Primality Testing In Polynomial Time From Randomized Algorithms To Primes Is In P
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Primality Testing In Polynomial Time From Randomized Algorithms To Primes Is In P
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Author : M. Dietzfelbinger
language : en
Publisher:
Release Date : 2004
Primality Testing In Polynomial Time From Randomized Algorithms To Primes Is In P written by M. Dietzfelbinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Primality Testing In Polynomial Time
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Author : Martin Dietzfelbinger
language : en
Publisher: Springer
Release Date : 2004-08-17
Primality Testing In Polynomial Time written by Martin Dietzfelbinger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-17 with Mathematics categories.
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.
Primality Testing In Polynomial Time
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Author : Martin Dietzfelbinger
language : en
Publisher:
Release Date : 2014-01-15
Primality Testing In Polynomial Time written by Martin Dietzfelbinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Interactive Theorem Proving
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Author : Christian Urban
language : en
Publisher: Springer
Release Date : 2015-08-18
Interactive Theorem Proving written by Christian Urban and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-18 with Mathematics categories.
This book constitutes the proceedings of the 6th International Conference on Interactive Theorem Proving, ITP 2015, held in Nanjing, China, in August 2015. The 27 papers presented in this volume were carefully reviewed and selected from 54 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematics.
Primality Testing For Beginners
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Author : Lasse Rempe-Gillen
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-11
Primality Testing For Beginners written by Lasse Rempe-Gillen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
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.
The Riemann Hypothesis
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Author : Peter B. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
The Riemann Hypothesis written by Peter B. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Randomized Algorithms
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Author : Rajeev Motwani
language : en
Publisher: Cambridge University Press
Release Date : 1995-08-25
Randomized Algorithms written by Rajeev Motwani and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-25 with Computers categories.
This book presents basic tools from probability theory used in algorithmic applications, with concrete examples.
Primality Testing And Integer Factorization In Public Key Cryptography
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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Primality Testing And Integer Factorization In Public Key Cryptography written by Song Y. Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Computers categories.
Intended for advanced level students in computer science and mathematics, this key text, now in a brand new edition, provides a survey of recent progress in primality testing and integer factorization, with implications for factoring based public key cryptography. For this updated and revised edition, notable new features include a comparison of the Rabin-Miller probabilistic test in RP, the Atkin-Morain elliptic curve test in ZPP and the AKS deterministic test.
Prime Numbers
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Author : Richard Crandall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-07
Prime Numbers written by Richard Crandall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-07 with Mathematics categories.
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
Quantum Computing Since Democritus
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Author : Scott Aaronson
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-14
Quantum Computing Since Democritus written by Scott Aaronson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Computers categories.
Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics.