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Modern Cryptography and Elliptic Curves

2017-07-31 Computers
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Release : 2017-07-31
Genre : Computers
Kind : eBook
Book Rating : 829/5 ( reviews)

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Book Synopsis Modern Cryptography and Elliptic Curves by : Thomas R. Shemanske

Download or read book Modern Cryptography and Elliptic Curves written by Thomas R. Shemanske. This book was released on 2017-07-31. 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

2004-01-08 Computers
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Release : 2004-01-08
Genre : Computers
Kind : eBook
Book Rating : 73X/5 ( reviews)

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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. This book was released on 2004-01-08. Available in PDF, EPUB and Kindle. Book excerpt: After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic * Distills complex mathematics and algorithms for easy understanding * Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software tools This comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

Elliptic Curves

2008-04-03 Computers
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Release : 2008-04-03
Genre : Computers
Kind : eBook
Book Rating : 475/5 ( reviews)

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Book Synopsis Elliptic Curves by : Lawrence C. Washington

Download or read book Elliptic Curves written by Lawrence C. Washington. This book was released on 2008-04-03. 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

Elliptic Curve Public Key Cryptosystems

2012-12-06 Technology & Engineering
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Release : 2012-12-06
Genre : Technology & Engineering
Kind : eBook
Book Rating : 985/5 ( reviews)

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Book Synopsis Elliptic Curve Public Key Cryptosystems by : Alfred J. Menezes

Download or read book Elliptic Curve Public Key Cryptosystems written by Alfred J. Menezes. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems. Elliptic Curve Public Key Cryptosystems provides an up-to-date and self-contained treatment of elliptic curve-based public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems. Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject.

An Introduction to Mathematical Cryptography

2008-12-15 Mathematics
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Release : 2008-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 949/5 ( reviews)

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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. This book was released on 2008-12-15. 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.

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