitioners in industry. A separate exercise/solution booklet is available as well, please go to www.springeronline.com under author: Vaudenay for additional details on how to purchase this booklet.