An Introduction to Mathematical Cryptography

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

Publisher: Springer

ISBN: 1493917110

Category: Mathematics

Page: 538

View: 5237

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.
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Komplexitätstheorie und Kryptologie

Eine Einführung in Kryptokomplexität

Author: Jörg Rothe

Publisher: Springer-Verlag

ISBN: 3540797459

Category: Computers

Page: 535

View: 5190

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.
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Einführung in die Kryptographie

Author: Johannes Buchmann

Publisher: Springer-Verlag

ISBN: 3642980600

Category: Computers

Page: 234

View: 1886

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.
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Kryptografie verständlich

Ein Lehrbuch für Studierende und Anwender

Author: Christof Paar,Jan Pelzl

Publisher: Springer-Verlag

ISBN: 3662492970

Category: Computers

Page: 416

View: 1814

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.
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Mathematik und Technologie

Author: Christiane Rousseau,Yvan Saint-Aubin

Publisher: Springer-Verlag

ISBN: 3642300928

Category: Mathematics

Page: 609

View: 482

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.
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An Introduction to Cryptography

Author: Richard A. Mollin

Publisher: CRC Press

ISBN: 9781584881278

Category: Mathematics

Page: 392

View: 7206

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.
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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: 8630

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.
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Introduction to Cryptography

Author: Johannes Buchmann

Publisher: Springer Science & Business Media

ISBN: 1441990038

Category: Mathematics

Page: 338

View: 5238

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
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The Arithmetic of Elliptic Curves

Author: Joseph H. Silverman

Publisher: Springer Science & Business Media

ISBN: 9780387094946

Category: Mathematics

Page: 513

View: 1060

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.
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Introduction to Calculus and Classical Analysis

Author: Omar Hijab

Publisher: Springer Science & Business Media

ISBN: 0387693165

Category: Mathematics

Page: 342

View: 649

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.
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Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Author: Kai L. Chung

Publisher: Springer-Verlag

ISBN: 3642670334

Category: Mathematics

Page: 346

View: 8650

Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1
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Von Fermat bis Minkowski

Eine Vorlesung über Zahlentheorie und ihre Entwicklung

Author: W. Scharlau,H. Opolka

Publisher: Springer-Verlag

ISBN: 3642618499

Category: Mathematics

Page: 226

View: 8748

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Calculus of Several Variables

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461210682

Category: Mathematics

Page: 619

View: 5825

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.
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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: 5822

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.
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Special Relativity

Author: Nicholas M.J. Woodhouse

Publisher: Springer-Verlag

ISBN: 3540466762

Category: Science

Page: 88

View: 9655

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Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 9767

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Visuelle Kryptographie

Author: Andreas Klein

Publisher: Springer-Verlag

ISBN: 3540723625

Category: Mathematics

Page: 167

View: 1180

Mit Erfindung der Schrift entstand gleichzeitig der Bedarf, Geschriebenes vor unbefugten Lesern zu verbergen. Als Wissenschaft im modernen Sinne ist die Kryptographie jedoch noch sehr jung. 1994 erfanden Naor und Shamir folgendes Verfahren: Sie verteilten ein Bild so auf zwei Folien, dass auf jeder einzelnen Folie nur ein zufälliges Punktmuster zu sehen ist, aber beide Folien übereinander gelegt ein geheimes Bild ergeben. Das Buch gibt einen Einblick in die aktuelle Forschung, verzichtet aber bewusst auf Höhere Mathematik. Daher eine ideale Grundlage für Proseminare und Mathematik-AGs der Sekundarstufe. Plus: Aufgaben mit Musterlösungen.
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Einführung in die Kryptologie

Lehrbuch für Unterricht und Selbststudium

Author: Karin Freiermuth,Juraj Hromkovič,Lucia Keller,Björn Steffen

Publisher: Springer-Verlag

ISBN: 3834822698

Category: Computers

Page: 399

View: 865

Mit großem didaktischen Geschick gelingt es den Autoren, Begeisterung für die Welt der geheimen Botschaften zu wecken. So gelingt der Einstieg in die Kryptologie ganz leicht. Viele Beispiele und Aufgaben regen dazu an, sich selbständig mit diesem faszinierenden Gebiet zu beschäftigen und helfen dabei, den erlernten Stoff weiter zu vertiefen.
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