Complexity Theory And Cryptology

Author : Jörg Rothe
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 54,7 Mb
Release : 2005-07-22
Category : Computers
ISBN : 9783540221470

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Complexity Theory and Cryptology by Jörg Rothe Pdf

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 : Jörg Rothe
Publisher : Springer
Page : 478 pages
File Size : 44,9 Mb
Release : 2009-09-02
Category : Computers
ISBN : 3540802088

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Complexity Theory and Cryptology by Jörg Rothe Pdf

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 : Jörg Rothe
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 54,6 Mb
Release : 2005-11-10
Category : Computers
ISBN : 9783540285205

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Complexity Theory and Cryptology by Jörg Rothe Pdf

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 : Oded Goldreich
Publisher : Springer
Page : 564 pages
File Size : 49,8 Mb
Release : 2011-08-03
Category : Computers
ISBN : 9783642226700

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Studies in Complexity and Cryptography by Oded Goldreich Pdf

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 : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Unknown
Page : 128 pages
File Size : 40,9 Mb
Release : 2012
Category : Combinatorial group theory
ISBN : OCLC:732847858

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Non-commutative Cryptography and Complexity of Group-theoretic Problems by Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov Pdf

Author : Igor Shparlinski
Publisher : Birkhäuser
Page : 402 pages
File Size : 45,9 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9783034880374

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Cryptographic Applications of Analytic Number Theory by Igor Shparlinski Pdf

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.

Author : Maria Isabel Gonzalez Vasco,Rainer Steinwandt
Publisher : CRC Press
Page : 244 pages
File Size : 55,6 Mb
Release : 2015-04-01
Category : Computers
ISBN : 9781584888376

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Group Theoretic Cryptography by Maria Isabel Gonzalez Vasco,Rainer Steinwandt Pdf

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 E. Shparlinski
Publisher : Unknown
Page : 411 pages
File Size : 44,9 Mb
Release : 2003
Category : Mathematics
ISBN : 0817666540

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Cryptographic Applications of Analytic Number Theory by Igor E. Shparlinski Pdf

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 : 49,6 Mb
Release : 2008-11-04
Category : Mathematics
ISBN : 9783764388270

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Group-based Cryptography by Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov Pdf

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 : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 44,9 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264

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Computational Complexity by Sanjeev Arora,Boaz Barak Pdf

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Author : Alain P. L. Hiltgen
Publisher : Unknown
Page : 156 pages
File Size : 52,6 Mb
Release : 1994
Category : Ciphers
ISBN : STANFORD:36105016449139

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Cryptographically Relevant Contributions to Combinational Complexity Theory by Alain P. L. Hiltgen Pdf

"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.

Author : Yehuda Lindell
Publisher : Springer
Page : 450 pages
File Size : 41,8 Mb
Release : 2017-04-05
Category : Computers
ISBN : 9783319570488

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Tutorials on the Foundations of Cryptography by Yehuda Lindell Pdf

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 : Carl Pomerance,Shafi Goldwasser
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 47,8 Mb
Release : 1990
Category : Computers
ISBN : 0821801554

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Cryptology and Computational Number Theory by Carl Pomerance,Shafi Goldwasser Pdf

In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.

Author : Zhiyong Zheng
Publisher : Springer Nature
Page : 364 pages
File Size : 51,5 Mb
Release : 2022
Category : Computer science
ISBN : 9789811909207

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Modern Cryptography Volume 1 by Zhiyong Zheng Pdf

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas. [Resumen de la editorial]

Author : Salil P. Vadhan
Publisher : Springer Science & Business Media
Page : 606 pages
File Size : 51,9 Mb
Release : 2007-02-07
Category : Business & Economics
ISBN : 9783540709350

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Theory of Cryptography by Salil P. Vadhan Pdf

This book constitutes the refereed proceedings of the 4th Theory of Cryptography Conference, TCC 2007, held in Amsterdam, The Netherlands in February 2007. The 31 revised full papers cover encryption, universally composable security, arguments and zero knowledge, notions of security, obfuscation, secret sharing and multiparty computation, signatures and watermarking, private approximation and black-box reductions, and key establishment.