A Course In Mathematical Cryptography

Author : Gilbert Baumslag
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311038616X
Total Pages : 389 pages
Book Rating : 4.65/5 ( download)

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Download or read book A Course in Mathematical Cryptography written by Gilbert Baumslag and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-06-16 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is mathematical cryptography. By this we mean the mathematics involved in cryptographic protocols. As the field has expanded, using both commutative and noncommutative algebraic objects as cryptographic platforms, a book describing and explaining all these mathematical methods is of immeasurable value.

Author : Jeffrey Hoffstein
Publisher : Springer
ISBN 13 : 1493917110
Total Pages : 549 pages
Book Rating : 4.12/5 ( download)

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Download or read book An Introduction to Mathematical Cryptography written by Jeffrey Hoffstein and published by Springer. This book was released on 2014-09-11 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Heiko Knospe
Publisher : American Mathematical Soc.
ISBN 13 : 1470450550
Total Pages : 323 pages
Book Rating : 4.57/5 ( download)

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Download or read book A Course in Cryptography written by Heiko Knospe and published by American Mathematical Soc.. This book was released on 2019-09-27 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a compact course in modern cryptography. The mathematical foundations in algebra, number theory and probability are presented with a focus on their cryptographic applications. The text provides rigorous definitions and follows the provable security approach. The most relevant cryptographic schemes are covered, including block ciphers, stream ciphers, hash functions, message authentication codes, public-key encryption, key establishment, digital signatures and elliptic curves. The current developments in post-quantum cryptography are also explored, with separate chapters on quantum computing, lattice-based and code-based cryptosystems. Many examples, figures and exercises, as well as SageMath (Python) computer code, help the reader to understand the concepts and applications of modern cryptography. A special focus is on algebraic structures, which are used in many cryptographic constructions and also in post-quantum systems. The essential mathematics and the modern approach to cryptography and security prepare the reader for more advanced studies. The text requires only a first-year course in mathematics (calculus and linear algebra) and is also accessible to computer scientists and engineers. This book is suitable as a textbook for undergraduate and graduate courses in cryptography as well as for self-study.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 1441985921
Total Pages : 245 pages
Book Rating : 4.27/5 ( download)

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Download or read book A Course in Number Theory and Cryptography written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-09-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Author : Steven D. Galbraith
Publisher : Cambridge University Press
ISBN 13 : 1107013925
Total Pages : 631 pages
Book Rating : 4.26/5 ( download)

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Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 1441990038
Total Pages : 342 pages
Book Rating : 4.37/5 ( download)

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Download or read book Introduction to Cryptography written by Johannes Buchmann and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Margaret Cozzens
Publisher : American Mathematical Soc.
ISBN 13 : 0821883216
Total Pages : 355 pages
Book Rating : 4.11/5 ( download)

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Download or read book The Mathematics of Encryption written by Margaret Cozzens and published by American Mathematical Soc.. This book was released on 2013-09-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.

Author : Tsuyoshi Takagi
Publisher : Springer
ISBN 13 : 9811050651
Total Pages : 368 pages
Book Rating : 4.57/5 ( download)

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Download or read book Mathematical Modelling for Next-Generation Cryptography written by Tsuyoshi Takagi and published by Springer. This book was released on 2017-07-25 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

Author : Jean-Philippe Aumasson
Publisher : No Starch Press
ISBN 13 : 1593278268
Total Pages : 313 pages
Book Rating : 4.67/5 ( download)

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Download or read book Serious Cryptography written by Jean-Philippe Aumasson and published by No Starch Press. This book was released on 2017-11-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical guide to modern encryption breaks down the fundamental mathematical concepts at the heart of cryptography without shying away from meaty discussions of how they work. You’ll learn about authenticated encryption, secure randomness, hash functions, block ciphers, and public-key techniques such as RSA and elliptic curve cryptography. You’ll also learn: - Key concepts in cryptography, such as computational security, attacker models, and forward secrecy - The strengths and limitations of the TLS protocol behind HTTPS secure websites - Quantum computation and post-quantum cryptography - About various vulnerabilities by examining numerous code examples and use cases - How to choose the best algorithm or protocol and ask vendors the right questions Each chapter includes a discussion of common implementation mistakes using real-world examples and details what could go wrong and how to avoid these pitfalls. Whether you’re a seasoned practitioner or a beginner looking to dive into the field, Serious Cryptography will provide a complete survey of modern encryption and its applications.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 3662036428
Total Pages : 214 pages
Book Rating : 4.26/5 ( download)

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Download or read book Algebraic Aspects of Cryptography written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews