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Primality Testing in Polynomial Time

Primality Testing in Polynomial Time Author Martin Dietzfelbinger
ISBN-10 9783540403449
Release 2004-06-29
Pages 147
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On August 6, 2002,a paper with the title “PRIMES is in P”, by M. Agrawal, N. Kayal, and N. Saxena, appeared on the website of the Indian Institute of Technology at Kanpur, India. In this paper it was shown that the “primality problem”hasa“deterministic algorithm” that runs in “polynomial time”. Finding out whether a given number n is a prime or not is a problem that was formulated in ancient times, and has caught the interest of mathema- ciansagainandagainfor centuries. Onlyinthe 20thcentury,with theadvent of cryptographic systems that actually used large prime numbers, did it turn out to be of practical importance to be able to distinguish prime numbers and composite numbers of signi?cant size. Readily, algorithms were provided that solved the problem very e?ciently and satisfactorily for all practical purposes, and provably enjoyed a time bound polynomial in the number of digits needed to write down the input number n. The only drawback of these algorithms is that they use “randomization” — that means the computer that carries out the algorithm performs random experiments, and there is a slight chance that the outcome might be wrong, or that the running time might not be polynomial. To ?nd an algorithmthat gets by without rand- ness, solves the problem error-free, and has polynomial running time had been an eminent open problem in complexity theory for decades when the paper by Agrawal, Kayal, and Saxena hit the web.



Design and Analysis of Randomized Algorithms

Design and Analysis of Randomized Algorithms Author J. Hromkovic
ISBN-10 9783540239499
Release 2005-06-14
Pages 277
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Systematically teaches key paradigmic algorithm design methods Provides a deep insight into randomization



Interactive Theorem Proving

Interactive Theorem Proving Author Christian Urban
ISBN-10 9783319221021
Release 2015-08-18
Pages 469
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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.



Algorithmic Adventures

Algorithmic Adventures Author Juraj Hromkovič
ISBN-10 9783540859864
Release 2009-06-22
Pages 363
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The ?rst and foremost goal of this lecture series was to show the beauty, depth and usefulness of the key ideas in computer science. While working on the lecture notes, we came to understand that one can recognize the true spirit of a scienti?c discipline only by viewing its contributions in the framework of science as a whole. We present computer science here as a fundamental science that, interacting with other scienti?c disciplines, changed and changes our view on the world, that contributes to our understanding of the fundamental concepts of science and that sheds new light on and brings new meaning to several of these concepts. We show that computer science is a discipline that discovers spectacular, unexpected facts, that ?nds ways out in seemingly unsolvable s- uations, and that can do true wonders. The message of this book is that computer science is a fascinating research area with a big impact on the real world, full of spectacular ideas and great ch- lenges. It is an integral part of science and engineering with an above-average dynamic over the last 30 years and a high degree of interdisciplinarity. The goal of this book is not typical for popular science writing, whichoftenrestrictsitselftooutliningtheimportanceofaresearch area. Whenever possible we strive to bring full understanding of the concepts and results presented.



The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic Author
ISBN-10 UCSD:31822036000701
Release 2006
Pages
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Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UOM:39015078588616
Release 2007
Pages
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The British National Bibliography

The British National Bibliography Author Arthur James Wells
ISBN-10 UOM:39015057956560
Release 2004
Pages
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Codes and Cryptography

Codes and Cryptography Author Dominic Welsh
ISBN-10 0198532873
Release 1988
Pages 257
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This textbook unifies the concepts of information, codes and cryptography as first considered by Shannon in his seminal papers on communication and secrecy systems. The book has been the basis of a very popular course in Communication Theory which the author has given over several years toundergraduate mathematicians and computer scientists at Oxford. The first five chapters of the book cover the fundamental ideas of information theory, compact encoding of messages, and an introduction to the theory of error-correcting codes. After a discussion of mathematical models of English, there is an introduction to the classical Shannon model ofcryptography. This is followed by a brief survey of those aspects of computational complexity needed for an understanding of modern cryptography, password systems and authentication techniques. Because the aim of the text is to make this exciting branch of modern applied mathematics available to readers with a wide variety of interests and backgrounds, the mathematical prerequisites have been kept to an absolute minimum. In addition to an extensive bibliography there are many exercises(easy) and problems together with solutions.



User s Guide to Cryptography and Standards

User s Guide to Cryptography and Standards Author Alexander W. Dent
ISBN-10 1580535305
Release 2005
Pages 382
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With the scope and frequency of attacks on valuable corporate data growing enormously in recent years, a solid understanding of cryptography is essential for anyone working in the computer/network security field. This timely book delivers the hands-on knowledge you need, offering comprehensive coverage on the latest and most-important standardized cryptographic techniques to help you protect your data and computing resources to the fullest. Rather than focusing on theory like other books on the market, this unique resource describes cryptography from an end-user perspective, presenting in-depth, highly practical comparisons of standards and techniques.



Primality testing and Abelian varieties over finite fields

Primality testing and Abelian varieties over finite fields Author Leonard M. Adleman
ISBN-10 UOM:39015028426131
Release 1992
Pages 142
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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.



A Computational Introduction to Number Theory and Algebra

A Computational Introduction to Number Theory and Algebra Author Victor Shoup
ISBN-10 0521851548
Release 2005-04-28
Pages 517
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This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.



STOC 06

STOC 06 Author ACM Special Interest Group for Algorithms and Computation Theory
ISBN-10 UCSC:32106018416344
Release 2006
Pages 768
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Reviews in Number Theory 1984 96

Reviews in Number Theory  1984 96 Author
ISBN-10 0821809369
Release 1997-01-01
Pages 764
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These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.



Proceedings of the ACM Symposium on Theory of Computing

Proceedings of the    ACM Symposium on Theory of Computing Author
ISBN-10 0897912217
Release 1987
Pages 471
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Philosophical Transactions Giving Some Accompt of the Present Undertakings Studies and Labours of the Ingenious in Many Considerable Parts of the World

Philosophical Transactions  Giving Some Accompt of the Present Undertakings  Studies  and Labours of the Ingenious in Many Considerable Parts of the World Author Royal Society (Great Britain)
ISBN-10 CHI:40314716
Release 1735
Pages
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Philosophical Transactions Giving Some Accompt of the Present Undertakings Studies and Labours of the Ingenious in Many Considerable Parts of the World has been writing in one form or another for most of life. You can find so many inspiration from Philosophical Transactions Giving Some Accompt of the Present Undertakings Studies and Labours of the Ingenious in Many Considerable Parts of the World also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Philosophical Transactions Giving Some Accompt of the Present Undertakings Studies and Labours of the Ingenious in Many Considerable Parts of the World book for free.



EURO PAR Parallel Processing

EURO PAR     Parallel Processing Author Patrick Amestoy
ISBN-10 UOM:39015048114931
Release 1999
Pages
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Art of Computer Programming Volume 2

Art of Computer Programming  Volume 2 Author Donald E. Knuth
ISBN-10 9780321635761
Release 2014-05-06
Pages 784
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The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming. —Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. —Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. —Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. —Jonathan Laventhol The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series.