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Perfect Amicable And Sociable Numbers A Computational Approach
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Book Synopsis Perfect, Amicable, and Sociable Numbers by : Song Y. Yan
Download or read book Perfect, Amicable, and Sociable Numbers written by Song Y. Yan and published by World Scientific. This book was released on 1996 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about perfect, amicable and sociable numbers, with an emphasis on amicable numbers, from both a mathematical and particularly a computational point of view. Perfect and amicable numbers have been studied since antiquity, nevertheless, many problems still remain. The book introduces the basic concepts and results of perfect, amicable and sociable numbers and reviews the long history of the search for these numbers. It examines various methods, both numerical and algebraic, of generating these numbers, and also includes a set of important and interesting open problems in the area. The book is self-contained, and accessible to researchers, students, and even amateurs in mathematics and computing science. The only prerequisites are some familiarity with high-school algebra and basic computing techniques.
Book Synopsis Computational Number Theory and Modern Cryptography by : Song Y. Yan
Download or read book Computational Number Theory and Modern Cryptography written by Song Y. Yan and published by John Wiley & Sons. This book was released on 2013-01-29 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.
Book Synopsis Program of the First International Conference on Smarandache Type Notions in Number Theory (University of Craiova, 1997) by : editors C. Dumitrescu, V. Seleacu
Download or read book Program of the First International Conference on Smarandache Type Notions in Number Theory (University of Craiova, 1997) written by editors C. Dumitrescu, V. Seleacu and published by Infinite Study. This book was released on with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cybercryptography: Applicable Cryptography for Cyberspace Security by : Song Y. Yan
Download or read book Cybercryptography: Applicable Cryptography for Cyberspace Security written by Song Y. Yan and published by Springer. This book was released on 2018-12-04 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the basic theory, techniques, and algorithms of modern cryptography that are applicable to network and cyberspace security. It consists of the following nine main chapters: Chapter 1 provides the basic concepts and ideas of cyberspace and cyberspace security, Chapters 2 and 3 provide an introduction to mathematical and computational preliminaries, respectively. Chapters 4 discusses the basic ideas and system of secret-key cryptography, whereas Chapters 5, 6, and 7 discuss the basic ideas and systems of public-key cryptography based on integer factorization, discrete logarithms, and elliptic curves, respectively. Quantum-safe cryptography is presented in Chapter 8 and offensive cryptography, particularly cryptovirology, is covered in Chapter 9. This book can be used as a secondary text for final-year undergraduate students and first-year postgraduate students for courses in Computer, Network, and Cyberspace Security. Researchers and practitioners working in cyberspace security and network security will also find this book useful as a reference.
Book Synopsis An Introduction to Formal Languages and Machine Computation by : Song Y. Yan
Download or read book An Introduction to Formal Languages and Machine Computation written by Song Y. Yan and published by World Scientific. This book was released on 1998 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.
Book Synopsis Quantum Attacks on Public-Key Cryptosystems by : Song Y. Yan
Download or read book Quantum Attacks on Public-Key Cryptosystems written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cryptosystems based on the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP) and the Elliptic Curve Discrete Logarithm Problem (ECDLP) are essentially the only three types of practical public-key cryptosystems in use. The security of these cryptosystems relies heavily on these three infeasible problems, as no polynomial-time algorithms exist for them so far. However, polynomial-time quantum algorithms for IFP, DLP and ECDLP do exist, provided that a practical quantum computer exists. Quantum Attacks on Public-Key Cryptosystems presemts almost all known quantum computing based attacks on public-key cryptosystems, with an emphasis on quantum algorithms for IFP, DLP, and ECDLP. It also discusses some quantum resistant cryptosystems to replace the IFP, DLP and ECDLP based cryptosystems. This book is intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the field.
Book Synopsis Perfect And Amicable Numbers by : Elena Deza
Download or read book Perfect And Amicable Numbers written by Elena Deza and published by World Scientific. This book was released on 2023-02-10 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a detailed presentation on the theory of two classes of special numbers, perfect numbers, and amicable numbers, as well as some of their generalizations. It also gives a large list of their properties, facts and theorems with full proofs. Perfect and amicable numbers, as well as most classes of special numbers, have many interesting properties, including numerous modern and classical applications as well as a long history connected with the names of famous mathematicians.The theory of perfect and amicable numbers is a part of pure Arithmetic, and in particular a part of Divisibility Theory and the Theory of Arithmetical Functions. Thus, for a perfect number n it holds σ(n) = 2n, where σ is the sum-of-divisors function, while for a pair of amicable numbers (n, m) it holds σ(n) = σ(m) = n + m. This is also an important part of the history of prime numbers, since the main formulas that generate perfect numbers and amicable pairs are dependent on the good choice of one or several primes of special form.Nowadays, the theory of perfect and amicable numbers contains many interesting mathematical facts and theorems, alongside many important computer algorithms needed for searching for new large elements of these two famous classes of special numbers.This book contains a list of open problems and numerous questions related to generalizations of the classical case, which provides a broad perspective on the theory of these two classes of special numbers. Perfect and Amicable Numbers can be useful and interesting to both professional and general audiences.
Book Synopsis Cryptanalytic Attacks on RSA by : Song Y. Yan
Download or read book Cryptanalytic Attacks on RSA written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: RSA is a public-key cryptographic system, and is the most famous and widely-used cryptographic system in today's digital world. Cryptanalytic Attacks on RSA, a professional book, covers almost all known cryptanalytic attacks and defenses of the RSA cryptographic system and its variants. Since RSA depends heavily on computational complexity theory and number theory, background information on complexity theory and number theory is presented first, followed by an account of the RSA cryptographic system and its variants. This book is also suitable as a secondary text for advanced-level students in computer science and mathematics.
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.
Download or read book Mathematics Today written by and published by . This book was released on 1996 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 1999 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elementary Number Theory by : William A. Stein
Download or read book Elementary Number Theory written by William A. Stein and published by . This book was released on 2013 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Encyclopedia Americana by : Grolier Educational Staff
Download or read book The Encyclopedia Americana written by Grolier Educational Staff and published by Grolier. This book was released on 2001-04 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis CRC Concise Encyclopedia of Mathematics by : Eric W. Weisstein
Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Download or read book The Encyclopedia Americana written by and published by . This book was released on 2002 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopedia Americana: A to Anjou by :
Download or read book Encyclopedia Americana: A to Anjou written by and published by . This book was released on 2005 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Essentials of Programming in Mathematica® by : Paul Wellin
Download or read book Essentials of Programming in Mathematica® written by Paul Wellin and published by Cambridge University Press. This book was released on 2015-12-17 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers Mathematica® for beginners. An example-driven text covering a wide variety of applications, containing over 350 exercises with solutions available online.
