Cryptographic Applications Of Analytic Number Theory

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Cryptographic Applications of Analytic Number Theory

Igor Shparlinski
Cryptographic Applications of Analytic Number Theory Book PDF

Author : Igor Shparlinski
Publisher : Birkhäuser
Page : 402 pages
File Size : 46,7 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9783034880374

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Cryptographic Applications of Analytic Number Theory by Igor Shparlinski Pdf

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.

Cryptographic Applications of Analytic Number Theory

Igor E. Shparlinski
Cryptographic Applications of Analytic Number Theory Book PDF

Author : Igor E. Shparlinski
Publisher : Unknown
Page : 411 pages
File Size : 51,6 Mb
Release : 2003
Category : Mathematics
ISBN : 0817666540

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Cryptographic Applications of Analytic Number Theory by Igor E. Shparlinski Pdf

The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.

Cryptology and Computational Number Theory

Carl Pomerance,Shafi Goldwasser
Cryptology and Computational Number Theory Book PDF

Author : Carl Pomerance,Shafi Goldwasser
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 55,6 Mb
Release : 1990
Category : Computers
ISBN : 0821801554

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Cryptology and Computational Number Theory by Carl Pomerance,Shafi Goldwasser Pdf

In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.

Number Theory and Applications

S.D. Adhikari,B. Ramakrishnan
Number Theory and Applications Book PDF

Author : S.D. Adhikari,B. Ramakrishnan
Publisher : Springer
Page : 285 pages
File Size : 44,5 Mb
Release : 2009-06-15
Category : Mathematics
ISBN : 9789386279460

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Number Theory and Applications by S.D. Adhikari,B. Ramakrishnan Pdf

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.

An Introduction to Number Theory with Cryptography

James S. Kraft,Lawrence C. Washington
An Introduction to Number Theory with Cryptography Book PDF

Author : James S. Kraft,Lawrence C. Washington
Publisher : CRC Press
Page : 568 pages
File Size : 55,9 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781482214420

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An Introduction to Number Theory with Cryptography by James S. Kraft,Lawrence C. Washington Pdf

Number theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number

Computational Number Theory and Modern Cryptography

Song Y. Yan
Computational Number Theory and Modern Cryptography Book PDF

Author : Song Y. Yan
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 55,6 Mb
Release : 2013-01-29
Category : Computers
ISBN : 9781118188583

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Computational Number Theory and Modern Cryptography by Song Y. Yan Pdf

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.

An Introduction to Number Theory with Cryptography

James Kraft,Lawrence Washington
An Introduction to Number Theory with Cryptography Book PDF

Author : James Kraft,Lawrence Washington
Publisher : CRC Press
Page : 578 pages
File Size : 42,7 Mb
Release : 2018-01-29
Category : Computers
ISBN : 9781315161006

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An Introduction to Number Theory with Cryptography by James Kraft,Lawrence Washington Pdf

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

Elliptic Curves

Lawrence C. Washington
Elliptic Curves Book PDF

Author : Lawrence C. Washington
Publisher : Chapman and Hall/CRC
Page : 440 pages
File Size : 55,6 Mb
Release : 2003-05-28
Category : Mathematics
ISBN : 1584883650

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Elliptic Curves by Lawrence C. Washington Pdf

Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students. Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired. By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.

Number Theory in Science and Communication

Manfred Schroeder
Number Theory in Science and Communication Book PDF

Author : Manfred Schroeder
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 51,6 Mb
Release : 2008-11-06
Category : Science
ISBN : 9783540852971

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Number Theory in Science and Communication by Manfred Schroeder Pdf

"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

A Course in Number Theory and Cryptography

Neal Koblitz
A Course in Number Theory and Cryptography Book PDF

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 42,9 Mb
Release : 2012-09-05
Category : Mathematics
ISBN : 9781441985927

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Elliptic Curves

Lawrence C. Washington
Elliptic Curves Book PDF

Author : Lawrence C. Washington
Publisher : CRC Press
Page : 533 pages
File Size : 55,9 Mb
Release : 2008-04-03
Category : Computers
ISBN : 9781420071474

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Elliptic Curves by Lawrence C. Washington Pdf

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application

Fundamental Number Theory with Applications

Richard A. Mollin
Fundamental Number Theory with Applications Book PDF

Author : Richard A. Mollin
Publisher : CRC Press
Page : 472 pages
File Size : 40,5 Mb
Release : 1997-09-10
Category : Mathematics
ISBN : 0849339871

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Fundamental Number Theory with Applications by Richard A. Mollin Pdf

Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to cryptography factoring primality testing complexity analysis computer arithmetic computational number theory Fundamental Number Theory with Applications also covers: Carmichael numbers Dirichlet products Jacobsthal sums Mersenne primes perfect numbers powerful numbers self-contained numbers Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material. Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory.

A Course in Number Theory and Cryptography

Neal Koblitz
A Course in Number Theory and Cryptography Book PDF

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468403107

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. Because number theory and cryptography are fast-moving fields, this new edition contains substantial revisions and updated references.

Number Theory in Science and Communication

Manfred R. Schroeder
Number Theory in Science and Communication Book PDF

Author : Manfred R. Schroeder
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662023952

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Number Theory in Science and Communication by Manfred R. Schroeder Pdf

"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.

Number Theory in Science and Communication

M.R. Schroeder
Number Theory in Science and Communication Book PDF

Author : M.R. Schroeder
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 41,8 Mb
Release : 2006-01-06
Category : Mathematics
ISBN : 9783540265986

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Number Theory in Science and Communication by M.R. Schroeder Pdf

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.