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Author: Alexei Myasnikov
Publisher: Springer Science & Business Media
ISBN: 3764388277
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography.
Author: Alexei Myasnikov
Publisher: Springer Science & Business Media
ISBN: 3764388277
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography.
Author: Maria Isabel Gonzalez Vasco
Publisher: CRC Press
ISBN: 1584888377
Category : Computers
Languages : en
Pages : 244
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Book Description
Group theory appears to be a promising source of hard computational problems for deploying new cryptographic constructions. This reference focuses on the specifics of using groups, including in particular non-Abelian groups, in the field of cryptography. It provides an introduction to cryptography with emphasis on the group theoretic perspective, making it one of the first books to use this approach. The authors provide the needed cryptographic and group theoretic concepts, full proofs of essential theorems, and formal security evaluations of the cryptographic schemes presented. They also provide references for further reading and exercises at the end of each chapter.
Author: Alexei Myasnikov
Publisher: Springer Science & Business Media
ISBN: 3764388269
Category : Language Arts & Disciplines
Languages : en
Pages : 192
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Book Description
This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far. Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.
Author: Steven D. Galbraith
Publisher: Cambridge University Press
ISBN: 1107013925
Category : Computers
Languages : en
Pages : 631
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Book Description
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Author: Jeffrey Hoffstein
Publisher: Springer
ISBN: 1493917110
Category : Mathematics
Languages : en
Pages : 549
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Book Description
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.
Author: Jonathan Katz
Publisher: CRC Press
ISBN: 1351133012
Category : Computers
Languages : en
Pages : 515
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Book Description
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 present the core principles of modern cryptography, with emphasis on formal definitions, rigorous proofs of security.
Author: Roger C. Lyndon
Publisher: Springer
ISBN: 3642618960
Category : Mathematics
Languages : en
Pages : 354
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Book Description
From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
Author: Fuchun Guo
Publisher: Springer
ISBN: 3319930494
Category : Computers
Languages : en
Pages : 262
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Book Description
This monograph illustrates important notions in security reductions and essential techniques in security reductions for group-based cryptosystems. Using digital signatures and encryption as examples, the authors explain how to program correct security reductions for those cryptographic primitives. Various schemes are selected and re-proven in this book to demonstrate and exemplify correct security reductions. This book is suitable for researchers and graduate students engaged with public-key cryptography.
Author: David Wong
Publisher: Simon and Schuster
ISBN: 1617296716
Category : Computers
Languages : en
Pages : 398
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Book Description
If you''re browsing the web, using public APIs, making and receiving electronic payments, registering and logging in users, or experimenting with blockchain, you''re relying on cryptography. And you''re probably trusting a collection of tools, frameworks, and protocols to keep your data, users, and business safe. It''s important to understand these tools so you can make the best decisions about how, where, and why to use them. Real-World Cryptography teaches you applied cryptographic techniques to understand and apply security at every level of your systems and applications. about the technology Cryptography is the foundation of information security. This simultaneously ancient and emerging science is based on encryption and secure communication using algorithms that are hard to crack even for high-powered computer systems. Cryptography protects privacy, secures online activity, and defends confidential information, such as credit cards, from attackers and thieves. Without cryptographic techniques allowing for easy encrypting and decrypting of data, almost all IT infrastructure would be vulnerable. about the book Real-World Cryptography helps you understand the cryptographic techniques at work in common tools, frameworks, and protocols so you can make excellent security choices for your systems and applications. There''s no unnecessary theory or jargon--just the most up-to-date techniques you''ll need in your day-to-day work as a developer or systems administrator. Cryptography expert David Wong takes you hands-on with cryptography building blocks such as hash functions and key exchanges, then shows you how to use them as part of your security protocols and applications. Alongside modern methods, the book also anticipates the future of cryptography, diving into emerging and cutting-edge advances such as cryptocurrencies, password-authenticated key exchange, and post-quantum cryptography. Throughout, all techniques are fully illustrated with diagrams and real-world use cases so you can easily see how to put them into practice. what''s inside Best practices for using cryptography Diagrams and explanations of cryptographic algorithms Identifying and fixing cryptography bad practices in applications Picking the right cryptographic tool to solve problems about the reader For cryptography beginners with no previous experience in the field. about the author David Wong is a senior engineer working on Blockchain at Facebook. He is an active contributor to internet standards like Transport Layer Security and to the applied cryptography research community. David is a recognized authority in the field of applied cryptography; he''s spoken at large security conferences like Black Hat and DEF CON and has delivered cryptography training sessions in the industry.
Author: Gilbert Baumslag
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311038616X
Category : Computers
Languages : en
Pages : 476
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Book Description
Cryptography has become essential as bank transactions, credit card infor-mation, contracts, and sensitive medical information are sent through inse-cure channels. This book is concerned with the mathematical, especially algebraic, aspects of cryptography. It grew out of many courses presented by the authors over the past twenty years at various universities and covers a wide range of topics in mathematical cryptography. It is primarily geared towards graduate students and advanced undergraduates in mathematics and computer science, but may also be of interest to researchers in the area. Besides the classical methods of symmetric and private key encryption, the book treats the mathematics of cryptographic protocols and several unique topics such as Group-Based Cryptography Gröbner Basis Methods in Cryptography Lattice-Based Cryptography
