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Author: Daniele Micciancio
Publisher: Springer Science & Business Media
ISBN: 1461508975
Category : Computers
Languages : en
Pages : 229
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Book Description
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: Daniele Micciancio
Publisher: Springer Science & Business Media
ISBN: 1461508975
Category : Computers
Languages : en
Pages : 229
Get Book
Book Description
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: Daniele Micciancio
Publisher: Springer Science & Business Media
ISBN: 9780792376880
Category : Computers
Languages : en
Pages : 234
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Book Description
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: Daniele Micciancio
Publisher: Springer
ISBN: 9781461352938
Category : Computers
Languages : en
Pages : 0
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Book Description
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:
ISBN: 9781680831122
Category : Computer networks
Languages : en
Pages : 156
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Book Description
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
ISBN: 3642033563
Category : Computers
Languages : en
Pages : 702
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Book Description
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: Josef Pawel Pieprzyk
Publisher: Springer
ISBN: 3540892559
Category : Computers
Languages : en
Pages : 572
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Book Description
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: Phong Q. Nguyen
Publisher: Springer Science & Business Media
ISBN: 3642022952
Category : Computers
Languages : en
Pages : 503
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Book Description
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
Publisher: Springer Science & Business Media
ISBN: 3540887024
Category : Mathematics
Languages : en
Pages : 246
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Book Description
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: Henri Gilbert
Publisher: Springer
ISBN: 3642131905
Category : Computers
Languages : en
Pages : 706
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Book Description
These are the proceedings of Eurocrypt 2010, the 29th in the series of Eu- pean conferences on the Theory and Application of Cryptographic Techniques. The conference was sponsored by the International Association for Cryptologic Research and held on the French Riviera, May 30–June 3, 2010. A total of 191 papers were received of which 188 were retained as valid submissions. These were each assigned to at least three Program Committee members and a total of 606 review reports were produced. The printed record of the reviews and extensive online discussions that followed would be almost as voluminous as these proceedings. In the end 35 submissions were accepted with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in these proceedings were not subject to a second review before publication and the authors are responsible for their contents. The ProgramCommittee, listed on the next page, deservesparticular thanks for all their hard work, their outstanding expertise, and their constant c- mitment to all aspects of the evaluation process. These thanks are of course extended to the very many external reviewers who took the time to help out during the evaluation process.It was also a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR Distinguished Lecture.
Author: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609
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Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
