# Search Results for "an-introduction-to-mathematical-cryptography-undergraduate-texts-in-mathematics"

## An Introduction to Mathematical Cryptography

**Author**: Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman**Publisher:**Springer**ISBN:**1493917110**Category:**Mathematics**Page:**538**View:**2354

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.

## Komplexitätstheorie und Kryptologie

*Eine Einführung in Kryptokomplexität*

**Author**: Jörg Rothe**Publisher:**Springer-Verlag**ISBN:**3540797459**Category:**Computers**Page:**535**View:**8291

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.

## Einführung in die Kryptographie

**Author**: Johannes Buchmann**Publisher:**Springer-Verlag**ISBN:**3642980600**Category:**Computers**Page:**234**View:**9352

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.

## Kryptografie verständlich

*Ein Lehrbuch für Studierende und Anwender*

**Author**: Christof Paar,Jan Pelzl**Publisher:**Springer-Verlag**ISBN:**3662492970**Category:**Computers**Page:**416**View:**5049

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.

## An Introduction to Cryptography

**Author**: Richard A. Mollin**Publisher:**CRC Press**ISBN:**9781584881278**Category:**Mathematics**Page:**392**View:**2083

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:**2539

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:**2210

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

## The Arithmetic of Elliptic Curves

**Author**: Joseph H. Silverman**Publisher:**Springer Science & Business Media**ISBN:**9780387094946**Category:**Mathematics**Page:**513**View:**6943

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.

## Introduction to Calculus and Classical Analysis

**Author**: Omar Hijab**Publisher:**Springer Science & Business Media**ISBN:**0387693165**Category:**Mathematics**Page:**342**View:**8365

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.

## Calculus of Several Variables

**Author**: Serge Lang**Publisher:**Springer Science & Business Media**ISBN:**1461210682**Category:**Mathematics**Page:**619**View:**2461

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.

## 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:**5270

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.

## Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

**Author**: Kai L. Chung**Publisher:**Springer-Verlag**ISBN:**3642670334**Category:**Mathematics**Page:**346**View:**5852

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

## 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:**603

## Special Relativity

**Author**: Nicholas M.J. Woodhouse**Publisher:**Springer-Verlag**ISBN:**3540466762**Category:**Science**Page:**88**View:**8470

## Naive Mengenlehre

**Author**: Paul R. Halmos**Publisher:**Vandenhoeck & Ruprecht**ISBN:**9783525405277**Category:**Arithmetic**Page:**132**View:**6318

## Codes: An Introduction to Information Communication and Cryptography

**Author**: Norman L. Biggs**Publisher:**Springer Science & Business Media**ISBN:**9781848002739**Category:**Computers**Page:**274**View:**2276

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.

## A Computational Introduction to Number Theory and Algebra

**Author**: Victor Shoup**Publisher:**Cambridge University Press**ISBN:**0521516447**Category:**Computers**Page:**580**View:**7938

An introductory graduate-level text emphasizing algorithms and applications. This second edition includes over 200 new exercises and examples.

## Kryptografie und Public-Key-Infrastrukturen im Internet

**Author**: Klaus Schmeh**Publisher:**N.A**ISBN:**9783932588907**Category:****Page:**562**View:**8660

## Angewandte Kryptographie

*Protokolle, Algorithmen und Sourcecode in C*

**Author**: Bruce Schneier**Publisher:**N.A**ISBN:**9783827372284**Category:**Computer security**Page:**844**View:**9753