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Prime Numbers And Computer Methods For Factorization
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Book Synopsis Prime Numbers and Computer Methods for Factorization by : Hans Riesel
Download or read book Prime Numbers and Computer Methods for Factorization written by Hans Riesel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.
Book Synopsis Prime Numbers and Computer Methods for Factorization by : H. Riesel
Download or read book Prime Numbers and Computer Methods for Factorization written by H. Riesel and published by . This book was released on 2014-01-15 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Prime Numbers and Computer Methods for Factorization by : H. Riesel
Download or read book Prime Numbers and Computer Methods for Factorization written by H. Riesel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author treats four fundamental and apparently simple problems. They are: the number of primes below a given limit, the ap proximate number of primes, the recognition of prime numbers and the factorization of large numbers. A chapter on the details of the distribution of the primes is included as well as a short description of a recent applica tion of prime numbers, the so-called RSA public-key cryptosystem. The author is also giving explicit algorithms and computer programs. Whilst not claiming completeness, the author has tried to give all important results known, including the latest discoveries. The use of computers has in this area promoted a development which has enormously enlarged the wealth of results known and that has made many older works and tables obsolete. As is often the case in number theory, the problems posed are easy to understand but the solutions are theoretically advanced. Since this text is aimed at the mathematically inclined layman, as well as at the more advanced student, not all of the proofs of the results given in this book are shown. Bibliographical references in these cases serve those readers who wish to probe deeper. References to recent original works are also given for those who wish to pursue some topic further. Since number theory is seldom taught in basic mathematics courses, the author has appended six sections containing all the algebra and number theory required for the main body of the book.
Download or read book Prime Numbers written by Richard Crandall and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field
Book Synopsis Primes and Programming by : P. J. Giblin
Download or read book Primes and Programming written by P. J. Giblin and published by Cambridge University Press. This book was released on 1993-09-02 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory book Dr Giblin describes methods that have been developed for testing the primality of numbers, provides Pascal programs for their implementation, and gives applications to coding.
Download or read book 1992 Census of Wholesale Trade written by and published by . This book was released on 1994 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stalking the Riemann Hypothesis by : Dan Rockmore
Download or read book Stalking the Riemann Hypothesis written by Dan Rockmore and published by Vintage. This book was released on 2006-05-09 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
Book Synopsis The Joy of Factoring by : Samuel S. Wagstaff (Jr.)
Download or read book The Joy of Factoring written by Samuel S. Wagstaff (Jr.) and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is about the theory and practice of integer factorization presented in a historic perspective. It describes about twenty algorithms for factoring and a dozen other number theory algorithms that support the factoring algorithms. Most algorithms are described both in words and in pseudocode to satisfy both number theorists and computer scientists. Each of the ten chapters begins with a concise summary of its contents. This book is written for readers who want to learn more about the best methods of factoring integers, many reasons for factoring, and some history of this fascinating subject. It can be read by anyone who has taken a first course in number theory." -- Publisher website.
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 The Distribution of Prime Numbers by : Albert Edward Ingham
Download or read book The Distribution of Prime Numbers written by Albert Edward Ingham and published by Cambridge University Press. This book was released on 1990-09-28 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
Book Synopsis The Book of Prime Number Records by : Paulo Ribenboim
Download or read book The Book of Prime Number Records written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A. J. Coleman and H. W. Ellis and to acknowledge their long-lasting interest in the quality of teaching undergraduate students. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book oj Records, reminded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will also include some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work. Paulo Ribenboim CONTENTS Preface vii Guiding the Reader xiii Index of Notations xv Introduction Chapter 1. How Many Prime Numbers Are There? 3 I. Euclid's Proof 3 II.
Book Synopsis The Development of the Number Field Sieve by : Arjen K. Lenstra
Download or read book The Development of the Number Field Sieve written by Arjen K. Lenstra and published by Springer. This book was released on 2006-11-15 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
Book Synopsis A Course in Computational Algebraic Number Theory by : Henri Cohen
Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Book Synopsis Elementary Number Theory: Primes, Congruences, and Secrets by : William Stein
Download or read book Elementary Number Theory: Primes, Congruences, and Secrets written by William Stein and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
Book Synopsis An Introduction to Cryptography by : Richard A. Mollin
Download or read book An Introduction to Cryptography written by Richard A. Mollin and published by CRC Press. This book was released on 2006-09-18 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field. With numerous additions and restructured material, this edition
Book Synopsis Factorization by : Steven H. Weintraub
Download or read book Factorization written by Steven H. Weintraub and published by CRC Press. This book was released on 2008-05-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications. This exposition of the classic theory leads the reader to an understanding of the current knowledge of the subject and its connections to other math
Book Synopsis Prime Obsession by : John Derbyshire
Download or read book Prime Obsession written by John Derbyshire and published by Joseph Henry Press. This book was released on 2003-04-15 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.
