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The LLL Algorithm

2009-12-02 Computers
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Release : 2009-12-02
Genre : Computers
Kind : eBook
Book Rating : 952/5 ( reviews)

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Book Synopsis The LLL Algorithm by : Phong Q. Nguyen

Download or read book The LLL Algorithm written by Phong Q. Nguyen. This book was released on 2009-12-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lattice Basis Reduction

2011-08-12 Computers
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Release : 2011-08-12
Genre : Computers
Kind : eBook
Book Rating : 043/5 ( reviews)

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Book Synopsis Lattice Basis Reduction by : Murray R. Bremner

Download or read book Lattice Basis Reduction written by Murray R. Bremner. This book was released on 2011-08-12. Available in PDF, EPUB and Kindle. Book excerpt: 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

Complexity of Lattice Problems

2012-12-06 Computers
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Release : 2012-12-06
Genre : Computers
Kind : eBook
Book Rating : 975/5 ( reviews)

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Book Synopsis Complexity of Lattice Problems by : Daniele Micciancio

Download or read book Complexity of Lattice Problems written by Daniele Micciancio. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of Public Key Cryptography

2012-03-15 Computers
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Release : 2012-03-15
Genre : Computers
Kind : eBook
Book Rating : 925/5 ( reviews)

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Book Synopsis Mathematics of Public Key Cryptography by : Steven D. Galbraith

Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith. This book was released on 2012-03-15. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

A Course in Computational Algebraic Number Theory

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 456/5 ( reviews)

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Book Synopsis A Course in Computational Algebraic Number Theory by : Henri Cohen

Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

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