Download or read book An Almost Polynomial Time Primality Testing Algorithm written by Jon George Hall and published by . This book was released on 1987 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Primality Testing in Polynomial Time written by Martin Dietzfelbinger and published by Springer Science & Business Media. This book was released on 2004-06-29 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained treatment of theoretically and practically important efficient algorithms for the primality problem. The text covers the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal and Saxena. The volume is written for students of computer science, in particular those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.
Download or read book Primality Testing in Polynomial Time from Randomized Algorithms to Primes Is in P written by M. Dietzfelbinger and published by . This book was released on 2004 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to algorithms for the venerable primality problem: Given a natural number n, decide whether it is prime or composite. The problem is basic in number theory, efficient algorithms that solve it, i.e., algorithms that run in a number of computational steps which is polynomial in the number of digits needed to write n, are important for theoretical computer science and for applications in algorithmics and cryptology. This book gives a self-contained account of theoretically and practically important efficient algorithms for the primality problem, covering the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal, and Saxena. The textbook is written for students of computer science, in particular for those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.
Download or read book An Exposition of the Deterministic Polynomial time Primality Testing Algorithm of Agrawal Kayal Saxena written by Robert Lawrence Anderson and published by . This book was released on 2005 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: I present a thorough examination of the unconditional deterministic polynomial-time algorithm for determining whether an input number is prime or composite proposed by Agrawal, Kayal and Saxena in their paper [1]. All proofs cited have been reworked with full details for the sake of completeness and readability.
Download or read book Primality Testing for Beginners written by Lasse Rempe-Gillen and published by American Mathematical Soc.. This book was released on 2013-12-11 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.
Download or read book An Exposition of the AKS Polynomial Time Primality Testing Algorithm written by Benjamin Linowitz and published by . This book was released on 2006 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Prime Numbers written by Richard Crandall and published by Springer Science & Business Media. This book was released on 2006-04-07 with total page 597 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
Download or read book Mathematics Unlimited 2001 and Beyond written by Björn Engquist and published by Springer. This book was released on 2017-04-05 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
Download or read book Introduction to Modern Number Theory written by Yu. I. Manin and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
Download or read book Mathematical Foundations of Computer Science 1981 written by J. Gruska and published by Springer Science & Business Media. This book was released on 1981-08 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithmic Number Theory written by J. P. Buhler and published by Cambridge University Press. This book was released on 2008-10-20 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to number theory for beginning graduate students with articles by the leading experts in the field.
Download or read book Algorithms and Theory of Computation Handbook Volume 1 written by Mikhail J. Atallah and published by CRC Press. This book was released on 2009-11-20 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many
Download or read book Algorithms and Theory of Computation Handbook 2 Volume Set written by Mikhail J. Atallah and published by CRC Press. This book was released on 2022-05-30 with total page 1944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition in a two volume set, provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. New to the Second Edition: Along with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, computational number theory, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics
Download or read book The Riemann Hypothesis written by Peter B. Borwein and published by Springer Science & Business Media. This book was released on 2008 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.
Download or read book Design and Analysis of Algorithms written by Parag H. Dave and published by Pearson Education India. This book was released on 2007-09 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: "All aspects pertaining to algorithm design and algorithm analysis have been discussed over the chapters in this book-- Design and Analysis of Algorithms"--Resource description page.
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.
Download or read book A Polynomial Time Algorithm for Prime Recognition written by Riaal Domingues and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Prime numbers are of the utmost importance in many applications and in particular cryptography. Firstly, number theory background is introduced in order to present the non-deterministic Solovay-Strassen primality test. Sec- ondly, the deterministic primality test discovered by Agrawal, Kayal and Sax- ena in 2002 is presented with the proofs following their original paper. Lastly, a remark will be made about the practical application of the deterministic algorithm versus using the non-deterministic algorithms in applications.
