Group Theoretic Cryptography

Author: Maria Isabel González Vasco
Publisher: CRC Press
ISBN: 9781584888376
Release Date: 2015-04-01
Genre: Computers

Group theoretic problems have propelled scientific achievements across a wide range of fields, including mathematics, physics, chemistry, and the life sciences. Many cryptographic constructions exploit the computational hardness of group theoretical problems, and the area is viewed as a potential source of quantum-resilient cryptographic primitives for the future. Group Theoretic Cryptography supplies an ideal introduction to cryptography for those who are interested in group theory and want to learn about the possible interplays between the two fields. Assuming an undergraduate-level understanding of linear algebra and discrete mathematics, it details the specifics of using non-Abelian groups in the field of cryptography. Moreover, the book evidences how group theoretic techniques help us gain new insight into well known, seemingly unrelated, cryptographic constructions, such as DES. The book starts with brief overviews of the fundamentals of group theory, complexity theory, and cryptography. Part two is devoted to public-key encryption, including provable security guarantees, public-key encryption in the standard model, and public-key encryption using infinite groups. The third part of the book covers secret-key encryption. It examines block ciphers, like the Advanced Encryption Standard, and cryptographic hash functions and message authentication codes. The last part delves into a number of cryptographic applications which are nowadays as relevant as encryption—identification protocols, key establishment, and signature schemes are covered. The book supplies formal security analyses and highlights potential vulnerabilities for cryptographic constructions involving group theory. Summaries and references for further reading, as well as exercises, are included at the end of each chapter. Selected solutions for exercises are provided in the back of the book.

Introduction to Modern Cryptography Second Edition

Author: Jonathan Katz
Publisher: CRC Press
ISBN: 9781466570276
Release Date: 2014-11-06
Genre: Computers

Cryptography is ubiquitous and plays a key role in ensuring data secrecy and integrity as well as in securing computer systems more broadly. Introduction to Modern Cryptography provides a rigorous yet accessible treatment of this fascinating subject. The authors introduce the core principles of modern cryptography, with an emphasis on formal definitions, clear assumptions, and rigorous proofs of security. The book begins by focusing on private-key cryptography, including an extensive treatment of private-key encryption, message authentication codes, and hash functions. The authors also present design principles for widely used stream ciphers and block ciphers including RC4, DES, and AES, plus provide provable constructions of stream ciphers and block ciphers from lower-level primitives. The second half of the book covers public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, and El Gamal cryptosystems (and others), followed by a thorough treatment of several standardized public-key encryption and digital signature schemes. Integrating a more practical perspective without sacrificing rigor, this widely anticipated Second Edition offers improved treatment of: Stream ciphers and block ciphers, including modes of operation and design principles Authenticated encryption and secure communication sessions Hash functions, including hash-function applications and design principles Attacks on poorly implemented cryptography, including attacks on chained-CBC encryption, padding-oracle attacks, and timing attacks The random-oracle model and its application to several standardized, widely used public-key encryption and signature schemes Elliptic-curve cryptography and associated standards such as DSA/ECDSA and DHIES/ECIES Containing updated exercises and worked examples, Introduction to Modern Cryptography, Second Edition can serve as a textbook for undergraduate- or graduate-level courses in cryptography, a valuable reference for researchers and practitioners, or a general introduction suitable for self-study.


Author: Richard Klima
Publisher: CRC Press
ISBN: 9781351692533
Release Date: 2018-11-30
Genre: Computers

Cryptology: Classical and Modern, Second Edition proficiently introduces readers to the fascinating field of cryptology. The book covers classical methods including substitution, transposition, Playfair, ADFGVX, Alberti, Vigenère, and Hill ciphers. It also includes coverage of the Enigma machine, Turing bombe, and Navajo code. Additionally, the book presents modern methods like RSA, ElGamal, and stream ciphers, as well as the Diffie-Hellman key exchange and Advanced Encryption Standard. When possible, the book details methods for breaking both classical and modern methods. The new edition expands upon the material from the first edition which was oriented for students in non-technical fields. At the same time, the second edition supplements this material with new content that serves students in more technical fields as well. Thus, the second edition can be fully utilized by both technical and non-technical students at all levels of study. The authors include a wealth of material for a one-semester cryptology course, and research exercises that can be used for supplemental projects. Hints and answers to selected exercises are found at the end of the book.

Guide to Pairing Based Cryptography

Author: Nadia El Mrabet
Publisher: CRC Press
ISBN: 9781498729512
Release Date: 2017-01-06
Genre: Computers

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.

Kryptografie verst ndlich

Author: Christof Paar
Publisher: Springer-Verlag
ISBN: 9783662492970
Release Date: 2016-08-23
Genre: Computers

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.

Introduction to Modern Cryptography Third Edition

Author: Jonathan Katz
Publisher: Chapman & Hall/CRC
ISBN: 0815354363
Release Date: 2019-11

Now the most used texbook for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections, topics, and exercises. The authors introduce the core principles of modern cryptography, with an emphasis on formal definitions, clear assumptions, and rigorous proofs of security. The book begins by focusing on private-key cryptography. The second half covers public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, and El Gamal cryptosystems (and others), and adds coverage of post-quantum cryptograpy to this edition.

Einf hrung in die Kryptographie

Author: Johannes Buchmann
Publisher: Springer-Verlag
ISBN: 9783642980602
Release Date: 2013-03-08
Genre: Computers

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.

Komplexit tstheorie und Kryptologie

Author: Jörg Rothe
Publisher: Springer-Verlag
ISBN: 9783540797456
Release Date: 2008-08-01
Genre: Computers

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.


Author: Friedrich L. Bauer
Publisher: Springer-Verlag
ISBN: 9783642788697
Release Date: 2013-03-07
Genre: Computers

Die Kryptologie, eine jahrtausendealte "Geheimwissenschaft", gewinnt für den Informatiker zusehends praktische Bedeutung in Verbindung mit Datenbanken und Telekommunikation. Neben ihre Nutzung in rechnergestützten öffentlichen Nachrichtensystemen ("öffentliche Schlüssel") treten interne Anwendungen, die sich auch auf Zugriffsberechtigungen und den Quellenschutz von Software erstrecken. Der erste Teil des Buches handelt in elf Kapiteln von den Geheimschriften und ihrem Gebrauch - von der Kryptographie. Im zweiten Teil wird in elf weiteren Kapiteln das Vorgehen zum unbefugten Entziffern einer Geheimschrift - die Kryptanalyse - besprochen, wobei sich insbesondere Hinweise für die Verfahrensbeurteilung ergeben. Das Buch setzt nur elementare mathematische Kenntnisse voraus. Mit einer Fülle spannender, lustiger und bisweilen anzüglicher Geschichten aus der historischen Kryptologie gewürzt, ist es selbst für den Laien reizvoll zu lesen.

Condensed Matter Optical Spectroscopy

Author: Iulian Ionita
Publisher: CRC Press
ISBN: 9781466569560
Release Date: 2014-08-20
Genre: Science

Discover a Modern Approach to the Study of Molecular Symmetry Classroom-tested from an author experienced in teaching a course on condensed matter spectroscopy, and introductory spectroscopy and lasers, Condensed Matter Optical Spectroscopy: An Illustrated Introduction contains over 200 color illustrations and provides a clear overview of the field. Intended for undergraduate students in a variety of majors, this text presents the application of molecular symmetry on optical spectra (ultraviolet, visible, infrared, and Raman) through group theory, and uses numerous examples to illustrate practical theory applications. Recognize the Symmetry of Any Atomic Arrangement and the Point Group to Which It Belongs Divided into five chapters, this book is designed to help students choose a method or several methods for material characterization, measure a correct spectrum, and interpret the spectrum or correlate the spectra obtained using different methods. It includes solid-state active media for lasers, as well as coordination and organometallic complexes, minerals, and metal ions in biological systems, and also provides 3D representations. This book addresses: Classifying molecules according to their symmetry What happens when an ion of transition metal enters an environment with a given symmetry How atomic orbitals are involved in molecular bonding Whether the molecule is a rigid construction or a dynamic structure (which can either interact with light or not at all) How to perform a reliable spectrum measurement Condensed Matter Optical Spectroscopy: An Illustrated Introduction does not require any prior knowledge on group theory.

Das BUCH der Beweise

Author: Martin Aigner
Publisher: Springer-Verlag
ISBN: 9783662064542
Release Date: 2013-07-29
Genre: Mathematics

Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit