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Primality Testing In Polynomial Time
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Book Synopsis Primality Testing in Polynomial Time by : Martin Dietzfelbinger
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.
Book Synopsis Primality Testing in Polynomial Time: from Randomized Algorithms to Primes Is in P by : M. Dietzfelbinger
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.
Book Synopsis Primality Testing and Integer Factorization in Public-Key Cryptography by : Song Y. Yan
Download or read book Primality Testing and Integer Factorization in Public-Key Cryptography written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primality Testing and Integer Factorization in Public-Key Cryptography introduces various algorithms for primality testing and integer factorization, with their applications in public-key cryptography and information security. More specifically, this book explores basic concepts and results in number theory in Chapter 1. Chapter 2 discusses various algorithms for primality testing and prime number generation, with an emphasis on the Miller-Rabin probabilistic test, the Goldwasser-Kilian and Atkin-Morain elliptic curve tests, and the Agrawal-Kayal-Saxena deterministic test for primality. Chapter 3 introduces various algorithms, particularly the Elliptic Curve Method (ECM), the Quadratic Sieve (QS) and the Number Field Sieve (NFS) for integer factorization. This chapter also discusses some other computational problems that are related to factoring, such as the square root problem, the discrete logarithm problem and the quadratic residuosity problem.
Book Synopsis Primality Testing for Beginners by : Lasse Rempe-Gillen
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.
Book Synopsis An Exposition of the Deterministic Polynomial-time Primality Testing Algorithm of Agrawal-Kayal-Saxena by : Robert Lawrence Anderson
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.
Book Synopsis Primality Testing in Polynomial Time by : Elena Kitti
Download or read book Primality Testing in Polynomial Time written by Elena Kitti and published by . This book was released on 2003 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis FST TCS 2002: Foundations of Software Technology and Theoretical Computer Science by : Manindra Agrawal
Download or read book FST TCS 2002: Foundations of Software Technology and Theoretical Computer Science written by Manindra Agrawal and published by Springer Science & Business Media. This book was released on 2002-11-29 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 22nd Conference on Foundations of Software Technology and Theoretical Computer Science, FST TCS 2002, held in Kanpur, India in December 2002. The 26 revised full papers presented together with 5 invited contributions were carefully reviewed and selected from 108 submissions. A broad variety of topics from the theory of computing are addressed, from algorithmics and discrete mathematics as well as from logics and programming theory.
Book Synopsis Primality Testing and Abelian Varieties Over Finite Fields by : Leonard M. Adleman
Download or read book Primality Testing and Abelian Varieties Over Finite Fields written by Leonard M. Adleman and published by Springer. This book was released on 2006-11-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Gauss to G|del, mathematicians have sought an efficient algorithm to distinguish prime numbers from composite numbers. This book presents a random polynomial time algorithm for the problem. The methods used are from arithmetic algebraic geometry, algebraic number theory and analyticnumber theory. In particular, the theory of two dimensional Abelian varieties over finite fields is developed. The book will be of interest to both researchers and graduate students in number theory and theoretical computer science.
Book Synopsis An Exposition of the AKS Polynomial Time Primality Testing Algorithm by : Benjamin Linowitz
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 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 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 An Almost Polynomial Time Primality Testing Algorithm by : Jon George Hall
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:
Book Synopsis Beyond the Worst-Case Analysis of Algorithms by : Tim Roughgarden
Download or read book Beyond the Worst-Case Analysis of Algorithms written by Tim Roughgarden and published by Cambridge University Press. This book was released on 2021-01-14 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks.
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
Book Synopsis Handbook of Product Graphs by : Richard Hammack
Download or read book Handbook of Product Graphs written by Richard Hammack and published by CRC Press. This book was released on 2011-06-06 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, this second edition presents full proofs of many important results as well as up-to-date research and conjectures. It illustrates applications of graph products in several areas and contains well over 300 exercises. Supplementary material is available on the book's website.
Book Synopsis Computational Complexity by : Sanjeev Arora
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
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.
