Modern Cryptography And Elliptic Curves A Beginners Guide

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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.

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.

Introduction to Modern Cryptography

Author : Jonathan Katz
Publisher : CRC Press
ISBN 13 : 1351133012
Total Pages : 435 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Introduction to Modern Cryptography by : Jonathan Katz

Download or read book Introduction to Modern Cryptography written by Jonathan Katz and published by CRC Press. This book was released on 2020-12-21 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now the most used texbook for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections, topics, and exercises. The authors present the core principles of modern cryptography, with emphasis on formal definitions, rigorous proofs of security.

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.

Modern Cryptography Volume 1

Author : Zhiyong Zheng
Publisher : Springer Nature
ISBN 13 : 9811909202
Total Pages : 364 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Modern Cryptography Volume 1 by : Zhiyong Zheng

Download or read book Modern Cryptography Volume 1 written by Zhiyong Zheng and published by Springer Nature. This book was released on 2022 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas. [Resumen de la editorial]

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.

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.

Modern Cryptography for Beginners

Author : Simon Edwards
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.6/5 (224 download)

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Book Synopsis Modern Cryptography for Beginners by : Simon Edwards

Download or read book Modern Cryptography for Beginners written by Simon Edwards and published by . This book was released on 2020-03-09 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Read This Complete Beginner's Guide and Discover Secrets of Modern Cryptography! Have you always been fascinated by secret messages and codes? Do you want to learn about cryptography and security in the modern age? THIS BOOK GIVES A DETAILED OVERVIEW OF HISTORY AND DEVELOPMENT OF CRYPTOGRAPHY AND IS FIT EVEN FOR ABSOLUTE BEGINNERS! Cryptography is the practice and study of secure communication. In the old times, cryptography was all about writing messages between that intruders couldn't read or understand. People wrote ciphers and keys and worked hard to decrypt and encrypt important notes. Cryptography was confined mostly to military and diplomatic activities, while regular people didn't have much to do with it in ordinary life. With the development of modern cryptography, we are now surrounded by its codes everywhere. Every message you send over your phone is encrypted. Our banks, schools, and governments rely on secure encryptions. With its prominence in our daily lives, it's a good idea to learn a thing or two about cryptography - not to mention interesting! Here's what you'll find in this book: History of encryption Cyphers from the Classical Era Introduction to modern cryptography Quantum cryptography Hash functions and digital signatures Public key infrastructure AND SO MUCH MORE! Even if you're an absolute beginner, you'll find this easy to read and follow. All it takes is a little curiosity! This book is your chance to learn about the hidden world underlying all our communication today. Cryptography, both traditional and modern, brings real value into our lives, and this book gives great reading material for both beginners and those who want to refresh their knowledge! Ready to crack some codes? Scroll up, Click on 'Buy Now with 1-Click', and Get Your Copy!

Modern Cryptography

Author : William Easttom
Publisher : Springer Nature
ISBN 13 : 3031123042
Total Pages : 460 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Modern Cryptography by : William Easttom

Download or read book Modern Cryptography written by William Easttom and published by Springer Nature. This book was released on 2022-10-29 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded textbook, now in its second edition, is a practical yet in depth guide to cryptography and its principles and practices. Now featuring a new section on quantum resistant cryptography in addition to expanded and revised content throughout, the book continues to place cryptography in real-world security situations using the hands-on information contained throughout the chapters. Prolific author Dr. Chuck Easttom lays out essential math skills and fully explains how to implement cryptographic algorithms in today's data protection landscape. Readers learn and test out how to use ciphers and hashes, generate random keys, handle VPN and Wi-Fi security, and encrypt VoIP, Email, and Web communications. The book also covers cryptanalysis, steganography, and cryptographic backdoors and includes a description of quantum computing and its impact on cryptography. This book is meant for those without a strong mathematics background with only just enough math to understand the algorithms given. The book contains a slide presentation, questions and answers, and exercises throughout. Presents new and updated coverage of cryptography including new content on quantum resistant cryptography; Covers the basic math needed for cryptography - number theory, discrete math, and algebra (abstract and linear); Includes a full suite of classroom materials including exercises, Q&A, and examples.

Cryptography 101: From Theory to Practice

Author : Rolf Oppliger
Publisher : Artech House
ISBN 13 : 163081847X
Total Pages : 650 pages
Book Rating : 4.6/5 (38 download)

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Book Synopsis Cryptography 101: From Theory to Practice by : Rolf Oppliger

Download or read book Cryptography 101: From Theory to Practice written by Rolf Oppliger and published by Artech House. This book was released on 2021-06-30 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exciting new resource provides a comprehensive overview of the field of cryptography and the current state of the art. It delivers an overview about cryptography as a field of study and the various unkeyed, secret key, and public key cryptosystems that are available, and it then delves more deeply into the technical details of the systems. It introduces, discusses, and puts into perspective the cryptographic technologies and techniques, mechanisms, and systems that are available today. Random generators and random functions are discussed, as well as one-way functions and cryptography hash functions. Pseudorandom generators and their functions are presented and described. Symmetric encryption is explored, and message authentical and authenticated encryption are introduced. Readers are given overview of discrete mathematics, probability theory and complexity theory. Key establishment is explained. Asymmetric encryption and digital signatures are also identified. Written by an expert in the field, this book provides ideas and concepts that are beneficial to novice as well as experienced practitioners.

Classical and Modern Cryptography for Beginners

Author : Rajkumar Banoth
Publisher : Springer Nature
ISBN 13 : 3031329597
Total Pages : 230 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Classical and Modern Cryptography for Beginners by : Rajkumar Banoth

Download or read book Classical and Modern Cryptography for Beginners written by Rajkumar Banoth and published by Springer Nature. This book was released on 2023-06-24 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers the knowledge and the mathematical background or techniques that are required to implement encryption/decryption algorithms or security techniques. It also provides the information on the cryptography and a cryptosystem used by organizations and applications to protect their data and users can explore classical and modern cryptography. The first two chapters are dedicated to the basics of cryptography and emphasize on modern cryptography concepts and algorithms. Cryptography terminologies such as encryption, decryption, cryptology, cryptanalysis and keys and key types included at the beginning of this textbook . The subsequent chapters cover basic phenomenon of symmetric and asymmetric cryptography with examples including the function of symmetric key encryption of websites and asymmetric key use cases. This would include security measures for websites, emails, and other types of encryptions that demand key exchange over a public network. Cryptography algorithms (Caesar cipher, Hill cipher, Playfair cipher, Vigenere cipher, DES, AES, IDEA, TEA, CAST, etc.) which are varies on algorithmic criteria like- scalability, flexibility, architecture, security, limitations in terms of attacks of adversary. They are the core consideration on which all algorithms differs and applicable as per application environment. The modern cryptography starts from invent of RSA (Rivest-Shamir-Adleman) which is an asymmetric key algorithm based on prime numbers. Nowadays it is enabled with email and digital transaction over the Internet. This textbook covers Chinese remainder theorem, Legendre, Jacobi symbol, Rabin cryptosystem, generalized ElGamal public key cryptosystem, key management, digital signatures, message authentication, differential cryptanalysis, linear cryptanalysis, time-memory trade-off attack, network security, cloud security, blockchain, bitcoin, etc. as well as accepted phenomenon under modern cryptograph. Advanced level students will find this textbook essential for course work and independent study. Computer scientists and engineers and researchers working within these related fields will also find this textbook useful.

Introduction to Cryptography with Open-Source Software

Author : Alasdair McAndrew
Publisher : CRC Press
ISBN 13 : 1439825718
Total Pages : 456 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Introduction to Cryptography with Open-Source Software by : Alasdair McAndrew

Download or read book Introduction to Cryptography with Open-Source Software written by Alasdair McAndrew and published by CRC Press. This book was released on 2016-04-19 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experienc

An Introduction to Mathematical Cryptography

Author : Jeffrey Hoffstein
Publisher : Springer
ISBN 13 : 9780387779935
Total Pages : 524 pages
Book Rating : 4.7/5 (799 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 2008-08-12 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises. It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.

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.

LMSST: 24 Lectures on Elliptic Curves

Author : John William Scott Cassels
Publisher : Cambridge University Press
ISBN 13 : 9780521425308
Total Pages : 148 pages
Book Rating : 4.4/5 (253 download)

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Book Synopsis LMSST: 24 Lectures on Elliptic Curves by : John William Scott Cassels

Download or read book LMSST: 24 Lectures on Elliptic Curves written by John William Scott Cassels and published by Cambridge University Press. This book was released on 1991-11-21 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.

Topics in Galois Fields

Author : Dirk Hachenberger
Publisher : Springer Nature
ISBN 13 : 3030608069
Total Pages : 785 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Topics in Galois Fields by : Dirk Hachenberger

Download or read book Topics in Galois Fields written by Dirk Hachenberger and published by Springer Nature. This book was released on 2020-09-29 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.