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An Introduction to Mathematical Cryptography

An Introduction to Mathematical Cryptography

  • Author: Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
  • Publisher: Springer
  • ISBN: 1493917110
  • Category: Mathematics
  • Page: 538
  • View: 7646
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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.

Einführung in die Kryptographie

Einführung in die Kryptographie

  • Author: Johannes Buchmann
  • Publisher: Springer-Verlag
  • ISBN: 3642397751
  • Category: Mathematics
  • Page: 330
  • View: 8803
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Dieses Kryptographiebuch ist geschrieben für Studierende der Mathematik, Informatik, Physik, Elektrotechnik oder andere Leser mit mathematischer Grundbildung und wurde in vielen Vorlesungen erfolgreich eingesetzt. Es behandelt die aktuellen Techniken der modernen Kryptographie, zum Beispiel Verschlüsselung und digitale Signaturen. Das Buch vermittelt auf elementare Weise alle mathematischen Grundlagen, die zu einem präzisen Verständnis der Kryptographie nötig sind, mit vielen Beispielen und Übungen. Die Leserinnen und Leser erhalten ein fundiertes Verständnis der modernen Kryptographie und werden in die Lage versetzt Forschungsliteratur zur Kryptographie zu verstehen.

Kryptografie verständlich

Kryptografie verständlich

Ein Lehrbuch für Studierende und Anwender

  • Author: Christof Paar,Jan Pelzl
  • Publisher: Springer-Verlag
  • ISBN: 3662492970
  • Category: Computers
  • Page: 416
  • View: 7934
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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.

Komplexitätstheorie und Kryptologie

Komplexitätstheorie und Kryptologie

Eine Einführung in Kryptokomplexität

  • Author: Jörg Rothe
  • Publisher: Springer-Verlag
  • ISBN: 3540797459
  • Category: Computers
  • Page: 535
  • View: 9337
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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

An Introduction to Cryptography

  • Author: Richard A. Mollin
  • Publisher: CRC Press
  • ISBN: 9781584881278
  • Category: Mathematics
  • Page: 392
  • View: 8877
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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.

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

  • Author: Kai L. Chung
  • Publisher: Springer-Verlag
  • ISBN: 3642670334
  • Category: Mathematics
  • Page: 346
  • View: 3317
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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

Introduction to Cryptography

Introduction to Cryptography

  • Author: Johannes Buchmann
  • Publisher: Springer Science & Business Media
  • ISBN: 1441990038
  • Category: Mathematics
  • Page: 338
  • View: 1922
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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

Einführung in die Analytische Zahlentheorie

Einführung in die Analytische Zahlentheorie

  • Author: Komaravolu Chandrasekharan
  • Publisher: Springer-Verlag
  • ISBN: 3540348557
  • Category: Mathematics
  • Page: 203
  • View: 5424
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The Arithmetic of Elliptic Curves

The Arithmetic of Elliptic Curves

  • Author: Joseph H. Silverman
  • Publisher: Springer Science & Business Media
  • ISBN: 9780387094946
  • Category: Mathematics
  • Page: 513
  • View: 2440
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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.

Post-Quantum Cryptography

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: 465
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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.

Naive Mengenlehre

Naive Mengenlehre

  • Author: Paul R. Halmos
  • Publisher: Vandenhoeck & Ruprecht
  • ISBN: 9783525405277
  • Category: Arithmetic
  • Page: 132
  • View: 9470
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Introduction to Cryptography with Maple

Introduction to Cryptography with Maple

  • Author: José Luis Gómez Pardo
  • Publisher: Springer Science & Business Media
  • ISBN: 3642321666
  • Category: Computers
  • Page: 706
  • View: 408
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This introduction to cryptography employs a programming-oriented approach to study the most important cryptographic schemes in current use and the main cryptanalytic attacks against them. Discussion of the theoretical aspects, emphasizing precise security definitions based on methodological tools such as complexity and randomness, and of the mathematical aspects, with emphasis on number-theoretic algorithms and their applications to cryptography and cryptanalysis, is integrated with the programming approach, thus providing implementations of the algorithms and schemes as well as examples of realistic size. A distinctive feature of the author's approach is the use of Maple as a programming environment in which not just the cryptographic primitives but also the most important cryptographic schemes are implemented following the recommendations of standards bodies such as NIST, with many of the known cryptanalytic attacks implemented as well. The purpose of the Maple implementations is to let the reader experiment and learn, and for this reason the author includes numerous examples. The book discusses important recent subjects such as homomorphic encryption, identity-based cryptography and elliptic curve cryptography. The algorithms and schemes which are treated in detail and implemented in Maple include AES and modes of operation, CMAC, GCM/GMAC, SHA-256, HMAC, RSA, Rabin, Elgamal, Paillier, Cocks IBE, DSA and ECDSA. In addition, some recently introduced schemes enjoying strong security properties, such as RSA-OAEP, Rabin-SAEP, Cramer--Shoup, and PSS, are also discussed and implemented. On the cryptanalysis side, Maple implementations and examples are used to discuss many important algorithms, including birthday and man-in-the-middle attacks, integer factorization algorithms such as Pollard's rho and the quadratic sieve, and discrete log algorithms such as baby-step giant-step, Pollard's rho, Pohlig--Hellman and the index calculus method. This textbook is suitable for advanced undergraduate and graduate students of computer science, engineering and mathematics, satisfying the requirements of various types of courses: a basic introductory course; a theoretically oriented course whose focus is on the precise definition of security concepts and on cryptographic schemes with reductionist security proofs; a practice-oriented course requiring little mathematical background and with an emphasis on applications; or a mathematically advanced course addressed to students with a stronger mathematical background. The main prerequisite is a basic knowledge of linear algebra and elementary calculus, and while some knowledge of probability and abstract algebra would be helpful, it is not essential because the book includes the necessary background from these subjects and, furthermore, explores the number-theoretic material in detail. The book is also a comprehensive reference and is suitable for self-study by practitioners and programmers.

Codes: An Introduction to Information Communication and Cryptography

Codes: An Introduction to Information Communication and Cryptography

  • Author: Norman L. Biggs
  • Publisher: Springer Science & Business Media
  • ISBN: 9781848002739
  • Category: Computers
  • Page: 274
  • View: 2901
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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.

Angewandte Kryptographie

Angewandte Kryptographie

Protokolle, Algorithmen und Sourcecode in C

  • Author: Bruce Schneier
  • Publisher: N.A
  • ISBN: 9783827372284
  • Category: Computer security
  • Page: 844
  • View: 8357
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Special Relativity

Special Relativity

  • Author: Nicholas M.J. Woodhouse
  • Publisher: Springer-Verlag
  • ISBN: 3540466762
  • Category: Science
  • Page: 88
  • View: 2297
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Einführung in die Kryptologie

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: 5870
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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.

Calculus of Several Variables

Calculus of Several Variables

  • Author: Serge Lang
  • Publisher: Springer Science & Business Media
  • ISBN: 1461210682
  • Category: Mathematics
  • Page: 619
  • View: 2843
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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.

Geometrische und analytische Zahlentheorie

Geometrische und analytische Zahlentheorie

  • Author: Edmund Hlawka,Johannes Schoissengeier,Rudolf Josef Taschner
  • Publisher: N.A
  • ISBN: N.A
  • Category: Number theory
  • Page: 194
  • View: 9144
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Gewinnen Strategien für mathematische Spiele

Gewinnen Strategien für mathematische Spiele

Band 3 Fallstudien

  • Author: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy
  • Publisher: Springer-Verlag
  • ISBN: 3322831728
  • Category: Technology & Engineering
  • Page: 274
  • View: 9826
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Der dritte Band ,,Fallstudien" bietet eine Fülle von speziellen Beispielen.

Lineare Algebra

Lineare Algebra

  • Author: Gilbert Strang
  • Publisher: Springer-Verlag
  • ISBN: 3642556310
  • Category: Mathematics
  • Page: 656
  • View: 6644
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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.