The LLL Algorithm - Survey and Applications
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منابع مشابه
A modified LLL algorithm for change of ordering of Grobner basis
In this paper, a modied version of LLL algorithm, which is a an algorithm with output-sensitivecomplexity, is presented to convert a given Grobner basis with respect to a specic order of a polynomialideal I in arbitrary dimensions to a Grobner basis of I with respect to another term order.Also a comparison with the FGLM conversion and Buchberger method is considered.
متن کاملUsing LLL-Reduction for Solving RSA and Factorization Problems: A Survey
25 years ago, Lenstra, Lenstra and Lovasz presented their celebrated LLL lattice reduction algorithm. Among the various applications of the LLL algorithm is a method due to Coppersmith for finding small roots of polynomial equations. We give a survey of the applications of this root finding method to the problem of inverting the RSA function and the factorization problem. As we will see, most o...
متن کاملSelected Applications of LLL in Number Theory
In this survey, I describe some applications of LLL in number theory. I show in particular how it can be used to solve many different linear problems, to solve quadratic equations, to compute efficiently in number fields...
متن کاملUsing LLL-Reduction for Solving RSA and Factorization Problems
25 years ago, Lenstra, Lenstra and Lovász presented their celebrated LLL lattice reduction algorithm. Among the various applications of the LLL algorithm is a method due to Coppersmith for finding small roots of polynomial equations. We give a survey of the applications of this root finding method to the problem of inverting the RSA function and the factorization problem. As we will see, most o...
متن کاملA : Lattice Algorithms and Applications Spring 2007 Lecture 4 : The LLL Algorithm
No efficient algorithm is known to find the shortest vector in a lattice (in arbitrary dimension), or even just computing its length λ1. A central tool in the algorithmic study of lattices (and their applications) is the LLL algorithm of Lenstra, Lenstra and Lovasz. The LLL algorithm runs in polynomial time and finds an approximate solution x to the shortest vector problem, in the sense that th...
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