# On Bounded Distance Decoding for General Lattices

@inproceedings{Liu2006OnBD, title={On Bounded Distance Decoding for General Lattices}, author={Yi-Kai Liu and Vadim Lyubashevsky and Daniele Micciancio}, booktitle={APPROX-RANDOM}, year={2006} }

- Published in APPROX-RANDOM 2006
DOI:10.1007/11830924_41

A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice $\mathcal{L}$ represented by some basis, and a target point $\vec{y}$, find the lattice point closest to $\vec{y}$. Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance $\lambda_1(\mathcal{L})$ of the lattice. Specifically, in the α-Bounded Distance Decoding problem (α-BDD), we are given a lattice… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 22 REFERENCES

## Improved Inapproximability of Lattice and Coding Problems With Preprocessing

VIEW 16 EXCERPTS

HIGHLY INFLUENTIAL

## Lattice Problems in NP ∩ coNP

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## The shortest vector problem is NP-hard to approximate to within some constant

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## Finding the closest lattice vector when it's unusually close

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Approximating-CVP to within almost-polynomial factors is NP-hard

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## The hardness of approximate optima in lattices, codes, and systems of linear equations

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## Hardness of Approximating the Closest Vector Problem with Pre-Processing

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Lattice problems and norm embeddings

VIEW 3 EXCERPTS

## Closest point search in lattices

VIEW 1 EXCERPT