Coding Theory and Cryptography

The Essentials, Second Edition

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Author: D.C. Hankerson,Gary Hoffman,D.A. Leonard,Charles C. Lindner,K.T. Phelps,C.A. Rodger,J.R. Wall

Publisher: CRC Press

ISBN: 0824704657

Category: Computers

Page: 368

View: 8288

Containing data on number theory, encryption schemes, and cyclic codes, this highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an "easy-to-use" manner appropriate for students with only a basic background in mathematics offering revised and updated material on the Berlekamp-Massey decoding algorithm and convolutional codes. Introducing the mathematics as it is needed and providing exercises with solutions, this edition includes an extensive section on cryptography, designed for an introductory course on the subject.

Universal Algebra

Fundamentals and Selected Topics

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Author: Clifford Bergman

Publisher: CRC Press

ISBN: 1439851298

Category: Computers

Page: 320

View: 4085

Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.

Advanced Calculus of a Single Variable

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Author: Tunc Geveci

Publisher: Springer

ISBN: 331927807X

Category: Mathematics

Page: 382

View: 3438

This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.

Handbook of Graph Drawing and Visualization

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Author: Roberto Tamassia

Publisher: CRC Press

ISBN: 1420010263

Category: Mathematics

Page: 862

View: 2146

Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications The Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references. The first several chapters of the book deal with fundamental topological and geometric concepts and techniques used in graph drawing, such as planarity testing and embedding, crossings and planarization, symmetric drawings, and proximity drawings. The following chapters present a large collection of algorithms for constructing drawings of graphs, including tree, planar straight-line, planar orthogonal and polyline, spine and radial, circular, rectangular, hierarchical, and three-dimensional drawings as well as labeling algorithms, simultaneous embeddings, and force-directed methods. The book then introduces the GraphML language for representing graphs and their drawings and describes three software systems for constructing drawings of graphs: OGDF, GDToolkit, and PIGALE. The final chapters illustrate the use of graph drawing methods in visualization applications for biological networks, computer security, data analytics, education, computer networks, and social networks. Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.

Algebraic Aspects of Cryptography

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Author: Neal Koblitz

Publisher: Springer Science & Business Media

ISBN: 3662036428

Category: Computers

Page: 206

View: 1668

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

Cryptography Made Simple

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Author: Nigel Smart

Publisher: Springer

ISBN: 3319219367

Category: Computers

Page: 481

View: 7179

In this introductory textbook the author explains the key topics in cryptography. He takes a modern approach, where defining what is meant by "secure" is as important as creating something that achieves that goal, and security definitions are central to the discussion throughout. The author balances a largely non-rigorous style — many proofs are sketched only — with appropriate formality and depth. For example, he uses the terminology of groups and finite fields so that the reader can understand both the latest academic research and "real-world" documents such as application programming interface descriptions and cryptographic standards. The text employs colour to distinguish between public and private information, and all chapters include summaries and suggestions for further reading. This is a suitable textbook for advanced undergraduate and graduate students in computer science, mathematics and engineering, and for self-study by professionals in information security. While the appendix summarizes most of the basic algebra and notation required, it is assumed that the reader has a basic knowledge of discrete mathematics, probability, and elementary calculus.

Design Theory, Second Edition

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Author: Charles C. Lindner,Christopher A. Rodger

Publisher: CRC Press

ISBN: 9781420082975

Category: Mathematics

Page: 272

View: 8162

Design Theory, Second Edition presents some of the most important techniques used for constructing combinatorial designs. It augments the descriptions of the constructions with many figures to help students understand and enjoy this branch of mathematics. This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs. The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems. By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs.

An Introduction To Chaotic Dynamical Systems

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Author: Robert Devaney

Publisher: CRC Press

ISBN: 0429981937

Category: Science

Page: 360

View: 4745

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.

An Introduction to Cryptography, Second Edition

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Author: Richard A. Mollin

Publisher: CRC Press

ISBN: 1420011243

Category: Mathematics

Page: 413

View: 539

Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field. With numerous additions and restructured material, this edition presents the ideas behind cryptography and the applications of the subject. The first chapter provides a thorough treatment of the mathematics necessary to understand cryptography, including number theory and complexity, while the second chapter discusses cryptographic fundamentals, such as ciphers, linear feedback shift registers, modes of operation, and attacks. The next several chapters discuss DES, AES, public-key cryptography, primality testing, and various factoring methods, from classical to elliptical curves. The final chapters are comprised of issues pertaining to the Internet, such as pretty good privacy (PGP), protocol layers, firewalls, and cookies, as well as applications, including login and network security, viruses, smart cards, and biometrics. The book concludes with appendices on mathematical data, computer arithmetic, the Rijndael S-Box, knapsack ciphers, the Silver-Pohlig-Hellman algorithm, the SHA-1 algorithm, radix-64 encoding, and quantum cryptography. New to the Second Edition: An introductory chapter that provides more information on mathematical facts and complexity theory Expanded and updated exercises sets, including some routine exercises More information on primality testing and cryptanalysis Accessible and logically organized, An Introduction to Cryptography, Second Edition is the essential book on the fundamentals of cryptography.

Coding Theory

The Essentials

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Author: D. G. Hoffman

Publisher: N.A

ISBN: 9780824786113

Category: Coding theory

Page: 277

View: 8342

A textbook for a two-quarter college course in coding theory for students of engineering, computer science, and mathematics, assuming only a good grounding in linear algebra. Unlike texts designed for mathematics majors, omits the general mathematic theories, and introduces the necessary mathematics

Extending the Frontiers of Mathematics

Inquiries Into Proof and Argumentation

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Author: Edward B. Burger

Publisher: Key College Pub

ISBN: N.A

Category: Computers

Page: 171

View: 7665

This book leads students to develop a mature process that will serve them throughout their professional careers, whether inside or outside of mathematics. Its inquiry-based approach to the foundations of mathematics promotes exploration of proofs and other advanced mathematical ideas. The book uses puzzles and patterns, teaches the "prove and extend or disprove and salvage" approach to problems and proofs, and builds mathematical challenge on challenge to boost skills.

Modern Cryptography: Applied Mathematics for Encryption and Information Security

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Author: Chuck Easttom

Publisher: McGraw Hill Professional

ISBN: 1259588092

Category: Computers

Page: 608

View: 7859

This comprehensive guide to modern data encryption makes cryptography accessible to information security professionals of all skill levels—with no math expertise required Cryptography underpins today’s cyber-security; however, few information security professionals have a solid understanding of these encryption methods due to their complex mathematical makeup. Modern Cryptography: Applied Mathematics for Encryption and Information Security leads readers through all aspects of the field, providing a comprehensive overview of cryptography and practical instruction on the latest encryption methods. The book begins with an overview of the evolution of cryptography and moves on to modern protocols with a discussion of hashes, cryptanalysis, and steganography. From there, seasoned security author Chuck Easttom provides readers with the complete picture—full explanations of real-world applications for cryptography along with detailed implementation instructions. Unlike similar titles on the topic, this reference assumes no mathematical expertise—the reader will be exposed to only the formulas and equations needed to master the art of cryptography. Concisely explains complex formulas and equations and makes the math easy Teaches even the information security novice critical encryption skills Written by a globally-recognized security expert who has taught cryptography to various government and civilian groups and organizations around the world

Differential Equations

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Author: Paul Blanchard,Robert L. Devaney,Glen R. Hall

Publisher: Cengage Learning

ISBN: 1133388086

Category: Mathematics

Page: 864

View: 5519

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

A Student's Guide to Coding and Information Theory

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Author: Stefan M. Moser,Po-Ning Chen

Publisher: Cambridge University Press

ISBN: 1107601967

Category: Technology & Engineering

Page: 206

View: 923

A concise, easy-to-read guide, introducing beginners to the engineering background of modern communication systems, from mobile phones to data storage. Assuming only basic knowledge of high-school mathematics and including many practical examples and exercises to aid understanding, this is ideal for anyone who needs a quick introduction to the subject.

MATLAB Primer

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Author: Kermit Sigmon,Timothy A. Davis

Publisher: CRC Press

ISBN: 9781420034950

Category: Mathematics

Page: 232

View: 2121

With the spread of the powerhouse MATLAB® software into nearly every area of math, science, and engineering, it is important to have a strong introduction to using the software. Updated for version 7.0, MATLAB® Primer, Seventh Edition offers such an introduction as well as a "pocketbook" reference for everyday users of the software. It offers an intuitive language for expressing problems and solutions both numerically and graphically. The latest edition in this best-selling series, MATLAB® Primer, Seventh Edition incorporates a number of enhancements such as changes to the desktop, new features for developing M-files, the JIT accelerator, and an easier way of importing Java classes. In addition to the features new to version 7.0, this book includes: A new section on M-Lint, the new debugger for M-files A new chapter on calling Java from MATLAB and using Java objects inside the MATLAB workspace A new chapter on calling Fortran from MATLAB A new chapter on solving equations: symbolic and numeric polynomials, nonlinear equations, and differential equations A new chapter on cell publishing, which replaces the "notebook" feature and allows the creation of Word, LaTeX, PowerPoint, and HTML documents with executable MATLAB commands and their outputs Expanded Graphics coverage-including the 3D parametrically defined seashells on the front and back covers Whether you are new to MATLAB, new to version 7.0, or simply in need of a hands-on, to-the-point reference, MATLAB® Primer provides the tools you need in a conveniently sized, economically priced pocketbook.

Applied Mathematical Modeling

A Multidisciplinary Approach

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Author: Douglas R. Shier,K.T. Wallenius

Publisher: CRC Press

ISBN: 9781420050042

Category: Mathematics

Page: 472

View: 5796

The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines. The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in practice. These chapters discuss the general components of the modeling process, and the evolutionary nature of successful model building. The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects. In keeping with the multidimensional nature of the models presented, the chapters in the second part are listed in alphabetical order by the contributor's last name. Unlike most mathematical books, in which you must master the concepts of early chapters to prepare for subsequent material, you may start with any chapter. Begin with cryptology, if that catches your fancy, or go directly to bursty traffic if that is your cup of tea. Applied Mathematical Modeling serves as a handbook of in-depth case studies that span the mathematical sciences, building upon a modest mathematical background. Readers in other applied disciplines will benefit from seeing how selected mathematical modeling philosophies and techniques can be brought to bear on problems in their disciplines. The models address actual situations studied in chemistry, physics, demography, economics, civil engineering, environmental engineering, industrial engineering, telecommunications, and other areas.

An Introduction to Mathematical Cryptography

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Author: Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman

Publisher: Springer

ISBN: 1493917110

Category: Mathematics

Page: 538

View: 6978

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

The Porous Medium Equation

Mathematical Theory

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Author: Juan Luis Vazquez

Publisher: Oxford University Press

ISBN: 0198569033

Category: Mathematics

Page: 624

View: 4845

Aimed at research students and academics in mathematics and engineering, as well as engineering specialists, this book provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation.