Guide To Elliptic Curve Cryptography

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Guide To Elliptic Curve Cryptography

Author : Darrel Hankerson
ISBN : 9780387218465
Genre : Computers
File Size : 84.2 MB
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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.
Category: Computers

Modern Cryptography And Elliptic Curves A Beginner S Guide

Author : Thomas R. Shemanske
ISBN : 9781470435820
Genre : Cryptography
File Size : 83.44 MB
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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.
Category: Cryptography

Elliptic Curve Cryptography

Author : Armand de Sandu
ISBN : 0648487202
Genre :
File Size : 36.43 MB
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Modern computer systems depend on the confidential exchange of data to facilitate daily life. Whether one is transferring money between countries, creating a virtual private network connection, of simply wishing to communicate using peer-to-peer technologies, encryption provides the basis for the secure exchange of data. Elliptic-curve cryptography (ECC) provides equivalent security to traditional Galois field-based encryption algorithms, while simultaneously requiring vastly smaller key sizes, speeding processing, establishment, and reducing computing overhead.Elliptic-curves may be used for key agreement and negotiation, digital signing, and may also underly foundations necessary for payload encryption and transport.Elliptic-Curve Cryptography delves into the mathematics and nuances necessary to understand modern key-based systems in operating systems such as Microsoft Windows, Linux, and Unix, as well as hardware platforms such as routers, VPN concentrators and complex firewall appliances. Included within this volume are discussions focusing on:¿Elliptic Curve Diffie Hellman¿National Security Agency Suite B¿Elliptic Curve Integrated Encryption Scheme¿Elliptic Curve Digital Signatures¿Elliptic Curve Certificate ServicesElliptic-Curve Cryptography is aimed for the academic researcher or cybersecurity professional who requires a detailed understanding of key management within ECC technology and the underlying mathematics involved.

Advances In Cryptology Eurocrypt 2009

Author : Antoine Joux
ISBN : 9783642010002
Genre : Business & Economics
File Size : 81.31 MB
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This book constitutes the refereed proceedings of the 28th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2009, held in Cologne, Germany, in April 2009. The 33 revised full papers presented together with 1 invited lecture were carefully reviewed and selected from 148 submissions. The papers address all current foundational, theoretical and research aspects of cryptology, cryptography, and cryptanalysis as well as advanced applications. The papers are organized in topical sections on security, proofs, and models, hash cryptanalysis, group and broadcast encryption, cryptosystems, cryptanalysis, side channels, curves, and randomness.
Category: Business & Economics

Handbook Of Elliptic And Hyperelliptic Curve Cryptography

Author : Henri Cohen
ISBN : 1420034987
Genre : Mathematics
File Size : 31.25 MB
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The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.
Category: Mathematics

Untangling The Web

Author :
ISBN : 9780984284498
Genre : Computer network resources
File Size : 36.91 MB
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Use the internet like a real spy. Untangling the Web is the National Security Agency's once-classified guide to finding information on the internet. From the basic to the advanced, this 650-page book offers a fascinating look at tricks the "real spies" use to uncover hidden (and not-so-hidden) information online. Chapters include: Google hacks Metasearch sites Custom search engines Maps & mapping Uncovering the invisible internet Beyond search engines: Specialized research tools Email lookups Finding people Researching companies A plain english guide to interworking Internet toolkits Finding ISPs Cybergeography Internet privacy and security ....and over a hundred more chapters. This quote from the authors hints at the investigative power of the techniques this book teaches: "Nothing I am going to describe to you is illegal, nor does it in any way involve accessing unauthorized data, [...but] involves using publicly available search engines to access publicly available information that almost certainly was not intended for public distribution." From search strings that will reveal secret documents from South Africa ("filetype: xls site: za confidential") to tracking down tables of Russian passwords ("filetype: xls site: ru login"), this is both an instructive and voyeuristic look at how the most powerful spy agency in the world uses Google.
Category: Computer network resources

Encyclopedia Of Cryptography And Security

Author : Henk C.A. van Tilborg
ISBN : 9781441959058
Genre : Computers
File Size : 56.29 MB
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Expanded into two volumes, the Second Edition of Springer’s Encyclopedia of Cryptography and Security brings the latest and most comprehensive coverage of the topic: Definitive information on cryptography and information security from highly regarded researchers Effective tool for professionals in many fields and researchers of all levels Extensive resource with more than 700 contributions in Second Edition 5643 references, more than twice the number of references that appear in the First Edition With over 300 new entries, appearing in an A-Z format, the Encyclopedia of Cryptography and Security provides easy, intuitive access to information on all aspects of cryptography and security. As a critical enhancement to the First Edition’s base of 464 entries, the information in the Encyclopedia is relevant for researchers and professionals alike. Topics for this comprehensive reference were elected, written, and peer-reviewed by a pool of distinguished researchers in the field. The Second Edition’s editorial board now includes 34 scholars, which was expanded from 18 members in the First Edition. Representing the work of researchers from over 30 countries, the Encyclopedia is broad in scope, covering everything from authentication and identification to quantum cryptography and web security. The text’s practical style is instructional, yet fosters investigation. Each area presents concepts, designs, and specific implementations. The highly-structured essays in this work include synonyms, a definition and discussion of the topic, bibliographies, and links to related literature. Extensive cross-references to other entries within the Encyclopedia support efficient, user-friendly searches for immediate access to relevant information. Key concepts presented in the Encyclopedia of Cryptography and Security include: Authentication and identification; Block ciphers and stream ciphers; Computational issues; Copy protection; Cryptanalysis and security; Cryptographic protocols; Electronic payment and digital certificates; Elliptic curve cryptography; Factorization algorithms and primality tests; Hash functions and MACs; Historical systems; Identity-based cryptography; Implementation aspects for smart cards and standards; Key management; Multiparty computations like voting schemes; Public key cryptography; Quantum cryptography; Secret sharing schemes; Sequences; Web Security. Topics covered: Data Structures, Cryptography and Information Theory; Data Encryption; Coding and Information Theory; Appl.Mathematics/Computational Methods of Engineering; Applications of Mathematics; Complexity. This authoritative reference will be published in two formats: print and online. The online edition features hyperlinks to cross-references, in addition to significant research.
Category: Computers

Quantum Computational Number Theory

Author : Song Y. Yan
ISBN : 9783319258232
Genre : Computers
File Size : 74.90 MB
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This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification. The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture. Quantum Computational Number Theory is self-contained and intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the related fields. Number theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset.
Category: Computers

Advances In Data And Information Sciences

Author : Mohan L. Kolhe
ISBN : 9789811083600
Genre : Technology & Engineering
File Size : 27.66 MB
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The book gathers a collection of high-quality peer-reviewed research papers presented at the International Conference on Data and Information Systems (ICDIS 2017), held at Indira Gandhi National Tribal University, India from November 3 to 4, 2017. The book covers all aspects of computational sciences and information security. In chapters written by leading researchers, developers and practitioner from academia and industry, it highlights the latest developments and technical solutions, helping readers from the computer industry capitalize on key advances in next-generation computer and communication technology.
Category: Technology & Engineering

Geometry Algebra And Applications From Mechanics To Cryptography

Author : Marco Castrillón López
ISBN : 9783319320854
Genre : Science
File Size : 58.11 MB
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This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.
Category: Science

Circuits And Systems For Security And Privacy

Author : Farhana Sheikh
ISBN : 9781315355733
Genre : Computers
File Size : 53.39 MB
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Circuits and Systems for Security and Privacy begins by introducing the basic theoretical concepts and arithmetic used in algorithms for security and cryptography, and by reviewing the fundamental building blocks of cryptographic systems. It then analyzes the advantages and disadvantages of real-world implementations that not only optimize power, area, and throughput but also resist side-channel attacks. Merging the perspectives of experts from industry and academia, the book provides valuable insight and necessary background for the design of security-aware circuits and systems as well as efficient accelerators used in security applications.
Category: Computers

Cryptographic Hardware And Embedded Systems Ches 2016

Author : Benedikt Gierlichs
ISBN : 9783662531402
Genre : Computers
File Size : 39.26 MB
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This book constitutes the proceedings of the 18th International Conference on Cryptographic Hardware and Embedded Systems, CHES 2016, held in Santa Barbara, CA, USA, in August 2016. The 30 full papers presented in this volume were carefully reviewed and selected from 148 submissions. They were organized in topical sections named: side channel analysis; automotive security; invasive attacks; side channel countermeasures; new directions; software implementations; cache attacks; physical unclonable functions; hardware implementations; and fault attacks.
Category: Computers

Progress In Cryptology Indocrypt 2007

Author : K. Srinathan
ISBN : 9783540770268
Genre : Computers
File Size : 31.35 MB
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This book constitutes the refereed proceedings of the 8th International Conference on Cryptology in India, INDOCRYPT 2007, held in Chennai, India, in December 2007. The papers and three invited lectures were carefully reviewed and selected. The papers are organized in topical sections on hashing, elliptic curve, cryptoanalysis, information theoretic security, elliptic curve cryptography, signature, side channel attack, symmetric cryptosystem, asymmetric cryptosystem, and short papers.
Category: Computers

Selected Areas In Cryptography Sac 2018

Author : Carlos Cid
ISBN : 9783030109707
Genre : Computers
File Size : 29.44 MB
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This book contains revised selected papers from the 25th International Conference on Selected Areas in Cryptography, SAC 2018, held in Calgary, AB, Canada in August 2018. The 22 full papers presented in this volume were carefully reviewed and selected from 57 submissions. They cover the following research areas: design and analysis of symmetric key primitives and cryptosystems, including block and stream ciphers, hash functions, MAC algorithms, and authenticated encryption schemes efficient implementations of symmetric and public key algorithms mathematical and algorithmic aspects of applied cryptology cryptography for the Internet of Things
Category: Computers

Ict Systems Security And Privacy Protection

Author : Audun Jøsang
ISBN : 9783030781200
Genre : Computer networks
File Size : 67.50 MB
Format : PDF
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This book constitutes the refereed proceedings of the 36th IFIP TC 11 International Conference on Information Security and Privacy Protection, SEC 2021, held in Oslo, Norway, in June 2021.* The 28 full papers presented were carefully reviewed and selected from 112 submissions. The papers present novel research on theoretical and practical aspects of security and privacy protection in ICT systems. They are organized in topical sections on digital signatures; vulnerability management; covert channels and cryptography; application and system security; privacy; network security; machine learning for security; and security management. *The conference was held virtually.
Category: Computer networks

Handbook Of Information And Communication Security

Author : Peter Stavroulakis
ISBN : 3642041175
Genre : Technology & Engineering
File Size : 65.30 MB
Format : PDF
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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.
Category: Technology & Engineering

Progress In Cryptology Indocrypt 2017

Author : Arpita Patra
ISBN : 9783319716671
Genre : Computers
File Size : 85.64 MB
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This book constitutes the refereed proceedings of the 18th International Conference on Cryptology in India, INDOCRYPT 2017, held in Chennai, India, in December 2017. The 19 revised full papers presented in this book were carefully reviewed and selected from 75 submissions. The focus of the conference includes works on Public-Key Cryptography, Cryptographic Protocols, Side-Channel Attacks, Implementation of Cryptographic Schemes, Functional Encryption, Symmetric-Key Cryptanalysis, Foundations, and New Cryptographic Constructions.
Category: Computers

Guide To Pairing Based Cryptography

Author : Nadia El Mrabet
ISBN : 9781498729512
Genre : Computers
File Size : 90.79 MB
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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.
Category: Computers