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Cryptographic Applications Of Analytic Number Theory
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Book Synopsis Cryptographic Applications of Analytic Number Theory by : Igor Shparlinski
Download or read book Cryptographic Applications of Analytic Number Theory written by Igor Shparlinski and published by Birkhäuser. This book was released on 2013-03-07 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces new techniques that imply rigorous lower bounds on the com plexity of some number-theoretic and cryptographic problems. It also establishes certain attractive pseudorandom properties of various cryptographic primitives. These methods and techniques are based on bounds of character sums and num bers of solutions of some polynomial equations over finite fields and residue rings. Other number theoretic techniques such as sieve methods and lattice reduction algorithms are used as well. The book also contains a number of open problems and proposals for further research. The emphasis is on obtaining unconditional rigorously proved statements. The bright side of this approach is that the results do not depend on any assumptions or conjectures. On the downside, the results are much weaker than those which are widely believed to be true. We obtain several lower bounds, exponential in terms of logp, on the degrees and orders of o polynomials; o algebraic functions; o Boolean functions; o linear recurrence sequences; coinciding with values of the discrete logarithm modulo a prime p at sufficiently many points (the number of points can be as small as pI/2+O:). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the rightmost bit of the discrete logarithm and defines whether the argument is a quadratic residue.
Book Synopsis Cryptographic Applications of Analytic Number Theory by : Igor E. Shparlinski
Download or read book Cryptographic Applications of Analytic Number Theory written by Igor E. Shparlinski and published by . This book was released on 2003 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.
Book Synopsis Number Theory and Applications by : S.D. Adhikari
Download or read book Number Theory and Applications written by S.D. Adhikari and published by Springer. This book was released on 2009-06-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.
Book Synopsis An Introduction to Number Theory with Cryptography by : James S. Kraft
Download or read book An Introduction to Number Theory with Cryptography written by James S. Kraft and published by CRC Press. This book was released on 2016-04-19 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Computational Number Theory and Modern Cryptography by : Song Y. Yan
Download or read book Computational Number Theory and Modern Cryptography written by Song Y. Yan and published by John Wiley & Sons. This book was released on 2013-01-29 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Number Theory with Cryptography by : James Kraft
Download or read book An Introduction to Number Theory with Cryptography written by James Kraft and published by CRC Press. This book was released on 2018-01-29 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
Book Synopsis An Introduction to Number Theory with Cryptography by : James Kraft
Download or read book An Introduction to Number Theory with Cryptography written by James Kraft and published by CRC Press. This book was released on 2018-01-29 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Course in Number Theory and Cryptography by : Neal Koblitz
Download or read book A Course in Number Theory and Cryptography written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-09-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elliptic Curves by : Lawrence C. Washington
Download or read book Elliptic Curves written by Lawrence C. Washington and published by Chapman and Hall/CRC. This book was released on 2003-05-28 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students. Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired. By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.
Book Synopsis Cryptology and Computational Number Theory by : Carl Pomerance
Download or read book Cryptology and Computational Number Theory written by Carl Pomerance and published by American Mathematical Soc.. This book was released on 1990 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Handbook of Algorithms in Number Theory by : N.B. Singh
Download or read book A Handbook of Algorithms in Number Theory written by N.B. Singh and published by N.B. Singh. This book was released on with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A Handbook of Algorithms in Number Theory" is designed for absolute beginners, providing a comprehensive introduction to the fundamental concepts of number theory and their applications in computer science. This book explores a range of topics, from cryptographic hash functions and primality testing to random number generation and error detection. Through clear, step-by-step descriptions, readers will gain a solid understanding of how number theory underpins modern algorithms and cryptographic protocols, making complex ideas accessible and engaging for those new to the subject.
Book Synopsis Coding, Cryptography and Combinatorics by : Keqin Feng
Download or read book Coding, Cryptography and Combinatorics written by Keqin Feng and published by Birkhäuser. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has long been recognized that there are fascinating connections between cod ing theory, cryptology, and combinatorics. Therefore it seemed desirable to us to organize a conference that brings together experts from these three areas for a fruitful exchange of ideas. We decided on a venue in the Huang Shan (Yellow Mountain) region, one of the most scenic areas of China, so as to provide the additional inducement of an attractive location. The conference was planned for June 2003 with the official title Workshop on Coding, Cryptography and Combi natorics (CCC 2003). Those who are familiar with events in East Asia in the first half of 2003 can guess what happened in the end, namely the conference had to be cancelled in the interest of the health of the participants. The SARS epidemic posed too serious a threat. At the time of the cancellation, the organization of the conference was at an advanced stage: all invited speakers had been selected and all abstracts of contributed talks had been screened by the program committee. Thus, it was de cided to call on all invited speakers and presenters of accepted contributed talks to submit their manuscripts for publication in the present volume. Altogether, 39 submissions were received and subjected to another round of refereeing. After care ful scrutiny, 28 papers were accepted for publication.
Book Synopsis The Prime Number Theorem by : G. J. O. Jameson
Download or read book The Prime Number Theorem written by G. J. O. Jameson and published by Cambridge University Press. This book was released on 2003-04-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Book Synopsis Algorithmic Number Theory by : Guillaume Hanrot
Download or read book Algorithmic Number Theory written by Guillaume Hanrot and published by Springer. This book was released on 2010-07-08 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Algorithmic Number Theory Symposium, ANTS 2010, held in Nancy, France, in July 2010. The 25 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.
Book Synopsis Mathematics of Public Key Cryptography by : Steven D. Galbraith
Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Book Synopsis Advanced Number Theory with Applications by : Richard A. Mollin
Download or read book Advanced Number Theory with Applications written by Richard A. Mollin and published by CRC Press. This book was released on 2009-08-26 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and mo
