Lattice Basis Reduction

Lattice Basis Reduction
Author: Murray R. Bremner
Publisher: CRC Press
Total Pages: 330
Release: 2011-08-12
Genre: Computers
ISBN: 1439807043

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

The LLL Algorithm

The LLL Algorithm
Author: Phong Q. Nguyen
Publisher: Springer Science & Business Media
Total Pages: 503
Release: 2009-12-02
Genre: Computers
ISBN: 3642022952

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.

Mathematics of Public Key Cryptography

Mathematics of Public Key Cryptography
Author: Steven D. Galbraith
Publisher: Cambridge University Press
Total Pages: 631
Release: 2012-03-15
Genre: Computers
ISBN: 1107013925

This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Lattice Basis Reduction

Lattice Basis Reduction
Author: Murray R. Bremner
Publisher: CRC Press
Total Pages: 336
Release: 2011-08-12
Genre: Computers
ISBN: 1439807027

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.

Advances in Cryptology – EUROCRYPT 2008

Advances in Cryptology – EUROCRYPT 2008
Author: Nigel Smart
Publisher: Springer
Total Pages: 576
Release: 2008-04-05
Genre: Computers
ISBN: 3540789677

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.

Complexity of Lattice Problems

Complexity of Lattice Problems
Author: Daniele Micciancio
Publisher: Springer Science & Business Media
Total Pages: 229
Release: 2012-12-06
Genre: Computers
ISBN: 1461508975

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.

Advances in Cryptology -- EUROCRYPT 2012

Advances in Cryptology -- EUROCRYPT 2012
Author: David Pointcheval
Publisher: Springer Science & Business Media
Total Pages: 769
Release: 2012-04-02
Genre: Computers
ISBN: 3642290108

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.

Advances in Cryptology - CRYPTO 2007

Advances in Cryptology - CRYPTO 2007
Author: Alfred Menezes
Publisher: Springer
Total Pages: 643
Release: 2007-08-10
Genre: Computers
ISBN: 3540741437

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.

Advances in Cryptology – EUROCRYPT 2010

Advances in Cryptology – EUROCRYPT 2010
Author: Henri Gilbert
Publisher: Springer
Total Pages: 706
Release: 2010-05-29
Genre: Computers
ISBN: 3642131905

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.