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Author : John Talbot,D. J. A. Welsh
Publisher : Cambridge University Press
Page : 310 pages
File Size : 49,6 Mb
Release : 2006-01-12
Category : Computers
ISBN : 0521617715
Introductory textbook on Cryptography.
Author : Jörg Rothe
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 45,6 Mb
Release : 2005-07-22
Category : Computers
ISBN : 9783540221470
Modern cryptology increasingly employs mathematically rigorous concepts and methods from complexity theory. Conversely, current research topics in complexity theory are often motivated by questions and problems from cryptology. This book takes account of this situation, and therefore its subject is what may be dubbed "cryptocomplexity'', a kind of symbiosis of these two areas. This book is written for undergraduate and graduate students of computer science, mathematics, and engineering, and can be used for courses on complexity theory and cryptology, preferably by stressing their interrelation. Moreover, it may serve as a valuable source for researchers, teachers, and practitioners working in these fields. Starting from scratch, it works its way to the frontiers of current research in these fields and provides a detailed overview of their history and their current research topics and challenges.
Author : Daniele Micciancio,Shafi Goldwasser
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461508977
Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.
Author : Yehuda Lindell
Publisher : Springer
Page : 450 pages
File Size : 51,7 Mb
Release : 2017-04-05
Category : Computers
ISBN : 9783319570488
This is a graduate textbook of advanced tutorials on the theory of cryptography and computational complexity. In particular, the chapters explain aspects of garbled circuits, public-key cryptography, pseudorandom functions, one-way functions, homomorphic encryption, the simulation proof technique, and the complexity of differential privacy. Most chapters progress methodically through motivations, foundations, definitions, major results, issues surrounding feasibility, surveys of recent developments, and suggestions for further study. This book honors Professor Oded Goldreich, a pioneering scientist, educator, and mentor. Oded was instrumental in laying down the foundations of cryptography, and he inspired the contributing authors, Benny Applebaum, Boaz Barak, Andrej Bogdanov, Iftach Haitner, Shai Halevi, Yehuda Lindell, Alon Rosen, and Salil Vadhan, themselves leading researchers on the theory of cryptography and computational complexity. The book is appropriate for graduate tutorials and seminars, and for self-study by experienced researchers, assuming prior knowledge of the theory of cryptography.
Author : Benny Applebaum
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 51,9 Mb
Release : 2013-12-19
Category : Computers
ISBN : 9783642173677
Locally computable (NC0) functions are "simple" functions for which every bit of the output can be computed by reading a small number of bits of their input. The study of locally computable cryptography attempts to construct cryptographic functions that achieve this strong notion of simplicity and simultaneously provide a high level of security. Such constructions are highly parallelizable and they can be realized by Boolean circuits of constant depth. This book establishes, for the first time, the possibility of local implementations for many basic cryptographic primitives such as one-way functions, pseudorandom generators, encryption schemes and digital signatures. It also extends these results to other stronger notions of locality, and addresses a wide variety of fundamental questions about local cryptography. The author's related thesis was honorably mentioned (runner-up) for the ACM Dissertation Award in 2007, and this book includes some expanded sections and proofs, and notes on recent developments. The book assumes only a minimal background in computational complexity and cryptography and is therefore suitable for graduate students or researchers in related areas who are interested in parallel cryptography. It also introduces general techniques and tools which are likely to interest experts in the area.
Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 50,5 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : Maria Isabel Gonzalez Vasco,Rainer Steinwandt
Publisher : CRC Press
Page : 244 pages
File Size : 55,8 Mb
Release : 2015-04-01
Category : Computers
ISBN : 9781584888376
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 : Igor Shparlinski
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 44,6 Mb
Release : 2003-02-12
Category : Computers
ISBN : 3764366540
The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.
Author : Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 52,8 Mb
Release : 2008-11-04
Category : Mathematics
ISBN : 9783764388270
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 : Oded Goldreich
Publisher : Springer
Page : 564 pages
File Size : 55,9 Mb
Release : 2011-08-03
Category : Computers
ISBN : 9783642226700
This book presents a collection of 36 pieces of scientific work in the areas of complexity theory and foundations of cryptography: 20 research contributions, 13 survey articles, and 3 programmatic and reflective viewpoint statements. These so far formally unpublished pieces were written by Oded Goldreich, some in collaboration with other scientists. The articles included in this book essentially reflect the topical scope of the scientific career of Oded Goldreich now spanning three decades. In particular the topics dealt with include average-case complexity, complexity of approximation, derandomization, expander graphs, hashing functions, locally testable codes, machines that take advice, NP-completeness, one-way functions, probabilistically checkable proofs, proofs of knowledge, property testing, pseudorandomness, randomness extractors, sampling, trapdoor permutations, zero-knowledge, and non-iterative zero-knowledge. All in all, this potpourri of studies in complexity and cryptography constitutes a most valuable contribution to the field of theoretical computer science centered around the personal achievements and views of one of its outstanding representatives.
Author : John Talbot,Dominic Welsh
Publisher : Cambridge University Press
Page : 29 pages
File Size : 42,7 Mb
Release : 2006-01-12
Category : Mathematics
ISBN : 9781139448390
Cryptography plays a crucial role in many aspects of today's world, from internet banking and ecommerce to email and web-based business processes. Understanding the principles on which it is based is an important topic that requires a knowledge of both computational complexity and a range of topics in pure mathematics. This book provides that knowledge, combining an informal style with rigorous proofs of the key results to give an accessible introduction. It comes with plenty of examples and exercises (many with hints and solutions), and is based on a highly successful course developed and taught over many years to undergraduate and graduate students in mathematics and computer science.
Author : Serge Vaudenay
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 54,8 Mb
Release : 2005-09-16
Category : Computers
ISBN : 0387254641
A Classical Introduction to Cryptography: Applications for Communications Security introduces fundamentals of information and communication security by providing appropriate mathematical concepts to prove or break the security of cryptographic schemes. This advanced-level textbook covers conventional cryptographic primitives and cryptanalysis of these primitives; basic algebra and number theory for cryptologists; public key cryptography and cryptanalysis of these schemes; and other cryptographic protocols, e.g. secret sharing, zero-knowledge proofs and undeniable signature schemes. A Classical Introduction to Cryptography: Applications for Communications Security is designed for upper-level undergraduate and graduate-level students in computer science. This book is also suitable for researchers and practitioners in industry. A separate exercise/solution booklet is available as well, please go to www.springeronline.com under author: Vaudenay for additional details on how to purchase this booklet.
Author : K. Ko
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781468468021
Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. On the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems. In addition, the theoretical studies of the notion of polynomial-time tractability some times also yield interesting new practical algorithms. A typical exam ple is the application of the ellipsoid algorithm to combinatorial op timization problems (see, for example, Lovasz [1986]). On the other hand, it has a strong influence on many different branches of mathe matics, including combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a construc tive proof which admits a polynomial-time algorithm for the solution. One of the examples is the recent work on algorithmic theory of per mutation groups. In the area of numerical computation, there are also two tradi tionally independent approaches: recursive analysis and numerical analysis.
Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783662036426
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
Author : Oded Goldreich
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 47,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662125212
Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.
