Paying witness to the author’s thirty-year career in science, these high-quality papers, some co-written with colleagues, reflect his professional range, covering material from average-case complexity to derandomization and ...

Author: Oded Goldreich

Publisher: Springer Science & Business Media

ISBN: 9783642226694

Category: Computers

Page: 563

View: 997

Paying witness to the author’s thirty-year career in science, these high-quality papers, some co-written with colleagues, reflect his professional range, covering material from average-case complexity to derandomization and probabilistically checkable proofs.

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.

Author: Jörg Rothe

Publisher: Springer Science & Business Media

ISBN: 9783540285205

Category: Computers

Page: 478

View: 778

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.

Another Motivation for Reducing the Randomness Complexity of Algorithms
Oded Goldreich Abstract. We observe that the randomness-complexity ... Studies
in Complexity and Cryptography, LNCS 6650, pp. 555–560, 2011. c Springer-
Verlag ...

Author: Oded Goldreich

Publisher: Springer

ISBN: 9783642226700

Category: Computers

Page: 563

View: 445

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 These so far formally unpublished pieces were written by Oded Goldreich, some in collaboration with other scientists.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.

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid.

Author: Daniele Micciancio

Publisher: Springer Science & Business Media

ISBN: 9781461508977

Category: Computers

Page: 220

View: 134

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.

This book provides that knowledge, combining an informal style with strong proofs of the key results to provide an accessible introduction.

Author: John Talbot

Publisher: Cambridge University Press

ISBN: 0521852315

Category: Mathematics

Page: 304

View: 968

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 strong proofs of the key results to provide an accessible introduction. It includes many examples and exercises, and is based on a highly successful course developed and taught over many years.

This second volume contains a thorough treatment of three basic applications: Encryption, Signatures, and General Cryptographic Protocols.

Author: Oded Goldreich

Publisher: Cambridge University Press

ISBN: 9781107393974

Category: Computers

Page:

View: 912

Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. Foundations of Cryptography presents a rigorous and systematic treatment of foundational issues, defining cryptographic tasks and solving cryptographic problems. The emphasis is on the clarification of fundamental concepts and on demonstrating the feasibility of solving several central cryptographic problems, as opposed to describing ad-hoc approaches. This second volume contains a thorough treatment of three basic applications: Encryption, Signatures, and General Cryptographic Protocols. It builds on the previous volume, which provided a treatment of one-way functions, pseudorandomness, and zero-knowledge proofs. It is suitable for use in a graduate course on cryptography and as a reference book for experts. The author assumes basic familiarity with the design and analysis of algorithms; some knowledge of complexity theory and probability is also useful.

This is a graduate textbook of advanced tutorials on the theory of cryptography and computational complexity.

Author: Yehuda Lindell

Publisher: Springer

ISBN: 9783319570488

Category: Computers

Page: 450

View: 878

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.

"The provability of certain cryptographic assumptions and, more generally, the existence of provable practical security is investigated.

Author: Alain P. L. Hiltgen

Publisher:

ISBN: STANFORD:36105016449139

Category: Ciphers

Page: 129

View: 409

"The provability of certain cryptographic assumptions and, more generally, the existence of provable practical security is investigated. It is argued why combinatorial complexity is the complexity measure that is most suited if the security of practical crytographic applications is to be proved."--p. iii.

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory.

Author: Alexei Myasnikov

Publisher: Springer Science & Business Media

ISBN: 9783764388263

Category: Mathematics

Page: 183

View: 419

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.

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.

Author: Benny Applebaum

Publisher: Springer Science & Business Media

ISBN: 9783642173677

Category: Computers

Page: 193

View: 832

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.

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 ...

Author: Delaram Kahrobaei

Publisher: American Mathematical Soc.

ISBN: 9780821898598

Category: Mathematics

Page: 123

View: 222

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.

Author: Joachim von zur GathenPublish On: 2015-11-20

This book offers an introduction to cryptology, the science that makes secure communications possible, and addresses its two complementary aspects: cryptography—--the art of making secure building blocks—--and cryptanalysis—--the art ...

Author: Joachim von zur Gathen

Publisher: Springer

ISBN: 9783662484258

Category: Computers

Page: 876

View: 186

This book offers an introduction to cryptology, the science that makes secure communications possible, and addresses its two complementary aspects: cryptography—--the art of making secure building blocks—--and cryptanalysis—--the art of breaking them. The text describes some of the most important systems in detail, including AES, RSA, group-based and lattice-based cryptography, signatures, hash functions, random generation, and more, providing detailed underpinnings for most of them. With regard to cryptanalysis, it presents a number of basic tools such as the differential and linear methods and lattice attacks. This text, based on lecture notes from the author’s many courses on the art of cryptography, consists of two interlinked parts. The first, modern part explains some of the basic systems used today and some attacks on them. However, a text on cryptology would not be complete without describing its rich and fascinating history. As such, the colorfully illustrated historical part interspersed throughout the text highlights selected inventions and episodes, providing a glimpse into the past of cryptology. The first sections of this book can be used as a textbook for an introductory course to computer science or mathematics students. Other sections are suitable for advanced undergraduate or graduate courses. Many exercises are included. The emphasis is on providing reasonably complete explanation of the background for some selected systems.

The focus of this book is the P versus NP Question and the theory of NP-completeness.

Author: Oded Goldreich

Publisher: Cambridge University Press

ISBN: 9781139490092

Category: Computers

Page:

View: 986

The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.

The book introduces new techniques that imply rigorous lower bounds on the com plexity of some number-theoretic and cryptographic problems.

Author: Igor Shparlinski

Publisher: Birkhäuser

ISBN: 9783034880374

Category: Mathematics

Page: 414

View: 527

The book introduces new techniques that imply rigorous lower bounds on the com plexity of some number-theoretic and cryptographic problems. It also establishes certain attractive pseudorandom properties of various cryptographic primitives. These methods and techniques are based on bounds of character sums and num bers of solutions of some polynomial equations over finite fields and residue rings. Other number theoretic techniques such as sieve methods and lattice reduction algorithms are used as well. The book also contains a number of open problems and proposals for further research. The emphasis is on obtaining unconditional rigorously proved statements. The bright side of this approach is that the results do not depend on any assumptions or conjectures. On the downside, the results are much weaker than those which are widely believed to be true. We obtain several lower bounds, exponential in terms of logp, on the degrees and orders of o polynomials; o algebraic functions; o Boolean functions; o linear recurrence sequences; coinciding with values of the discrete logarithm modulo a prime p at sufficiently many points (the number of points can be as small as pI/2+O:). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the rightmost bit of the discrete logarithm and defines whether the argument is a quadratic residue.

Abstract: "The DIMACS Workshop on Structural Complexity and Crytography took place at Rutgers on December 3-6, 1990. It was part of the program for the DIMACS Special Year on the Complexity of Interactive Computation.

Author: DIMACS (GROUP)

Publisher:

ISBN: OCLC:25600908

Category: Cryptography

Page: 52

View: 135

Abstract: "The DIMACS Workshop on Structural Complexity and Crytography took place at Rutgers on December 3-6, 1990. It was part of the program for the DIMACS Special Year on the Complexity of Interactive Computation. This report contains the abstracts of the talks given at the workshop and a directory of all participants."

At the 1983 meeting in Santa Barbara the International Association for Cryptologic Research was launched and it now sponsors all the meetings of the series. This volume presents the proceedings of Eurocrypt '92, held in Hungary.

Author: Rainer A. Rueppel

Publisher: Springer

ISBN: 9783540475552

Category: Computers

Page: 491

View: 865

A series of workshops devoted to modern cryptography began in Santa Barbara,California in 1981 and was followed in 1982 by a European counterpart in Burg Feuerstein, Germany. The series has been maintained with summer meetings in Santa Barbara and spring meetings somewhere in Europe. At the 1983 meeting in Santa Barbara the International Association for Cryptologic Research was launched and it now sponsors all the meetings of the series. This volume presents the proceedings of Eurocrypt '92, held in Hungary. The papers are organized into the following parts: Secret sharing, Hash functions, Block ciphers, Stream ciphers, Public key I, Factoring, Trapdoor primes and moduli (panel report), Public key II, Pseudo-random permutation generators, Complexity theory and cryptography I, Zero-knowledge, Digital knowledge and electronic cash, Complexity theory andcryptography II, Applications, and selected papers from the rump session. Following the tradition of the series, the authors produced full papers after the meeting, in some cases with revisions.

This book offers a comprehensive perspective to modern topics in complexity theory, which is a central field of the theoretical foundations of computer science.

Author: Oded Goldreich

Publisher: Cambridge University Press

ISBN: 052188473X

Category: Computers

Page: 632

View: 663

This book offers a comprehensive perspective to modern topics in complexity theory, which is a central field of the theoretical foundations of computer science. It addresses the looming question of what can be achieved within a limited amount of time with or without other limited natural computational resources. Can be used as an introduction for advanced undergraduate and graduate students as either a textbook or for self-study, or to experts, since it provides expositions of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness and probabilistic proof systems.