Complexity Of Lattice Problems

Author : Daniele Micciancio,Shafi Goldwasser
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461508977

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Complexity of Lattice Problems by Daniele Micciancio,Shafi Goldwasser Pdf

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 : Chris Peikert
Publisher : Unknown
Page : 156 pages
File Size : 42,8 Mb
Release : 2016-03-07
Category : Computer networks
ISBN : 1680831127

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A Decade of Lattice Cryptography by Chris Peikert Pdf

Surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems, their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.

Author : Shai Halevi
Publisher : Springer
Page : 702 pages
File Size : 42,7 Mb
Release : 2009-08-18
Category : Computers
ISBN : 9783642033568

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Advances in Cryptology - CRYPTO 2009 by Shai Halevi Pdf

This book constitutes the refereed proceedings of the 29th Annual International Cryptology Conference, CRYPTO 2009, held in Santa Barbara, CA, USA in August 2009. The 38 revised full papers presented were carefully reviewed and selected from 213 submissions. Addressing all current foundational, theoretical and research aspects of cryptology, cryptography, and cryptanalysis as well as advanced applications, the papers are organized in topical sections on key leakage, hash-function cryptanalysis, privacy and anonymity, interactive proofs and zero-knowledge, block-cipher cryptanalysis, modes of operation, elliptic curves, cryptographic hardness, merkle puzzles, cryptography in the physical world, attacks on signature schemes, secret sharing and secure computation, cryptography and game-theory, cryptography and lattices, identity-based encryption and cryptographers’ toolbox.

Author : Phong Q. Nguyen,Brigitte Vallée
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 43,9 Mb
Release : 2009-12-02
Category : Computers
ISBN : 9783642022951

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The LLL Algorithm by Phong Q. Nguyen,Brigitte Vallée Pdf

The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.

Author : Daniel J. Bernstein,Johannes Buchmann,Erik Dahmen
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 47,5 Mb
Release : 2009-02-01
Category : Mathematics
ISBN : 9783540887027

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Post-Quantum Cryptography by Daniel J. Bernstein,Johannes Buchmann,Erik Dahmen Pdf

Quantum computers will break today's most popular public-key cryptographic systems, including RSA, DSA, and ECDSA. This book introduces the reader to the next generation of cryptographic algorithms, the systems that resist quantum-computer attacks: in particular, post-quantum public-key encryption systems and post-quantum public-key signature systems. Leading experts have joined forces for the first time to explain the state of the art in quantum computing, hash-based cryptography, code-based cryptography, lattice-based cryptography, and multivariate cryptography. Mathematical foundations and implementation issues are included. This book is an essential resource for students and researchers who want to contribute to the field of post-quantum cryptography.

Author : Josef Pawel Pieprzyk
Publisher : Springer
Page : 572 pages
File Size : 48,6 Mb
Release : 2008-12-02
Category : Computers
ISBN : 9783540892557

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Advances in Cryptology - ASIACRYPT 2008 by Josef Pawel Pieprzyk Pdf

This book constitutes the refereed proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2008, held in Melbourne, Australia, in December 2008. The 33 revised full papers presented together with the abstract of 1 invited lecture were carefully reviewed and selected from 208 submissions. The papers are organized in topical sections on muliti-party computation, cryptographic protocols, cryptographic hash functions, public-key cryptograhy, lattice-based cryptography, private-key cryptograhy, and analysis of stream ciphers.

Author : Joseph H. Silverman
Publisher : Springer
Page : 224 pages
File Size : 44,8 Mb
Release : 2003-06-30
Category : Computers
ISBN : 9783540446705

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Cryptography and Lattices by Joseph H. Silverman Pdf

This book constitutes the thoroughly refereed post-proceedings of the International Conference on Cryptography and Lattices, CaLC 2001, held in Providence, RI, USA in March 2001. The 14 revised full papers presented together with an overview paper were carefully reviewed and selected for inclusion in the book. All current aspects of lattices and lattice reduction in cryptography, both for cryptographic construction and cryptographic analysis, are addressed.

Author : Wieb Bosma
Publisher : Springer
Page : 612 pages
File Size : 43,7 Mb
Release : 2006-12-30
Category : Mathematics
ISBN : 9783540449942

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Algorithmic Number Theory by Wieb Bosma Pdf

This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.

Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 53,6 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 : Volker Diekert,Michel Habib
Publisher : Springer Science & Business Media
Page : 674 pages
File Size : 40,8 Mb
Release : 2004-03-18
Category : Computers
ISBN : 9783540212362

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STACS 2004 by Volker Diekert,Michel Habib Pdf

This book constitutes the refereed proceedings of the 21st Annual Symposium on Theoretical Aspects of Computer Science, STACS 2004, held in Montpellier, France, in March 2004. The 54 revised full papers presented together with two invited contributions were carefully reviewed and selected from more than 200 submissions. The papers are organized in topical sections on structural complexity, graph algorithms, quantum computing, satisfiability - constraint satisfaction problems, scheduling, algorithms, networks, automata theory and words, path algorithms, cryptography, logic and formal languages, game theory and complexity, and algorithmic information.

Author : Burton S.Jr. Kaliski
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 48,8 Mb
Release : 1997-08-06
Category : Computers
ISBN : 3540633847

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Advances in Cryptology - CRYPTO '97 by Burton S.Jr. Kaliski Pdf

This book constitutes the refereed proceedings of the 17th Annual International Cryptology Conference, CRYPTO'97, held in Santa Barbara, California, USA, in August 1997 under the sponsorship of the International Association for Cryptologic Research (IACR). The volume presents 35 revised full papers selected from 160 submissions received. Also included are two invited presentations. The papers are organized in sections on complexity theory, cryptographic primitives, lattice-based cryptography, digital signatures, cryptanalysis of public-key cryptosystems, information theory, elliptic curve implementation, number-theoretic systems, distributed cryptography, hash functions, cryptanalysis of secret-key cryptosystems.

Author : Murray R. Bremner
Publisher : CRC Press
Page : 330 pages
File Size : 46,8 Mb
Release : 2011-08-12
Category : Computers
ISBN : 9781439807040

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Lattice Basis Reduction by Murray R. Bremner Pdf

First developed in the early 1980s by Lenstra, Lenstra, and Lovasz, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an i

Author : Henk C.A. van Tilborg,Sushil Jajodia
Publisher : Springer Science & Business Media
Page : 1457 pages
File Size : 45,7 Mb
Release : 2014-07-08
Category : Computers
ISBN : 9781441959065

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Encyclopedia of Cryptography and Security by Henk C.A. van Tilborg,Sushil Jajodia Pdf

Expanded into two volumes, the Second Edition of Springer’s Encyclopedia of Cryptography and Security brings the latest and most comprehensive coverage of the topic: Definitive information on cryptography and information security from highly regarded researchers Effective tool for professionals in many fields and researchers of all levels Extensive resource with more than 700 contributions in Second Edition 5643 references, more than twice the number of references that appear in the First Edition With over 300 new entries, appearing in an A-Z format, the Encyclopedia of Cryptography and Security provides easy, intuitive access to information on all aspects of cryptography and security. As a critical enhancement to the First Edition’s base of 464 entries, the information in the Encyclopedia is relevant for researchers and professionals alike. Topics for this comprehensive reference were elected, written, and peer-reviewed by a pool of distinguished researchers in the field. The Second Edition’s editorial board now includes 34 scholars, which was expanded from 18 members in the First Edition. Representing the work of researchers from over 30 countries, the Encyclopedia is broad in scope, covering everything from authentication and identification to quantum cryptography and web security. The text’s practical style is instructional, yet fosters investigation. Each area presents concepts, designs, and specific implementations. The highly-structured essays in this work include synonyms, a definition and discussion of the topic, bibliographies, and links to related literature. Extensive cross-references to other entries within the Encyclopedia support efficient, user-friendly searches for immediate access to relevant information. Key concepts presented in the Encyclopedia of Cryptography and Security include: Authentication and identification; Block ciphers and stream ciphers; Computational issues; Copy protection; Cryptanalysis and security; Cryptographic protocols; Electronic payment and digital certificates; Elliptic curve cryptography; Factorization algorithms and primality tests; Hash functions and MACs; Historical systems; Identity-based cryptography; Implementation aspects for smart cards and standards; Key management; Multiparty computations like voting schemes; Public key cryptography; Quantum cryptography; Secret sharing schemes; Sequences; Web Security. Topics covered: Data Structures, Cryptography and Information Theory; Data Encryption; Coding and Information Theory; Appl.Mathematics/Computational Methods of Engineering; Applications of Mathematics; Complexity. This authoritative reference will be published in two formats: print and online. The online edition features hyperlinks to cross-references, in addition to significant research.

Author : Ugo Montanari
Publisher : Springer Science & Business Media
Page : 964 pages
File Size : 43,6 Mb
Release : 2000
Category : Electronic
ISBN : 9783540677154

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Automata, Languages and Programming by Ugo Montanari Pdf

Author : Manuel Bodirsky
Publisher : Cambridge University Press
Page : 537 pages
File Size : 51,7 Mb
Release : 2021-06-10
Category : Computers
ISBN : 9781107042841

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Complexity of Infinite-Domain Constraint Satisfaction by Manuel Bodirsky Pdf

Introduces the universal-algebraic approach to classifying the computational complexity of constraint satisfaction problems.