## Handbook of Elliptic and Hyperelliptic Curve Cryptography

Author: Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe Doche,Tanja Lange,Kim Nguyen,Frederik Vercauteren

Publisher: CRC Press

ISBN: 9781420034981

Category: Mathematics

Page: 842

View: 9641

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.

## Kryptografie verständlich

Ein Lehrbuch für Studierende und Anwender

Author: Christof Paar,Jan Pelzl

Publisher: Springer-Verlag

ISBN: 3662492970

Category: Computers

Page: 416

View: 8477

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.

## Progress in Cryptology – AFRICACRYPT 2014

7th International Conference on Cryptology in Africa, Marrakesh, Morocco, May 28-30, 2014. Proceedings

Author: David Pointcheval,Damien Vergnaud

Publisher: Springer

ISBN: 3319067346

Category: Computers

Page: 476

View: 4686

This book constitutes the refereed proceedings of the 7th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICA CRYPT 2014, held in Marrakesh, Morocco in May 2014. The 26 papers presented together with 1 invited talk were carefully reviewed and selected from 83 submissions. The aim of Africa crypt 2014 is to provide an international forum for practitioners and researchers from industry, academia and government from all over the world for a wide ranging discussion of all forms of cryptography and its applications as follows: Public-Key Cryptography, Hash Functions, Secret-Key Cryptanalysis, Number Theory, Hardware Implementation, Protocols and Lattice-based Cryptography.

## Guide to Pairing-Based Cryptography

Publisher: CRC Press

ISBN: 1315353148

Category: Computers

Page: 420

View: 796

This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes. As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes. Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography.

## Selected Areas in Cryptography -- SAC 2014

21st International Conference, Montreal, QC, Canada, August 14-15, 2014, Revised Selected Papers

Author: Antoine Joux,Amr Youssef

Publisher: Springer

ISBN: 331913051X

Category: Computers

Page: 381

View: 8988

This book constitutes the proceedings of the 21st International Conference on Selected Areas in Cryptography, SAC 2014, held in Montreal, QC, Canada, in August 2014. The 22 papers presented in this volume were carefully reviewed and selected from 103 submissions. There are four areas covered at each SAC conference. The three permanent areas are: design and analysis of symmetric key primitives and cryptosystems, including block and stream ciphers, hash function, MAC algorithms, cryptographic permutations, and authenticated encryption schemes; efficient implementations of symmetric and public key algorithms; mathematical and algorithmic aspects of applied cryptology. This year, the fourth area for SAC 2014 is: algorithms for cryptography, cryptanalysis and their complexity analysis.

## Quantum Communication, Measurement and Computing (QCMC)

Ninth International Conference on QCMC

Author: Alexander Lvovsky

Publisher: American Inst. of Physics

ISBN: N.A

Category: Computers

Page: 484

View: 6836

The volume contains the proceedings of the 2008 International Conference on Quantum Communication, Measurement and Computing. This meeting has been the leading conference in the field for more than two decades. The articles cover quantum information theory, quantum optics, quantum cryptography, experimental tools for quantum information science and related subjects.

## Pearls of discrete mathematics

Author: Martin J. Erickson

Publisher: CRC

ISBN: 9781439816165

Category: Computers

Page: 270

View: 5082

This book presents intriguing examples, facts, theorems, and proofs from the world of discrete mathematics. The author presents special topics that are not found elsewhere, including the upward extension of Pascal's triangle, the problem of counting Rook paths and Queen paths, higher-dimensional tic-tac-toe, recurrence relations and generating functions, the pigeonhole principle, information theory and codes, and game theory. He also explores connections between discrete structures and other branches of mathematics, such as combinatorics and algebra. The text includes examples, exercises, and appendices containing Mathematica ® calculations and related Internet resources.

## Einführung in die Kryptographie

Author: Johannes Buchmann

Publisher: Springer-Verlag

ISBN: 3642980600

Category: Computers

Page: 234

View: 7370

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.

## Zahlentheorie

Algebraische Zahlen und Funktionen

Author: Helmut Koch

Publisher: Springer-Verlag

ISBN: 3322803120

Category: Mathematics

Page: 344

View: 3760

Hauptziel des Buches ist die Vermittlung des Grundbestandes der Algebraischen Zahlentheorie einschließlich der Theorie der normalen Erweiterungen bis hin zu einem Ausblick auf die Klassenkörpertheorie. Gleichberechtigt mit algebraischen Zahlen werden auch algebraische Funktionen behandelt. Dies geschieht einerseits um die Analogie zwischen Zahl- und Funktionenkörpern aufzuzeigen, die besonders deutlich im Falle eines endlichen Konstantenkörpers ist. Andererseits erhält man auf diese Weise eine Einführung in die Theorie der "höheren Kongruenzen" als eines wesentlichen Bestandteils der "Arithmetischen Geometrie". Obgleich das Buch hauptsächlich algebraischen Methoden gewidmet ist, findet man in der Einleitung auch einen kurzen Beweis des Primzahlsatzes nach Newman. In den Kapiteln 7 und 8 wird die Theorie der Heckeschen L-Reihen behandelt einschließlich der Verteilung der Primideale algebraischer Zahlkörper in Kegeln.

## Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6208

## Handbook of Finite Fields

Author: Gary L. Mullen,Daniel Panario

Publisher: CRC Press

ISBN: 1439873828

Category: Computers

Page: 1068

View: 3128

Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and each chapter is self contained and peer reviewed. The first part of the book traces the history of finite fields through the eighteenth and nineteenth centuries. The second part presents theoretical properties of finite fields, covering polynomials, special functions, sequences, algorithms, curves, and related computational aspects. The final part describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas. The book provides a comprehensive index and easy access to over 3,000 references, enabling you to quickly locate up-to-date facts and results regarding finite fields.

## A Java Library of Graph Algorithms and Optimization

Author: Hang T. Lau

Publisher: Chapman and Hall/CRC

ISBN: N.A

Category: Computers

Page: 386

View: 8302

Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization. Self-contained and largely independent, each topic starts with a problem description and an outline of the solution procedure, followed by its parameter list specification, source code, and a test example that illustrates the usage of the code. An accompanying CD-ROM contains all of the Java code included in the book.

## Applications of abstract algebra with Maple and MATLAB

Author: Richard E. Klima,Neil Sigmon,Ernest Stitzinger

Publisher: CRC Press

ISBN: 9781584886105

Category: Computers

Page: 505

View: 4590

Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields. Carefully integrating Maple and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems. New to the Second Edition Three new chapters on Vigenère ciphers, the Advanced Encryption Standard (AES), and graph theory as well as new MATLAB and Maple sections Expanded exercises and additional research exercises Maple and MATLAB files and functions available for download online and from a CD-ROM With the incorporation of MATLAB, this second edition further illuminates the topics discussed by eliminating extensive computations of abstract algebraic techniques. The clear organization of the book as well as the inclusion of two of the most respected mathematical software packages available make the book a useful tool for students, mathematicians, and computer scientists.

## Introduction to Combinatorial Designs, Second Edition

Author: W.D. Wallis

Publisher: Chapman and Hall/CRC

ISBN: 9781584888383

Category: Mathematics

Page: 328

View: 4106

Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the existence theorem of Bruck, Ryser, and Chowla, the book discusses Latin squares, one-factorizations, triple systems, Hadamard matrices, and Room squares. It concludes with a number of statistical applications of designs. Reflecting recent results in design theory and outlining several applications, this new edition of a standard text presents a comprehensive look at the combinatorial theory of experimental design. Suitable for a one-semester course or for self-study, it will prepare readers for further exploration in the field. To access supplemental materials for this volume, visit the author’s website at http://www.math.siu.edu/Wallis/designs

## Idealtheorie

Author: Wolfgang Krull

Publisher: Springer-Verlag

ISBN: 3642870333

Category: Mathematics

Page: 160

View: 8311

## Komplexitätstheorie und Kryptologie

Eine Einführung in Kryptokomplexität

Author: Jörg Rothe

Publisher: Springer-Verlag

ISBN: 3540797459

Category: Computers

Page: 535

View: 951

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.

## Annales de l'Institut Fourier

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Science

Page: N.A

View: 1169

## Wartacrypt '04

Author: Jerzy Jaworski,Mieczyław Kula,Karol Nemoga,Matematický ústav SAV.

Publisher: N.A

ISBN: N.A

Category: Computers

Page: 227

View: 2791

## Lagerungen in der Ebene auf der Kugel und im Raum

Author: L. Fejes Toth

Publisher: Springer-Verlag

ISBN: 3662012065

Category: Mathematics

Page: 198

View: 2356

## Mathematik und Technologie

Author: Christiane Rousseau,Yvan Saint-Aubin

Publisher: Springer-Verlag

ISBN: 3642300928

Category: Mathematics

Page: 609

View: 8483

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.