# On the Lattice Distortion Problem

@article{Bennett2016OnTL,
title={On the Lattice Distortion Problem},
author={Huck Bennett and Daniel Dadush and Noah Stephens-Davidowitz},
journal={ArXiv},
year={2016},
volume={abs/1605.03613}
}
• Published 2016
• Computer Science, Mathematics
• ArXiv
• We introduce and study the \emph{Lattice Distortion Problem} (LDP). LDP asks how "similar" two lattices are. I.e., what is the minimal distortion of a linear bijection between the two lattices? LDP generalizes the Lattice Isomorphism Problem (the lattice analogue of Graph Isomorphism), which simply asks whether the minimal distortion is one. As our first contribution, we show that the distortion between any two lattices is approximated up to a $n^{O(\log n)}$ factor by a simple function of… CONTINUE READING
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## A Block Enumeration Technique for Lattice Basis Reduction

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 46 REFERENCES

• L. Babai
• 2016

## Lattices with Symmetry

• Computer Science, Mathematics, Physics
• Journal of Cryptology
• 2016

## Dimension-preserving reductions between lattice problems

• Noah Stephens-Davidowitz
• http://noahsd.com/latticeproblems.pdf,
• 2015

## Lattice-based FHE as secure as PKE

• Physics, Mathematics, Computer Science
• ITCS '14
• 2014

## On the Lattice Isomorphism Problem

• Computer Science, Mathematics
• SODA
• 2014

## Tracy . An improved lll algorithm

• Franklin T. Luk, M. Daniel
• Linear Algebra and its Applications
• 2014

## Approximate Graph Isomorphism

• Mathematics, Computer Science
• Electronic Colloquium on Computational Complexity
• 2012

## Numerical Linear Algebra

• Computer Science
• Encyclopedia of Parallel Computing
• 2011

## A deterministic single exponential time algorithm for most lattice problems based on voronoi cell computations

• Mathematics, Computer Science
• STOC '10
• 2010