Guide To Elliptic Curve Cryptography

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Guide to Elliptic Curve Cryptography

Darrel Hankerson,Alfred J. Menezes,Scott Vanstone
Guide to Elliptic Curve Cryptography Book PDF

Author : Darrel Hankerson,Alfred J. Menezes,Scott Vanstone
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 44,7 Mb
Release : 2006-06-01
Category : Computers
ISBN : 9780387218465

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Guide to Elliptic Curve Cryptography by Darrel Hankerson,Alfred J. Menezes,Scott Vanstone Pdf

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

Thomas R. Shemanske
Modern Cryptography and Elliptic Curves A Beginner s Guide Book PDF

Author : Thomas R. Shemanske
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 48,7 Mb
Release : 2017-07-31
Category : Cryptography
ISBN : 9781470435820

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

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

Neal Koblitz
Random Curves Book PDF

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 51,9 Mb
Release : 2009-05-03
Category : Mathematics
ISBN : 9783540740780

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Random Curves by Neal Koblitz Pdf

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

Lawrence C. Washington
Elliptic Curves Book PDF

Author : Lawrence C. Washington
Publisher : CRC Press
Page : 533 pages
File Size : 51,5 Mb
Release : 2008-04-03
Category : Computers
ISBN : 9781420071474

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Elliptic Curves by Lawrence C. Washington Pdf

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

Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe Doche,Tanja Lange,Kim Nguyen,Frederik Vercauteren
Handbook of Elliptic and Hyperelliptic Curve Cryptography Book PDF

Author : Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe Doche,Tanja Lange,Kim Nguyen,Frederik Vercauteren
Publisher : CRC Press
Page : 842 pages
File Size : 46,6 Mb
Release : 2005-07-19
Category : Mathematics
ISBN : 9781420034981

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Handbook of Elliptic and Hyperelliptic Curve Cryptography by Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe Doche,Tanja Lange,Kim Nguyen,Frederik Vercauteren Pdf

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

Nadia El Mrabet,Marc Joye
Guide to Pairing Based Cryptography Book PDF

Author : Nadia El Mrabet,Marc Joye
Publisher : CRC Press
Page : 410 pages
File Size : 42,5 Mb
Release : 2017-01-06
Category : Computers
ISBN : 9781498729512

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Guide to Pairing-Based Cryptography by Nadia El Mrabet,Marc Joye Pdf

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

Jean-Philippe Aumasson
Serious Cryptography Book PDF

Author : Jean-Philippe Aumasson
Publisher : No Starch Press
Page : 313 pages
File Size : 43,9 Mb
Release : 2017-11-06
Category : Computers
ISBN : 9781593278267

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Serious Cryptography by Jean-Philippe Aumasson Pdf

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.

Mathematics of Public Key Cryptography

Steven D. Galbraith
Mathematics of Public Key Cryptography Book PDF

Author : Steven D. Galbraith
Publisher : Cambridge University Press
Page : 631 pages
File Size : 42,5 Mb
Release : 2012-03-15
Category : Computers
ISBN : 9781107013926

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Mathematics of Public Key Cryptography by Steven D. Galbraith Pdf

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

Elliptic Curves in Cryptography

Ian F. Blake,G. Seroussi,N. Smart
Elliptic Curves in Cryptography Book PDF

Author : Ian F. Blake,G. Seroussi,N. Smart
Publisher : Cambridge University Press
Page : 228 pages
File Size : 40,7 Mb
Release : 1999-07-08
Category : Mathematics
ISBN : 0521653746

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Elliptic Curves in Cryptography by Ian F. Blake,G. Seroussi,N. Smart Pdf

This book explains the mathematics behind practical implementations of elliptic curve systems.

Elliptic Curves and Their Applications to Cryptography

Andreas Enge
Elliptic Curves and Their Applications to Cryptography Book PDF

Author : Andreas Enge
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461552079

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Elliptic Curves and Their Applications to Cryptography by Andreas Enge Pdf

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.

Implementing Elliptic Curve Cryptography

Michael Rosing
Implementing Elliptic Curve Cryptography Book PDF

Author : Michael Rosing
Publisher : Manning Publications
Page : 0 pages
File Size : 42,6 Mb
Release : 1999
Category : Computer security
ISBN : 1884777694

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Implementing Elliptic Curve Cryptography by Michael Rosing Pdf

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.

IoT Security

Madhusanka Liyanage,An Braeken,Pardeep Kumar,Mika Ylianttila
IoT Security Book PDF

Author : Madhusanka Liyanage,An Braeken,Pardeep Kumar,Mika Ylianttila
Publisher : John Wiley & Sons
Page : 327 pages
File Size : 49,7 Mb
Release : 2019-12-24
Category : Technology & Engineering
ISBN : 9781119527947

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IoT Security by Madhusanka Liyanage,An Braeken,Pardeep Kumar,Mika Ylianttila Pdf

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

Peter Stavroulakis,Mark Stamp
Handbook of Information and Communication Security Book PDF

Author : Peter Stavroulakis,Mark Stamp
Publisher : Springer Science & Business Media
Page : 867 pages
File Size : 44,7 Mb
Release : 2010-02-23
Category : Technology & Engineering
ISBN : 9783642041174

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Handbook of Information and Communication Security by Peter Stavroulakis,Mark Stamp Pdf

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.

Cryptography and Public Key Infrastructure on the Internet

Klaus Schmeh
Cryptography and Public Key Infrastructure on the Internet Book PDF

Author : Klaus Schmeh
Publisher : John Wiley & Sons
Page : 488 pages
File Size : 53,7 Mb
Release : 2006-01-04
Category : Computers
ISBN : 9780470862483

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Cryptography and Public Key Infrastructure on the Internet by Klaus Schmeh Pdf

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

Guide to Pairing-Based Cryptography

Nadia El Mrabet,Marc Joye
Guide to Pairing Based Cryptography Book PDF

Author : Nadia El Mrabet,Marc Joye
Publisher : CRC Press
Page : 475 pages
File Size : 54,9 Mb
Release : 2017-01-06
Category : Computers
ISBN : 9781315353142

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Guide to Pairing-Based Cryptography by Nadia El Mrabet,Marc Joye Pdf

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.