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: 9781466570269
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.

Handbook of Financial Cryptography and Security

Author: Burton Rosenberg
Publisher: CRC Press
ISBN: 1420059823
Release Date: 2010-08-02
Genre: Computers

The Handbook of Financial Cryptography and Security elucidates the theory and techniques of cryptography and illustrates how to establish and maintain security under the framework of financial cryptography. It applies various cryptographic techniques to auctions, electronic voting, micropayment systems, digital rights, financial portfolios, routing networks, and more. In the first part, the book examines blind signatures and other important cryptographic techniques with respect to digital cash/e-cash. It also looks at the role of cryptography in auctions and voting, describes properties that can be required of systems implementing value exchange, and presents methods by which selected receivers can decrypt signals sent out to everyone. The second section begins with a discussion on lowering transaction costs of settling payments so that commerce can occur at the sub-penny level. The book then addresses the challenge of a system solution for the protection of intellectual property, before presenting an application of cryptography to financial exchanges and markets. Exploring financial cryptography in the real world, the third part discusses the often-complex issues of phishing, privacy and anonymity, and protecting the identity of objects and users. With a focus on human factors, the final section considers whether systems will elicit or encourage the desired behavior of the participants of the system. It also explains how the law and regulations impact financial cryptography. In the real world, smart and adaptive adversaries employ all types of means to circumvent inconvenient security restraints. This useful handbook provides answers to general questions about the field of financial cryptography as well as solutions to specific real-world security problems.

Algorithmic Cryptanalysis

Author: Antoine Joux
Publisher: CRC Press
ISBN: 1420070037
Release Date: 2009-06-15
Genre: Computers

Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program. Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applications. The final part addresses more sophisticated cryptographic applications, including LFSR-based stream ciphers and index calculus methods. Accounting for the impact of current computer architectures, this book explores the algorithmic and implementation aspects of cryptanalysis methods. It can serve as a handbook of algorithmic methods for cryptographers as well as a textbook for undergraduate and graduate courses on cryptanalysis and cryptography.

Introduction to Modern Cryptography Second Edition

Author: Jonathan Katz
Publisher: CRC Press
ISBN: 9781466570269
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.

Cryptology

Author: Richard E. Klima
Publisher: CRC Press
ISBN: 9781466569041
Release Date: 2012-06-20
Genre: Computers

Easily Accessible to Students with Nontechnical Backgrounds In a clear, nontechnical manner, Cryptology: Classical and Modern with Maplets explains how fundamental mathematical concepts are the bases of cryptographic algorithms. Designed for students with no background in college-level mathematics, the book assumes minimal mathematical prerequisites and incorporates student-friendly Maplets throughout that provide practical examples of the techniques used. Technology Resource By using the Maplets, students can complete complicated tasks with relative ease. They can encrypt, decrypt, and cryptanalyze messages without the burden of understanding programming or computer syntax. The authors explain topics in detail first before introducing one or more Maplets. All Maplet material and exercises are given in separate, clearly labeled sections. Instructors can omit the Maplet sections without any loss of continuity and non-Maplet examples and exercises can be completed with, at most, a simple hand-held calculator. The Maplets are available for download at www.radford.edu/~npsigmon/cryptobook.html. A Gentle, Hands-On Introduction to Cryptology After introducing elementary methods and techniques, the text fully develops the Enigma cipher machine and Navajo code used during World War II, both of which are rarely found in cryptology textbooks. The authors then demonstrate mathematics in cryptology through monoalphabetic, polyalphabetic, and block ciphers. With a focus on public-key cryptography, the book describes RSA ciphers, the Diffie–Hellman key exchange, and ElGamal ciphers. It also explores current U.S. federal cryptographic standards, such as the AES, and explains how to authenticate messages via digital signatures, hash functions, and certificates.

Handbook of Applied Cryptography

Author: Alfred J. Menezes
Publisher: CRC Press
ISBN: 9781439821916
Release Date: 1996-10-16
Genre: Mathematics

Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional: It serves as an introduction to the more practical aspects of both conventional and public-key cryptography It is a valuable source of the latest techniques and algorithms for the serious practitioner It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit It provides a mathematical treatment to accompany practical discussions It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussed Now in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.

Elliptic Curves

Author: Lawrence C. Washington
Publisher: CRC Press
ISBN: 1420071475
Release Date: 2008-04-03
Genre: Mathematics

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition Chapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues A more complete treatment of the Weil and Tate–Lichtenbaum pairings Doud’s analytic method for computing torsion on elliptic curves over Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

Access Control Security and Trust

Author: Shiu-Kai Chin
Publisher: CRC Press
ISBN: 9781584888635
Release Date: 2011-07-01
Genre: Computers

Developed from the authors’ courses at Syracuse University and the U.S. Air Force Research Laboratory, Access Control, Security, and Trust: A Logical Approach equips readers with an access control logic they can use to specify and verify their security designs. Throughout the text, the authors use a single access control logic based on a simple propositional modal logic. The first part of the book presents the syntax and semantics of access control logic, basic access control concepts, and an introduction to confidentiality and integrity policies. The second section covers access control in networks, delegation, protocols, and the use of cryptography. In the third section, the authors focus on hardware and virtual machines. The final part discusses confidentiality, integrity, and role-based access control. Taking a logical, rigorous approach to access control, this book shows how logic is a useful tool for analyzing security designs and spelling out the conditions upon which access control decisions depend. It is designed for computer engineers and computer scientists who are responsible for designing, implementing, and verifying secure computer and information systems.

Mathematics of Public Key Cryptography

Author: Steven D. Galbraith
Publisher: Cambridge University Press
ISBN: 9781107013926
Release Date: 2012-03-15
Genre: Computers

This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

An Introduction to Number Theory with Cryptography

Author: James S. Kraft
Publisher: CRC Press
ISBN: 9781482214420
Release Date: 2016-04-19
Genre: Mathematics

Number theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number theory along with many interesting applications. Designed for an undergraduate-level course, it covers standard number theory topics and gives instructors the option of integrating several other topics into their coverage. The "Check Your Understanding" problems aid in learning the basics, and there are numerous exercises, projects, and computer explorations of varying levels of difficulty.

Communication System Security

Author: Lidong Chen
Publisher: CRC Press
ISBN: 9781439840368
Release Date: 2012-05-29
Genre: Computers

Helping current and future system designers take a more productive approach in the field, Communication System Security shows how to apply security principles to state-of-the-art communication systems. The authors use previous design failures and security flaws to explain common pitfalls in security design. Divided into four parts, the book begins with the necessary background on practical cryptography primitives. This part describes pseudorandom sequence generators, stream and block ciphers, hash functions, and public-key cryptographic algorithms. The second part covers security infrastructure support and the main subroutine designs for establishing protected communications. The authors illustrate design principles through network security protocols, including transport layer security (TLS), Internet security protocols (IPsec), the secure shell (SSH), and cellular solutions. Taking an evolutionary approach to security in today’s telecommunication networks, the third part discusses general access authentication protocols, the protocols used for UMTS/LTE, the protocols specified in IETF, and the wireless-specific protection mechanisms for the air link of UMTS/LTE and IEEE 802.11. It also covers key establishment and authentication in broadcast and multicast scenarios. Moving on to system security, the last part introduces the principles and practice of a trusted platform for communication devices. The authors detail physical-layer security as well as spread-spectrum techniques for anti-jamming attacks. With much of the material used by the authors in their courses and drawn from their industry experiences, this book is appropriate for a wide audience, from engineering, computer science, and mathematics students to engineers, designers, and computer scientists. Illustrating security principles with existing protocols, the text helps readers understand the principles and practice of security analysis.

An Introduction to Cryptography Second Edition

Author: Richard A. Mollin
Publisher: CRC Press
ISBN: 9781420011241
Release Date: 2006-09-18
Genre: Mathematics

Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field. With numerous additions and restructured material, this edition presents the ideas behind cryptography and the applications of the subject. The first chapter provides a thorough treatment of the mathematics necessary to understand cryptography, including number theory and complexity, while the second chapter discusses cryptographic fundamentals, such as ciphers, linear feedback shift registers, modes of operation, and attacks. The next several chapters discuss DES, AES, public-key cryptography, primality testing, and various factoring methods, from classical to elliptical curves. The final chapters are comprised of issues pertaining to the Internet, such as pretty good privacy (PGP), protocol layers, firewalls, and cookies, as well as applications, including login and network security, viruses, smart cards, and biometrics. The book concludes with appendices on mathematical data, computer arithmetic, the Rijndael S-Box, knapsack ciphers, the Silver-Pohlig-Hellman algorithm, the SHA-1 algorithm, radix-64 encoding, and quantum cryptography. New to the Second Edition: An introductory chapter that provides more information on mathematical facts and complexity theory Expanded and updated exercises sets, including some routine exercises More information on primality testing and cryptanalysis Accessible and logically organized, An Introduction to Cryptography, Second Edition is the essential book on the fundamentals of cryptography.

Computational Trust Models and Machine Learning

Author: Xin Liu
Publisher: CRC Press
ISBN: 9781482226669
Release Date: 2014-10-29
Genre: Computers

Computational Trust Models and Machine Learning provides a detailed introduction to the concept of trust and its application in various computer science areas, including multi-agent systems, online social networks, and communication systems. Identifying trust modeling challenges that cannot be addressed by traditional approaches, this book: Explains how reputation-based systems are used to determine trust in diverse online communities Describes how machine learning techniques are employed to build robust reputation systems Explores two distinctive approaches to determining credibility of resources—one where the human role is implicit, and one that leverages human input explicitly Shows how decision support can be facilitated by computational trust models Discusses collaborative filtering-based trust aware recommendation systems Defines a framework for translating a trust modeling problem into a learning problem Investigates the objectivity of human feedback, emphasizing the need to filter out outlying opinions Computational Trust Models and Machine Learning effectively demonstrates how novel machine learning techniques can improve the accuracy of trust assessment.

Algorithmic Problems of Group Theory Their Complexity and Applications to Cryptography

Author: Delaram Kahrobaei
Publisher: American Mathematical Soc.
ISBN: 9780821898598
Release Date: 2015-02-25
Genre: Mathematics

This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9-10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6-7, 2013 at Boston College, Chestnut Hill, MA. Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.