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An Exposition Of The Deterministic Polynomial Time Primality Testing Algorithm Of Agrawal Kayal Saxena
Download An Exposition Of The Deterministic Polynomial Time Primality Testing Algorithm Of Agrawal Kayal Saxena full books in PDF, epub, and Kindle. Read online An Exposition Of The Deterministic Polynomial Time Primality Testing Algorithm Of Agrawal Kayal Saxena ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Introduction to Modern Number Theory by : Yu. I. Manin
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.
Book Synopsis The Mathematics of Encryption by : Margaret Cozzens
Download or read book The Mathematics of Encryption written by Margaret Cozzens and published by American Mathematical Soc.. This book was released on 2013-09-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.
Book Synopsis Solving Polynomial Equation Systems I by : Teo Mora
Download or read book Solving Polynomial Equation Systems I written by Teo Mora and published by Cambridge University Press. This book was released on 2003-03-27 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational algebra; computational number theory; commutative algebra; handbook; reference; algorithmic; modern.
Book Synopsis Interactive Theorem Proving by : Christian Urban
Download or read book Interactive Theorem Proving written by Christian Urban and published by Springer. This book was released on 2015-08-18 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cryptography by : Douglas R. Stinson
Download or read book Cryptography written by Douglas R. Stinson and published by CRC Press. This book was released on 2005-11-01 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE LEGACY... First introduced in 1995, Cryptography: Theory and Practice garnered enormous praise and popularity, and soon became the standard textbook for cryptography courses around the world. The second edition was equally embraced, and enjoys status as a perennial bestseller. Now in its third edition, this authoritative text continues to provide a solid foundation for future breakthroughs in cryptography. WHY A THIRD EDITION? The art and science of cryptography has been evolving for thousands of years. Now, with unprecedented amounts of information circling the globe, we must be prepared to face new threats and employ new encryption schemes on an ongoing basis. This edition updates relevant chapters with the latest advances and includes seven additional chapters covering: Pseudorandom bit generation in cryptography Entity authentication, including schemes built from primitives and special purpose "zero-knowledge" schemes Key establishment including key distribution and protocols for key agreement, both with a greater emphasis on security models and proofs Public key infrastructure, including identity-based cryptography Secret sharing schemes Multicast security, including broadcast encryption and copyright protection THE RESULT... Providing mathematical background in a "just-in-time" fashion, informal descriptions of cryptosystems along with more precise pseudocode, and a host of numerical examples and exercises, Cryptography: Theory and Practice, Third Edition offers comprehensive, in-depth treatment of the methods and protocols that are vital to safeguarding the mind-boggling amount of information circulating around the world.
Book Synopsis Cryptography by : Douglas Robert Stinson
Download or read book Cryptography written by Douglas Robert Stinson and published by CRC Press. This book was released on 2018-08-14 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through three editions, Cryptography: Theory and Practice, has been embraced by instructors and students alike. It offers a comprehensive primer for the subject’s fundamentals while presenting the most current advances in cryptography. The authors offer comprehensive, in-depth treatment of the methods and protocols that are vital to safeguarding the seemingly infinite and increasing amount of information circulating around the world. Key Features of the Fourth Edition: New chapter on the exciting, emerging new area of post-quantum cryptography (Chapter 9). New high-level, nontechnical overview of the goals and tools of cryptography (Chapter 1). New mathematical appendix that summarizes definitions and main results on number theory and algebra (Appendix A). An expanded treatment of stream ciphers, including common design techniques along with coverage of Trivium. Interesting attacks on cryptosystems, including: padding oracle attack correlation attacks and algebraic attacks on stream ciphers attack on the DUAL-EC random bit generator that makes use of a trapdoor. A treatment of the sponge construction for hash functions and its use in the new SHA-3 hash standard. Methods of key distribution in sensor networks. The basics of visual cryptography, allowing a secure method to split a secret visual message into pieces (shares) that can later be combined to reconstruct the secret. The fundamental techniques cryptocurrencies, as used in Bitcoin and blockchain. The basics of the new methods employed in messaging protocols such as Signal, including deniability and Diffie-Hellman key ratcheting.
Book Synopsis Finite Fields, with Applications to Combinatorics by : Kannan Soundararajan
Download or read book Finite Fields, with Applications to Combinatorics written by Kannan Soundararajan and published by American Mathematical Society. This book was released on 2022-11-09 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Book Synopsis The Art of Computer Programming by : Donald E. Knuth
Download or read book The Art of Computer Programming written by Donald E. Knuth and published by Addison-Wesley Professional. This book was released on 2014-05-06 with total page 1092 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP),http://msp.org
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 The Riemann Hypothesis by : Peter Borwein
Download or read book The Riemann Hypothesis written by Peter Borwein and published by Springer Science & Business Media. This book was released on 2007-11-21 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.
Book Synopsis Proceedings of the ...ACM Symposium on Theory of Computing by :
Download or read book Proceedings of the ...ACM Symposium on Theory of Computing written by and published by . This book was released on 2003 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Disquisitiones Arithmeticae by : Carl Friedrich Gauss
Download or read book Disquisitiones Arithmeticae written by Carl Friedrich Gauss and published by Springer. This book was released on 2018-02-07 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
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 Mathematics and Computation by : Avi Wigderson
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
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 Proceedings of the 35th Annual ACM Symposium on the Theory of Computing by :
Download or read book Proceedings of the 35th Annual ACM Symposium on the Theory of Computing written by and published by . This book was released on 2003 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis written by Terence Tao and published by . This book was released on 2006 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to real analysis, this text is suitable for honours undergraduates. It starts at the very beginning - the construction of the number systems and set theory, then to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.
