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arXiv · 1311.0366

On the Lattice Isomorphism Problem

Ishay Haviv·Oded Regev
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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.

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Ishay Haviv, Oded Regev. 2013-11-02. On the Lattice Isomorphism Problem. https://arxiv.org/abs/1311.0366

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