On the lattice isomorphism problem

Ishay Haviv, Oded Regev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the Lattice Isomorphism Problem (LIP), in which given two lattices L1 and L2 the goal is to decide whether there exists an orthogonal linear transformation mapping L1 to L2. 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 Zn and might be useful elsewhere. We also prove that LIP lies in the complexity class SZK.

Original languageEnglish (US)
Title of host publicationProceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
PublisherAssociation for Computing Machinery
Pages391-404
Number of pages14
ISBN (Print)9781611973389
StatePublished - 2014
Event25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States
Duration: Jan 5 2014Jan 7 2014

Other

Other25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
CountryUnited States
CityPortland, OR
Period1/5/141/7/14

Fingerprint

Isomorphism Problem
Linear transformations
Polynomials
Complexity Classes
Linear transformation
Isolation
Lemma
Linearly
Polynomial
Subset

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Haviv, I., & Regev, O. (2014). On the lattice isomorphism problem. In Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 (pp. 391-404). Association for Computing Machinery.

On the lattice isomorphism problem. / Haviv, Ishay; Regev, Oded.

Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Association for Computing Machinery, 2014. p. 391-404.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Haviv, I & Regev, O 2014, On the lattice isomorphism problem. in Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Association for Computing Machinery, pp. 391-404, 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, OR, United States, 1/5/14.
Haviv I, Regev O. On the lattice isomorphism problem. In Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Association for Computing Machinery. 2014. p. 391-404
Haviv, Ishay ; Regev, Oded. / On the lattice isomorphism problem. Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Association for Computing Machinery, 2014. pp. 391-404
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