Author : Murray R. Bremner
Publisher : CRC Press
Page : 330 pages
File Size : 11,99 MB
Release : 2011-08-12
Category : 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
Author : Steven D. Galbraith
Publisher : Cambridge University Press
Page : 631 pages
File Size : 23,80 MB
Release : 2012-03-15
Category : Computers
ISBN : 1107013925
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Author : Phong Q. Nguyen
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 29,98 MB
Release : 2009-12-02
Category : 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.
Author : Murray R. Bremner
Publisher : CRC Press
Page : 336 pages
File Size : 48,78 MB
Release : 2011-08-12
Category : 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.
Author : Daniele Micciancio
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 25,17 MB
Release : 2012-12-06
Category : 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.
Author : Laszlo Lovasz
Publisher : SIAM
Page : 95 pages
File Size : 20,50 MB
Release : 1987-01-01
Category : Mathematics
ISBN : 0898712033
Studies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.
Author : Nigel Smart
Publisher : Springer
Page : 576 pages
File Size : 14,16 MB
Release : 2008-04-05
Category : 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.
Author : Alfred Menezes
Publisher : Springer
Page : 643 pages
File Size : 24,68 MB
Release : 2007-08-10
Category : 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.
Author : Alexander Schrijver
Publisher : John Wiley & Sons
Page : 488 pages
File Size : 21,76 MB
Release : 1998-06-11
Category : Mathematics
ISBN : 9780471982326
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
Author : M. Jason Hinek
Publisher : CRC Press
Page : 272 pages
File Size : 37,62 MB
Release : 2009-07-21
Category : Computers
ISBN : 1420075195
Thirty years after RSA was first publicized, it remains an active research area. Although several good surveys exist, they are either slightly outdated or only focus on one type of attack. Offering an updated look at this field, Cryptanalysis of RSA and Its Variants presents the best known mathematical attacks on RSA and its main variants, includin
