An Introduction To Number Theory With Cryptography

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An Introduction to Number Theory with Cryptography

James Kraft,Lawrence Washington
An Introduction to Number Theory with Cryptography Book PDF

Author : James Kraft,Lawrence Washington
Publisher : CRC Press
Page : 300 pages
File Size : 51,9 Mb
Release : 2018-01-29
Category : Computers
ISBN : 9781351664103

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An Introduction to Number Theory with Cryptography by James Kraft,Lawrence Washington Pdf

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

A Course in Number Theory and Cryptography

Neal Koblitz
A Course in Number Theory and Cryptography Book PDF

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 52,5 Mb
Release : 2012-09-05
Category : Mathematics
ISBN : 9781441985927

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

An Introduction to Number Theory with Cryptography

James Kraft,Lawrence Washington
An Introduction to Number Theory with Cryptography Book PDF

Author : James Kraft,Lawrence Washington
Publisher : CRC Press
Page : 578 pages
File Size : 43,6 Mb
Release : 2018-01-29
Category : Computers
ISBN : 9781315161006

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An Introduction to Number Theory with Cryptography by James Kraft,Lawrence Washington Pdf

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

Elementary Number Theory, Cryptography and Codes

M. Welleda Baldoni,Ciro Ciliberto,G.M. Piacentini Cattaneo
Elementary Number Theory Cryptography and Codes Book PDF

Author : M. Welleda Baldoni,Ciro Ciliberto,G.M. Piacentini Cattaneo
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 43,9 Mb
Release : 2008-11-28
Category : Mathematics
ISBN : 9783540692003

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Elementary Number Theory, Cryptography and Codes by M. Welleda Baldoni,Ciro Ciliberto,G.M. Piacentini Cattaneo Pdf

In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.

An Introduction to Number Theory with Cryptography

James S. Kraft,Lawrence C. Washington
An Introduction to Number Theory with Cryptography Book PDF

Author : James S. Kraft,Lawrence C. Washington
Publisher : CRC Press
Page : 568 pages
File Size : 43,5 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781482214420

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An Introduction to Number Theory with Cryptography by James S. Kraft,Lawrence C. Washington Pdf

Number theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number

An Introduction to Mathematical Cryptography

Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
An Introduction to Mathematical Cryptography Book PDF

Author : Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
Publisher : Springer
Page : 549 pages
File Size : 50,5 Mb
Release : 2014-09-11
Category : Mathematics
ISBN : 9781493917112

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An Introduction to Mathematical Cryptography by Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman Pdf

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.

Number Theory and Cryptography

J. H. Loxton
Number Theory and Cryptography Book PDF

Author : J. H. Loxton
Publisher : Cambridge University Press
Page : 249 pages
File Size : 44,5 Mb
Release : 1990-04-19
Category : Mathematics
ISBN : 9780521398770

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Number Theory and Cryptography by J. H. Loxton Pdf

Papers presented by prominent contributors at a workshop on Number Theory and Cryptography, and the annual meeting of the Australian Mathematical Society.

Elliptic Curves

Lawrence C. Washington
Elliptic Curves Book PDF

Author : Lawrence C. Washington
Publisher : CRC Press
Page : 533 pages
File Size : 41,6 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

Introduction to Number Theory

Anthony Vazzana,Martin Erickson,David Garth
Introduction to Number Theory Book PDF

Author : Anthony Vazzana,Martin Erickson,David Garth
Publisher : CRC Press
Page : 530 pages
File Size : 42,7 Mb
Release : 2007-10-30
Category : Computers
ISBN : 9781584889380

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Introduction to Number Theory by Anthony Vazzana,Martin Erickson,David Garth Pdf

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi

Computational Number Theory and Modern Cryptography

Song Y. Yan
Computational Number Theory and Modern Cryptography Book PDF

Author : Song Y. Yan
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 43,7 Mb
Release : 2013-01-29
Category : Computers
ISBN : 9781118188583

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Computational Number Theory and Modern Cryptography by Song Y. Yan Pdf

The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.

An Introduction to Number Theory

G. Everest,Thomas Ward
An Introduction to Number Theory Book PDF

Author : G. Everest,Thomas Ward
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 41,7 Mb
Release : 2007-05-21
Category : Mathematics
ISBN : 9781852339173

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An Introduction to Number Theory by G. Everest,Thomas Ward Pdf

Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight

An Experimental Introduction to Number Theory

Benjamin Hutz
An Experimental Introduction to Number Theory Book PDF

Author : Benjamin Hutz
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 50,8 Mb
Release : 2018-04-17
Category : Number theory
ISBN : 9781470430979

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An Experimental Introduction to Number Theory by Benjamin Hutz Pdf

This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.

A Computational Introduction to Number Theory and Algebra

Victor Shoup
A Computational Introduction to Number Theory and Algebra Book PDF

Author : Victor Shoup
Publisher : Cambridge University Press
Page : 544 pages
File Size : 40,5 Mb
Release : 2005-04-28
Category : Computers
ISBN : 0521851548

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A Computational Introduction to Number Theory and Algebra by Victor Shoup Pdf

This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.

Cryptology and Computational Number Theory

Carl Pomerance,Shafi Goldwasser
Cryptology and Computational Number Theory Book PDF

Author : Carl Pomerance,Shafi Goldwasser
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 54,8 Mb
Release : 1990
Category : Computers
ISBN : 0821801554

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Cryptology and Computational Number Theory by Carl Pomerance,Shafi Goldwasser Pdf

In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.

Number Theory for Computing

Song Y. Yan
Number Theory for Computing Book PDF

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 55,8 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783662047736

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Number Theory for Computing by Song Y. Yan Pdf

This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.