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Author: Murray R. Bremner
Publisher: CRC Press
ISBN: 1439807043
Category : Computers
Languages : en
Pages : 330
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Book Description
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: Murray R. Bremner
Publisher: CRC Press
ISBN: 1439807043
Category : Computers
Languages : en
Pages : 330
Get Book Here
Book Description
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: 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: Steven D. Galbraith
Publisher: Cambridge University Press
ISBN: 1107013925
Category : Computers
Languages : en
Pages : 631
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Book Description
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
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: Murray R. Bremner
Publisher: CRC Press
ISBN: 1439807027
Category : Computers
Languages : en
Pages : 336
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Book Description
First developed in the early 1980s by Lenstra, Lenstra, and Lovász, 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 introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.
Author: Nigel Smart
Publisher: Springer
ISBN: 3540789677
Category : Computers
Languages : en
Pages : 576
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Book Description
Here are the refereed proceedings of the 27th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2008. The 31 revised full papers presented were carefully reviewed and selected from 163 submissions.
Author: David Pointcheval
Publisher: Springer Science & Business Media
ISBN: 3642290108
Category : Computers
Languages : en
Pages : 769
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Book Description
This book constitutes the refereed proceedings of the 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2012, held in Cambgridge, UK, in April 2012. The 41 papers, presented together with 2 invited talks, were carefully reviewed and selected from 195 submissions. The papers are organized in topical sections on index calculus, symmetric constructions, secure computation, protocols, lossy trapdoor functions, tools, symmetric cryptanalysis, fully homomorphic encryption, asymmetric cryptanalysis, efficient reductions, public-key schemes, security models, and lattices.
Author: Alfred Menezes
Publisher: Springer
ISBN: 3540741437
Category : Computers
Languages : en
Pages : 643
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Book Description
This volume constitutes the refereed proceedings of the 27th Annual International Cryptology Conference held in Santa Barbara, California, in August 2007. Thirty-three full papers are presented along with one important invited lecture. The papers address current foundational, theoretical, and research aspects of cryptology, cryptography, and cryptanalysis. In addition, readers will discover many advanced and emerging applications.
Author: Laszlo Lovasz
Publisher: SIAM
ISBN: 0898712033
Category : Mathematics
Languages : en
Pages : 95
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Book Description
Studies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.
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.
