On the Lattice Isomorphism Problem
Data Structures and Algorithms
2013-11-05 v1 Computational Complexity
Discrete Mathematics
Combinatorics
Abstract
We study the Lattice Isomorphism Problem (LIP), in which given two lattices L_1 and L_2 the goal is to decide whether there exists an orthogonal linear transformation mapping L_1 to L_2. Our main result is an algorithm for this problem running in time n^{O(n)} times a polynomial in the input size, where n is the rank of the input lattices. A crucial component is a new generalized isolation lemma, which can isolate n linearly independent vectors in a given subset of Z^n and might be useful elsewhere. We also prove that LIP lies in the complexity class SZK.
Cite
@article{arxiv.1311.0366,
title = {On the Lattice Isomorphism Problem},
author = {Ishay Haviv and Oded Regev},
journal= {arXiv preprint arXiv:1311.0366},
year = {2013}
}
Comments
23 pages, SODA 2014