Low|dimensional lattice basis reduction revisited

Low-dimensional lattice basis reduction revisited - ACM Digital Library

Lattice reduction is a geometric generalization of the problem of computing greatest common divisors. Most of the interesting algorithmic problems related to ...

Low-Dimensional Lattice Basis Reduction Revisited

0, 00 2008. Page 3. Low-Dimensional Lattice Basis Reduction Revisited. · 3. In this paper, we generalize Lagrange's algorithm to arbitrary dimension. Al ...

Low-Dimensional Lattice Basis Reduction Revisited - SpringerLink

Most of the interesting algorithmic problems in the geometry of numbers are NP-hard as the lattice dimension increases. This article deals with the ...

Low-dimensional lattice basis reduction revisited - ACM Digital Library

However, finding a Minkowski-reduced basis or a HKZ-reduced basis is NP- hard under randomized reductions as the dimension increases, because such bases contain ...

Low-Dimensional Lattice Basis Reduction Revisited

Low-Dimensional Lattice Basis Reduction Revisited. Phong Q. Nguyen and Damien Stehlé. Abstract: Most of the interesting algorithmic problems in the geometry ...

Low-Dimensional Lattice Basis Reduction Revisited (Extended ...

We show that up to dimension four, the greedy algorithm computes a Minkowski-reduced basis in quadratic time without fast arithmetic. This implies that a ...

Low-dimensional lattice basis reduction revisited - Hal-Inria

This article deals with the low-dimensional case. We study a greedy lattice basis reduction algorithm for the Euclidean norm.

Low-dimensional lattice basis reduction revisited - ResearchGate

From a mathematical point of view, we show that up to dimension four, the output of the greedy algorithm is optimal: the output basis reaches all the successive ...

Low-dimensional lattice basis reduction revisited - Scholar Archive

Low-dimensional lattice basis reduction revisited. ACM. Transactions on Algorithms, Association for Computing Machinery, 2009, To appear, pp ...

Low-dimensional lattice basis reduction revisited

Cite this ... Nguyen, Phong Q. ; Stehle, Damien. / Low-dimensional lattice basis reduction revisited. In: ACM Transactions on Algorithms. 2009 ; Vol. 5, No. 4. pp ...

Low-dimensional lattice basis reduction revisited

Low-dimensional lattice basis reduction revisited ; Title of host publication, Proceedings of the 6th International Symposium on Algorithmic Number Theory (ANTS ...

Lenstra–Lenstra–Lovász lattice basis reduction algorithm - Wikipedia

... basis vectors are as short as possible for lattices of dimensions greater than 4. ... "Low-dimensional lattice basis reduction revisited". ACM Transactions on ...

glwhart/MinkowskiReduction.jl: Lattice reduction in three dimensions

(See Phong Nguyen and Damien Stehlé, "Low-Dimensional Lattice Basis Reduction Revisited ") The implementation in this repo for three dimensions (and two ...

Gauss' algorithm revisited - ScienceDirect.com

2011, Lattice Basis Reduction: An Introduction to the LLL Algorithm and its Applications. Low-dimensional lattice basis reduction revisited. 2009, ACM ...

Algorithm to solve SVP (shortest vector problem) using LLL reduction

The problem is the time/memory complexity: for a 3-dimensional input lattice ... Lattice Basis Reduction: Improved Practical Algorithms and ...

Floating-Point LLL Revisited - IACR

Given an integer d-dimensional lattice basis with vec- tors of norm less than B in an n-dimensional space, L3 outputs a so- called L3-reduced basis in ...

Computing a Lattice Basis Revisited - Hal-Inria

The fastest algorithms known do not run in time quasi-linear in the input size: instead, the time is polynomial in the dimension and quasi-linear w.r.t. the ...

Lattice basis reduction over rings of number fields - MathOverflow

Can one use lattice basis reduction algorithms, such as LLL over (low-rank) module lattices over rings of number fields of degree greater than 1?

(PDF) A note on the low-dimensional Minkowski-reduction

and a basis which contains only minimum vectors is reduced by Hermite. In every lattice we can use the following algorithm to get a linearly ...

Practical, Predictable Lattice Basis Reduction

Low-dimensional lattice basis reduction revisited. In D. A. Buell, editor, Algorithmic number theory: 6th international symposium - ANTS-VI ...