Add to ORKGFastest algorithms and implementations for LLL basis reduction are highly hybrid symbolic-numeric. A "numerical engine" computes, via a orthogonalization process, the unimodular transformations that will improve the quality of the basis. Then, for example in the case of integer lattice bases, the transformations are applied in exact arithmetic. We focus on several aspects concerning the choice of the precision than can be used for the numerical computations. We present theoretical bounds based on reducedness perturbation results, and on a "fully numerical view" of the algorithms. This leads to new methods for certifying reducedness. We also adopt a practical point of view for looking at approches with a dynamical tuning of the precision, an...
Adaptive precision floating point LLL The LLL algorithm is one of the most studied lattice basis red...
... introduced an efficiently computable notion of reduction of basis of a Euclidean lattice that is...
Given a lattice basis of n vectors in Z^n, we propose an algorithm using 12n^3+O(n^2) floating point...
Fastest algorithms and implementations for LLL basis reduction are highly hybrid symbolic-numeric. A...
The LLL basis reduction algorithm was the first polynomial-time algorithm to compute a reduced basis...
Lattice basis reduction arises from many applications, such as cryptography, communications, GPS and...
AbstractWe modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lo...
The LLL algorithm is recognized as one of the most important achievements of twentieth century with ...
The LLL algorithm is recognized as one of the most important achievements of twentieth century with ...
International audienceQuadratic form reduction and lattice reduction are fundamental tools in comput...
International audienceAs a typical application, the Lenstra-Lenstra-Lovász lattice basis reduction a...
International audienceQuadratic form reduction and lattice reduction are fundamental tools in comput...
Let B be a basis of a Euclidean lattice, and B ̃ an approxima-tion thereof. We give a sufficient con...
Let B be a basis of a Euclidean lattice, and B ̃ an approxima-tion thereof. We give a sufficient con...
The Lenstra-Lenstra-Lovász basis reduction algorithm, also known as LLL algorithm, is an algorithm t...
Adaptive precision floating point LLL The LLL algorithm is one of the most studied lattice basis red...
... introduced an efficiently computable notion of reduction of basis of a Euclidean lattice that is...
Given a lattice basis of n vectors in Z^n, we propose an algorithm using 12n^3+O(n^2) floating point...
Fastest algorithms and implementations for LLL basis reduction are highly hybrid symbolic-numeric. A...
The LLL basis reduction algorithm was the first polynomial-time algorithm to compute a reduced basis...
Lattice basis reduction arises from many applications, such as cryptography, communications, GPS and...
AbstractWe modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lo...
The LLL algorithm is recognized as one of the most important achievements of twentieth century with ...
The LLL algorithm is recognized as one of the most important achievements of twentieth century with ...
International audienceQuadratic form reduction and lattice reduction are fundamental tools in comput...
International audienceAs a typical application, the Lenstra-Lenstra-Lovász lattice basis reduction a...
International audienceQuadratic form reduction and lattice reduction are fundamental tools in comput...
Let B be a basis of a Euclidean lattice, and B ̃ an approxima-tion thereof. We give a sufficient con...
Let B be a basis of a Euclidean lattice, and B ̃ an approxima-tion thereof. We give a sufficient con...
The Lenstra-Lenstra-Lovász basis reduction algorithm, also known as LLL algorithm, is an algorithm t...
Adaptive precision floating point LLL The LLL algorithm is one of the most studied lattice basis red...
... introduced an efficiently computable notion of reduction of basis of a Euclidean lattice that is...
Given a lattice basis of n vectors in Z^n, we propose an algorithm using 12n^3+O(n^2) floating point...