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Author : Vassil Dimitrov
Publisher :
ISBN 13 : 9789512245598
Total Pages : 74 pages
Book Rating : 4.2/5 (455 download)
Download or read book Number Theory and Its Applications in Digital Signal Processing and Cryptography written by Vassil Dimitrov and published by . This book was released on 1999 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vassil Dimitrov
Publisher : CRC Press
ISBN 13 : 1351833669
Total Pages : 304 pages
Book Rating : 4.3/5 (518 download)
Download or read book Multiple-Base Number System written by Vassil Dimitrov and published by CRC Press. This book was released on 2017-12-19 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer arithmetic has become so fundamentally embedded into digital design that many engineers are unaware of the many research advances in the area. As a result, they are losing out on emerging opportunities to optimize its use in targeted applications and technologies. In many cases, easily available standard arithmetic hardware might not necessarily be the most efficient implementation strategy. Multiple-Base Number System: Theory and Applications stands apart from the usual books on computer arithmetic with its concentration on the uses and the mathematical operations associated with the recently introduced multiple-base number system (MBNS). The book identifies and explores several diverse and never-before-considered MBNS applications (and their implementation issues) to enhance computation efficiency, specifically in digital signal processing (DSP) and public key cryptography. Despite the recent development and increasing popularity of MBNS as a specialized tool for high-performance calculations in electronic hardware and other fields, no single text has compiled all the crucial, cutting-edge information engineers need to optimize its use. The authors’ main goal was to disseminate the results of extensive design research—including much of their own—to help the widest possible audience of engineers, computer scientists, and mathematicians. Dedicated to helping readers apply discoveries in advanced integrated circuit technologies, this single reference is packed with a wealth of vital content previously scattered throughout limited-circulation technical and mathematical journals and papers—resources generally accessible only to researchers and designers working in highly specialized fields. Leveling the informational playing field, this resource guides readers through an in-depth analysis of theory, architectural techniques, and the latest research on the subject, subsequently laying the groundwork users require to begin applying MBNS.
Author : Manfred Schroeder
Publisher : Springer Science & Business Media
ISBN 13 : 3540852972
Total Pages : 424 pages
Book Rating : 4.5/5 (48 download)
Download or read book Number Theory in Science and Communication written by Manfred Schroeder and published by Springer Science & Business Media. This book was released on 2008-11-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner
Author : Manfred R. Schroeder
Publisher : Springer Science & Business Media
ISBN 13 : 3662023954
Total Pages : 340 pages
Book Rating : 4.6/5 (62 download)
Download or read book Number Theory in Science and Communication written by Manfred R. Schroeder and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Beauty is the first test: there is no permanent place in the world for ugly mathematics. " - G. H. Hardy N umber theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science. "Mathematics is the queen of sciences - and number theory is the queen of mathematics," according to Carl Friedrich Gauss, the lifelong Wunderkind, who hirnself enjoyed the epithet "Princeps Mathematicorum. " What could be more beautiful than a deep, satisfying relation between whole numbers. {One is almost tempted to call them wholesome numbersJ In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the "untouched ones". How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex number- whose first names virtually exude unsavory involvement with the complex realities of everyday life! Yet, as we shall see in this book, the theory of integers can provide totally unexpected answers to real-world problems. In fact, discrete mathematics is ta king on an ever more important role. If nothing else, the advent of the digital computer and digital communication has seen to that. But even earlier, in physics the emergence of quantum mechanics and discrete elementary particles put a premium on the methods and, indeed, the spirit of discrete mathematics.
Author : M.R. Schroeder
Publisher : Springer Science & Business Media
ISBN 13 : 3540265988
Total Pages : 390 pages
Book Rating : 4.5/5 (42 download)
Download or read book Number Theory in Science and Communication written by M.R. Schroeder and published by Springer Science & Business Media. This book was released on 2006-01-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory in Science and Communication introductes non-mathematicians to the fascinating and diverse applications of number theory. This best-selling book stresses intuitive understanding rather than abstract theory. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.
Author : Richard A. Mollin
Publisher : CRC Press
ISBN 13 : 1420066617
Total Pages : 382 pages
Book Rating : 4.4/5 (2 download)
Download or read book Fundamental Number Theory with Applications written by Richard A. Mollin and published by CRC Press. This book was released on 2008-02-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
Author : Amos R. Omondi
Publisher : Imperial College Press
ISBN 13 : 1860948677
Total Pages : 311 pages
Book Rating : 4.8/5 (69 download)
Download or read book Residue Number Systems written by Amos R. Omondi and published by Imperial College Press. This book was released on 2007 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great deal of computing now takes place in embedded processors, such as those found in mobile devices, for which high speed and low-power consumption are critical; the absence of carry propagation facilitates the realization of high-speed, low-power arithmetic. Second, computer chips are now getting to be so dense that full testing will no longer be possible; so fault tolerance and the general area of computational integrity have become more important. RNSs are extremely good for applications such as digital signal processing, communications engineering, computer security (cryptography), image processing, speech processing, and transforms, all of which are extremely important in computing today. This book provides an up-to-date account of RNSs and arithmetic. It covers the underlying mathematical concepts of RNSs; the conversion between conventional number systems and RNSs; the implementation of arithmetic operations; various related applications are also introduced. In addition, numerous detailed examples and analysis of different implementations are provided. Sample Chapter(s). Chapter 1: Introduction (301 KB). Contents: Introduction; Mathematical Fundamentals; Forward Conversion; Addition; Multiplication; Comparison, Overflow-Detection, Sign-Determination, Scaling, and Division; Reverse Conversion; Applications. Readership: Graduate students, academics and researchers in computer engineering and electrical & electronic engineering.
Author : Kenneth H. Rosen
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 572 pages
Book Rating : 4.3/5 (91 download)
Download or read book Elementary Number Theory and Its Applications written by Kenneth H. Rosen and published by Addison Wesley Publishing Company. This book was released on 1993 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: New edition of a standard text. Integrates classical material with applications to cryptography and computer science. The author is with AT&T Bell Labs. Annotation copyright Book News, Inc. Portland, Or.
Author : S.D. Adhikari
Publisher : Springer
ISBN 13 : 9386279460
Total Pages : 285 pages
Book Rating : 4.3/5 (862 download)
Download or read book Number Theory and Applications written by S.D. Adhikari and published by Springer. This book was released on 2009-06-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.
Author : Igor Shparlinski
Publisher : Birkhäuser
ISBN 13 : 3034880375
Total Pages : 402 pages
Book Rating : 4.0/5 (348 download)
Download or read book Cryptographic Applications of Analytic Number Theory written by Igor Shparlinski and published by Birkhäuser. This book was released on 2013-03-07 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces new techniques that imply rigorous lower bounds on the com plexity of some number-theoretic and cryptographic problems. It also establishes certain attractive pseudorandom properties of various cryptographic primitives. These methods and techniques are based on bounds of character sums and num bers of solutions of some polynomial equations over finite fields and residue rings. Other number theoretic techniques such as sieve methods and lattice reduction algorithms are used as well. The book also contains a number of open problems and proposals for further research. The emphasis is on obtaining unconditional rigorously proved statements. The bright side of this approach is that the results do not depend on any assumptions or conjectures. On the downside, the results are much weaker than those which are widely believed to be true. We obtain several lower bounds, exponential in terms of logp, on the degrees and orders of o polynomials; o algebraic functions; o Boolean functions; o linear recurrence sequences; coinciding with values of the discrete logarithm modulo a prime p at sufficiently many points (the number of points can be as small as pI/2+O:). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the rightmost bit of the discrete logarithm and defines whether the argument is a quadratic residue.
Author : Hari Krishna
Publisher : CRC Press
ISBN 13 : 9780849371776
Total Pages : 352 pages
Book Rating : 4.3/5 (717 download)
Download or read book Computational Number Theory and Digital Signal Processing written by Hari Krishna and published by CRC Press. This book was released on 1994-08-16 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Military service involves exposure to multiple sources of chronic, acute, and potentially traumatic stress, especially during deployment and combat. Notoriously variable, the effects of stress can be subtle to severe, immediate or delayed, impairing individual and group readiness, operational performance, and—ultimately—survival. A comprehensive compilation on the state of the science, Biobehavioral Resilience to Stress identifies key factors and characteristics that are essential to a scientifically useful and behaviorally predictive understanding of resilience to stress. Contributions from Uniquely Qualified Military and Civilian Experts Initiated by the Military Operational Medicine Research Directorate of the US Army Medical Research and Material Command (USAMRMC), this seminal volume integrates recent research and experience from military and civilian experts in behavioral and social sciences, human performance, and physiology. Each chapter is grounded in vigorous research with emphasis on relevance to a variety of real-world operations and settings, including extreme environments encountered in modern war. Logical Progression, Cross-Disciplinary Appeal Organized into four sections, the text begins with a discussion of the relevant aspects of stress in the context of military life to offer civilian readers a window into contemporary military priorities. Later chapters consider biological, physiological, and genetic factors, psychosocial aspects of resilience, and “community capacity” variables that influence psychological responses to stressful events. This multidisciplinary effort concludes with an overview of emergent themes and related issues to advance the science of resilience toward predictive research, theory, and application for all those—military and civilian—who serve in the national defense.
Author : Manfred R. Schroeder
Publisher : Springer Science & Business Media
ISBN 13 : 9783540158004
Total Pages : 374 pages
Book Rating : 4.1/5 (58 download)
Download or read book Number Theory in Science and Communication written by Manfred R. Schroeder and published by Springer Science & Business Media. This book was released on 1990 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates the application of Number Theory to practical problems in physics, digital information processing. computing, cryptography, acoustics, crystallography (quasicrystals), fractals and self-similarity. Its aim is to widen the horizon of readers with a minimum of mathematicasl training to the basic facts of number theory. The otpics treated informally, stressing intuition rather then formal proofs. The book demonstrates that there are a surprising numbe rof applications of a field which is tradiationally considered raterh abstract, and from this realization readers are led to a depp appreciation of tzhe usefulness of finite mathematics and its multi-faeted interactions with the real world. The Second Edition includes much new material on self-similarity, factals, quasicrystals, Cantor sets, Hausdorff dimensions, detemrinicstic chaos, errof-free computation, spread-spectrum communication systems, optimal ambiguity functions for radar and sonar, and Fibonacci numbers. From the reviews "A lighthearted and readable volume with a wide range of applications to which the author has been a pA1/4roductive contributor - useful mathematics given outside the formalities of theorem and proof. Philip Morrison - Scientific American NTS***
Author : Song Y. Yan
Publisher : Springer Science & Business Media
ISBN 13 : 366204773X
Total Pages : 454 pages
Book Rating : 4.6/5 (62 download)
Download or read book Number Theory for Computing written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.
Author : Marty Lewinter
Publisher : John Wiley & Sons
ISBN 13 : 1119062764
Total Pages : 240 pages
Book Rating : 4.1/5 (19 download)
Download or read book Elementary Number Theory with Programming written by Marty Lewinter and published by John Wiley & Sons. This book was released on 2015-06-02 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area. Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes: Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor’s Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.
Author : Hailong Li
Publisher : World Scientific Publishing Company
ISBN 13 : 9813231610
Total Pages : 289 pages
Book Rating : 4.8/5 (132 download)
Download or read book Number Theory And Its Applications Ii written by Hailong Li and published by World Scientific Publishing Company. This book was released on 2017-11-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of practical examples and worked-out exercises, and the scope ranging from these basic subjects made applicable to number-theoretic settings to advanced number theory, this book can then be read without tears. It will be of immense help to the reader to acquire basic sound skills in number theory and its applications.Number theory used to be described as the queen of mathematics, that is, there is no practical use. However, with the development of computers and the security of internet communications, the importance of number theory has been exponentially increasing daily. The raison d'être of the present book in this situation is that it is extremely reader-friendly while keeping the rigor of serious mathematics and in-depth analysis of practical applications to various subjects including control theory and pseudo-random number generation. The use of operators is prevailing rather abundantly in anticipation of applications to electrical engineering, allowing the reader to master these skills without much difficulty. It also delivers a very smooth bridging between elementary subjects including linear algebra and group theory (and algebraic number theory) for the reader to be well-versed in an efficient and effortless way. One of the main features of the book is that it gives several different approaches to the same topic, helping the reader to gain deeper insight and comprehension. Even just browsing through the materials would be beneficial to the reader.
Author : Michal Křížek
Publisher : Springer Nature
ISBN 13 : 3030838994
Total Pages : 342 pages
Book Rating : 4.0/5 (38 download)
Download or read book From Great Discoveries in Number Theory to Applications written by Michal Křížek and published by Springer Nature. This book was released on 2021-09-21 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Author : Thomas W. Cusick
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444516312
Total Pages : 502 pages
Book Rating : 4.5/5 (163 download)
Download or read book Stream Ciphers and Number Theory written by Thomas W. Cusick and published by Gulf Professional Publishing. This book was released on 2004-02-17 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields. · Unique book on interactions of stream ciphers and number theory. · Research monograph with many results not available elsewhere. · A revised edition with the most recent advances in this subject. · Over thirty research problems for stimulating interactions between the two areas. · Written by leading researchers in stream ciphers and number theory.
