Mathematical Foundations of Public Key Cryptography, Wang, Xiaoyun
Автор: Jeffrey Hoffstein and Jill Pipher Название: Introduction to Mathematical Cryptography ISBN: 1493917102 ISBN-13(EAN): 9781493917105 Издательство: Springer Рейтинг: Цена: 83850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: An Introduction to Mathematical Cryptography
Автор: Goldreich, Oded Название: Foundations of cryptography: volume 2, basic applications ISBN: 052111991X ISBN-13(EAN): 9780521119917 Издательство: Cambridge Academ Рейтинг: Цена: 60190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Building on the basic tools presented in the first volume, this second volume of Foundations of Cryptography contains a rigorous and systematic treatment of three basic applications: Encryption, Signatures, and General Cryptographic Protocols. It is suitable for use in a graduate course on cryptography and as a reference book for experts.
Автор: Oded Goldreich Название: Foundations of Cryptography ISBN: 0521035368 ISBN-13(EAN): 9780521035361 Издательство: Cambridge Academ Рейтинг: Цена: 55970.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Focuses on the basic mathematical tools needed for cryptographic design: computational difficulty (one-way functions), pseudorandomness and zero-knowledge proofs.
Автор: Mazur Название: Prime Numbers and the Riemann Hypothesis ISBN: 1107499437 ISBN-13(EAN): 9781107499430 Издательство: Cambridge Academ Рейтинг: Цена: 25350.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book introduces prime numbers and explains the celebrated, unsolved Riemann hypothesis in a direct manner. Suitable for both scholars and those with a minimal mathematical background.
Автор: Sadri Hassani Название: Mathematical Physics: A Modern Introduction To Its Foundations ISBN: 3319011944 ISBN-13(EAN): 9783319011943 Издательство: Springer Рейтинг: Цена: 86310.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
Автор: Isaac Goldbring Название: Ultrafilters Throughout Mathematics ISBN: 1470469618 ISBN-13(EAN): 9781470469610 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 71060.00 T Наличие на складе: Поставка под заказ. Описание: Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters; the second part presents the classical ultraproduct construction.
Автор: Bauer Название: Secret History ISBN: 1466561866 ISBN-13(EAN): 9781466561861 Издательство: Taylor&Francis Рейтинг: Цена: 79610.00 T Наличие на складе: Нет в наличии. Описание: Winner of an Outstanding Academic Title Award from CHOICE Magazine Most available cryptology books primarily focus on either mathematics or history. Breaking this mold, Secret History: The Story of Cryptology gives a thorough yet accessible treatment of both the mathematics and history of cryptology. Requiring minimal mathematical prerequisites, the book presents the mathematics in sufficient detail and weaves the history throughout the chapters. In addition to the fascinating historical and political sides of cryptology, the author—a former Scholar-in-Residence at the U.S. National Security Agency (NSA) Center for Cryptologic History—includes interesting instances of codes and ciphers in crime, literature, music, and art. Following a mainly chronological development of concepts, the book focuses on classical cryptology in the first part. It covers Greek and Viking cryptography, the Vigenere cipher, the one-time pad, transposition ciphers, Jefferson’s cipher wheel, the Playfair cipher, ADFGX, matrix encryption, World War II cipher systems (including a detailed examination of Enigma), and many other classical methods introduced before World War II. The second part of the book examines modern cryptology. The author looks at the work of Claude Shannon and the origin and current status of the NSA, including some of its Suite B algorithms such as elliptic curve cryptography and the Advanced Encryption Standard. He also details the controversy that surrounded the Data Encryption Standard and the early years of public key cryptography. The book not only provides the how-to of the Diffie-Hellman key exchange and RSA algorithm, but also covers many attacks on the latter. Additionally, it discusses Elgamal, digital signatures, PGP, and stream ciphers and explores future directions such as quantum cryptography and DNA computing. With numerous real-world examples and extensive references, this book skillfully balances the historical aspects of cryptology with its mathematical details. It provides readers with a sound foundation in this dynamic field. Please visit Dr. Bauer's website, which provides access to exercise sets: http://depts.ycp.edu/~cbauer/
Автор: Katz Название: Introduction to Modern Cryptography, Second Edition ISBN: 1466570261 ISBN-13(EAN): 9781466570269 Издательство: Taylor&Francis Рейтинг: Цена: 102070.00 T Наличие на складе: Нет в наличии. Описание:
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.
Автор: Steven R. Finch Название: Mathematical Constants II ISBN: 1108470599 ISBN-13(EAN): 9781108470599 Издательство: Cambridge Academ Рейтинг: Цена: 160510.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The author continues his outstanding scholarly attempt to bring together all significant mathematical constants in one place. Using this book, students and professionals will discover hidden links between apparently disconnected fields of inquiry. Unsolved problems - the lifeblood of mathematics - appear virtually everywhere as well.
Автор: Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf Название: Discrete Algebraic Methods: Arithmetic, Cryptography, Automata and Groups ISBN: 3110413329 ISBN-13(EAN): 9783110413328 Издательство: Walter de Gruyter Цена: 43330.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups
Автор: Wang Название: Mathematical Foundations of Public Key Cryptography ISBN: 1498702236 ISBN-13(EAN): 9781498702232 Издательство: Taylor&Francis Рейтинг: Цена: 80630.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.
Rather than simply combining number theory and modern algebra, this textbook features the interdisciplinary characteristics of cryptography--revealing the integrations of mathematical theories and public-key cryptographic applications. Incorporating the complexity theory of algorithms throughout, it introduces the basic number theoretic and algebraic algorithms and their complexities to provide a preliminary understanding of the applications of mathematical theories in cryptographic algorithms. Supplying a seamless integration of cryptography and mathematics, the book includes coverage of elementary number theory; algebraic structure and attributes of group, ring, and field; cryptography-related computing complexity and basic algorithms, as well as lattice and fundamental methods of lattice cryptanalysis. The text consists of 11 chapters. Basic theory and tools of elementary number theory, such as congruences, primitive roots, residue classes, and continued fractions, are covered in Chapters 1-6. The basic concepts of abstract algebra are introduced in Chapters 7-9, where three basic algebraic structures of groups, rings, and fields and their properties are explained. Chapter 10 is about computational complexities of several related mathematical algorithms, and hard problems such as integer factorization and discrete logarithm. Chapter 11 presents the basics of lattice theory and the lattice basis reduction algorithm--the LLL algorithm and its application in the cryptanalysis of the RSA algorithm. Containing a number of exercises on key algorithms, the book is suitable for use as a textbook for undergraduate students and first-year graduate students in information security programs. It is also an ideal reference book for cryptography professionals looking to master public-key cryptography.
