An Introduction to Mathematical Cryptography

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

Publisher: Springer

ISBN: 1493917110

Category: Mathematics

Page: 538

View: 9764

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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.

Kryptografie verständlich

Ein Lehrbuch für Studierende und Anwender

Author: Christof Paar,Jan Pelzl

Publisher: Springer-Verlag

ISBN: 3662492970

Category: Computers

Page: 416

View: 2182

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Das Buch gibt eine umfassende Einführung in moderne angewandte Kryptografie. Es behandelt nahezu alle kryptografischen Verfahren mit praktischer Relevanz. Es werden symmetrische Verfahren (DES, AES, PRESENT, Stromchiffren), asymmetrische Verfahren (RSA, Diffie-Hellmann, elliptische Kurven) sowie digitale Signaturen, Hash-Funktionen, Message Authentication Codes sowie Schlüsselaustauschprotokolle vorgestellt. Für alle Krypto-Verfahren werden aktuelle Sicherheitseinschätzungen und Implementierungseigenschaften beschrieben.

Einführung in die Kryptographie

Author: Johannes Buchmann

Publisher: Springer-Verlag

ISBN: 3642980600

Category: Computers

Page: 234

View: 3624

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Dieses Kryptographiebuch behandelt die grundlegenden Techniken der modernen Kryptographie. Es eignet sich hervorragend für Studierende der Mathematik und der Informatik ab dem dritten Semester. Das Buch setzt nur minimale Kenntnisse voraus und vermittelt auf elementare Weise die notwendigen mathematischen Kenntnisse, insbesondere die aus der Zahlentheorie. Die Leser werden durch diese Einführung in die Lage versetzt, fortgeschrittene Literatur zur Kryptographie zu verstehen.

Komplexitätstheorie und Kryptologie

Eine Einführung in Kryptokomplexität

Author: Jörg Rothe

Publisher: Springer-Verlag

ISBN: 3540797459

Category: Computers

Page: 535

View: 5795

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Während die Kryptologie Konzepte und Methoden aus der Komplexitätstheorie verwendet, ist die Forschung in der Komplexitätstheorie wiederum oft durch Fragen aus der Kryptologie motiviert. Der Band hebt die enge Verflechtung dieser beiden Gebiete hervor und führt auf verständlicher Weise in das faszinierende Gebiet der „Kryptokomplexität" ein. Das Buch enthält zahlreiche Abbildungen und Übungsaufgaben sowie ein ausführliches Stichwort- und Literaturverzeichnis. Es eignet sich für Studierende der Informatik, Mathematik oder Ingenieurswissenschaften.

An Introduction to Cryptography

Author: Richard A. Mollin

Publisher: CRC Press

ISBN: 9781584881278

Category: Mathematics

Page: 392

View: 5180

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INTRODUCTION FOR THE UNINITIATED Heretofore, there has been no suitable introductory book that provides a solid mathematical treatment of cryptography for students with little or no background in number theory. By presenting the necessary mathematics as needed, An Introduction to Cryptography superbly fills that void. Although it is intended for the undergraduate student needing an introduction to the subject of cryptography, it contains enough optional, advanced material to challenge even the most informed reader, and provides the basis for a second course on the subject. Beginning with an overview of the history of cryptography, the material covers the basics of computer arithmetic and explores complexity issues. The author then presents three comprehensive chapters on symmetric-key cryptosystems, public-key cryptosystems, and primality testing. There is an optional chapter on four factoring methods: Pollard's p-1 method, the continued fraction algorithm, the quadratic sieve, and the number field sieve. Another optional chapter contains detailed development of elliptic curve cryptosystems, zero-knowledge, and quantum cryptography. He illustrates all methods with worked examples and includes a full, but uncluttered description of the numerous cryptographic applications. SUSTAINS INTEREST WITH ENGAGING MATERIAL Throughout the book, the author gives a human face to cryptography by including more than 50 biographies of the individuals who helped develop cryptographic concepts. He includes a number of illustrative and motivating examples, as well as optional topics that go beyond the basics presented in the core data. With an extensive index and a list of symbols for easy reference, An Introduction to Cryptography is the essential fundamental text on cryptography.

Number Theory and Geometry: An Introduction to Arithmetic Geometry

Author: Álvaro Lozano-Robledo

Publisher: American Mathematical Soc.

ISBN: 147045016X

Category: Arithmetical algebraic geometry

Page: 488

View: 1198

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Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.

Introduction to Cryptography

Author: Johannes Buchmann

Publisher: Springer Science & Business Media

ISBN: 1441990038

Category: Mathematics

Page: 338

View: 6729

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This book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. From the reviews: "Gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to all who would like to learn about cryptography." --ZENTRALBLATT MATH

Mathematik und Technologie

Author: Christiane Rousseau,Yvan Saint-Aubin

Publisher: Springer-Verlag

ISBN: 3642300928

Category: Mathematics

Page: 609

View: 1568

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Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.

Post-Quantum Cryptography

6th International Workshop, PQCrypto 2014, Waterloo, ON, Canada, October 1-3, 2014. Proceedings

Author: Michele Mosca

Publisher: Springer

ISBN: 3319116592

Category: Computers

Page: 284

View: 6608

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This book constitutes the refereed proceedings of the 6th International Workshop on Post-Quantum Cryptography, PQCrypto 2014, held in Waterloo, ON, Canada, in October 2014. The 16 revised full papers presented were carefully reviewed and selected from 37 submissions. The papers cover all technical aspects of cryptographic research related to the future world with large quantum computers such as code-based cryptography, lattice-based cryptography, multivariate cryptography, isogeny-based cryptography, security proof frameworks, cryptanalysis and implementations.

Introduction to Calculus and Classical Analysis

Author: Omar Hijab

Publisher: Springer Science & Business Media

ISBN: 0387693165

Category: Mathematics

Page: 342

View: 4653

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Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.

The Arithmetic of Elliptic Curves

Author: Joseph H. Silverman

Publisher: Springer Science & Business Media

ISBN: 9780387094946

Category: Mathematics

Page: 513

View: 3260

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The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Calculus of Several Variables

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461210682

Category: Mathematics

Page: 619

View: 7818

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This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

A Beginner’s Guide to Discrete Mathematics

Author: W. D. Wallis

Publisher: Springer Science & Business Media

ISBN: 9780817642693

Category: Mathematics

Page: 367

View: 5518

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This introduction to discrete mathematics is aimed at freshmen and sophomores in mathematics and computer science. It begins with a survey of number systems and elementary set theory before moving on to treat data structures, counting, probability, relations and functions, graph theory, matrices, number theory and cryptography. The end of each section contains problem sets with selected solutions, and good examples occur throughout the text.

Computing the Continuous Discretely

Integer-point Enumeration in Polyhedra

Author: Matthias Beck,Sinai Robins

Publisher: Springer Science & Business Media

ISBN: 0387461124

Category: Mathematics

Page: 227

View: 7620

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This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.

Introduction to Cryptography

Principles and Applications

Author: Hans Delfs,Helmut Knebl

Publisher: Springer Science & Business Media

ISBN: 3540492437

Category: Computers

Page: 367

View: 963

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The opening section of this book covers key concepts of cryptography, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash. The second part addresses advanced topics, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. Examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed. The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises. The second edition presents new material, including a complete description of the AES, an extended section on cryptographic hash functions, a new section on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks.

Cryptography

An Introduction

Author: V. V. I͡Ashchenko

Publisher: American Mathematical Soc.

ISBN: 0821829866

Category: Computers

Page: 229

View: 3236

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Learning about cryptography requires examining fundamental issues about information security. Questions abound, ranging from 'From whom are we protecting ourselves?' and 'How can we measure levels of security?' to 'What are our opponent's capabilities?' and 'What are their goals?' Answering these questions requires an understanding of basic cryptography. This book, written by Russian cryptographers, explains those basics.Chapters are independent and can be read in any order. The introduction gives a general description of all the main notions of modern cryptography: a cipher, a key, security, an electronic digital signature, a cryptographic protocol, etc. Other chapters delve more deeply into this material. The final chapter presents problems and selected solutions from ""Cryptography Olympiads for (Russian) High School Students"". This is an English translation of a Russian textbook. It is suitable for advanced high school students and undergraduates studying information security. It is also appropriate for a general mathematical audience interested in cryptography. Also on cryptography and available from the AMS is ""Codebreakers: Ame Beurling and the Swedish Crypto Program during World War II"".

Codes: An Introduction to Information Communication and Cryptography

Author: Norman L. Biggs

Publisher: Springer Science & Business Media

ISBN: 9781848002739

Category: Computers

Page: 274

View: 1984

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Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.