More Books:

The LLL Algorithm
Language: en
Pages: 496
Authors: Phong Q. Nguyen, Brigitte Vallée
Categories: Computers
Type: BOOK - Published: 2009-12-02 - Publisher: Springer Science & Business Media

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
Language: en
Pages: 332
Authors: Murray R. Bremner
Categories: Computers
Type: BOOK - Published: 2011-08-12 - Publisher: CRC Press

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
An Application of the LLL Algorithm to Integer Factorization
Language: en
Pages: 56
Authors: Gerwin Pineda
Categories: Algorithms
Type: BOOK - Published: 2018 - Publisher:

Solving the shortest vector problem algorithmically gained a boom with the publication of the LLL algorithm in 1982. Many problems can be reformulated as finding the shortest vector in a lattice, and the LLL can provide very good approximations to their true solutions. One of these problems is the factorization
Modified LLL Algorithms
Language: en
Pages: 83
Authors: Tianyang Zhou
Categories: Algorithms
Type: BOOK - Published: 2006 - Publisher:

"Lattice basis reduction arises from many applications, such as cryptography, communications, GPS and so on. This thesis is concerned with the widely used LLL reduction. We cast it as a QRZ matrix factorization for real bases. Based on the matrix factorization, we first give the real version of the LLL
Number-Theoretic Algorithms in Cryptography
Language: en
Pages: 243
Authors: Oleg Nikolaevich Vasilenko
Categories: Mathematics
Type: BOOK - Published: 2007 - Publisher: American Mathematical Soc.

Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important: algorithms for primality testing; factorization algorithms for integers and for polynomials in one