Conference Paper

Some Sieving Algorithms for Lattice Problems.

DOI: 10.4230/LIPIcs.FSTTCS.2008.1738 Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008, December 9-11, 2008, Bangalore, India
Source: OAI

ABSTRACT We study the algorithmic complexity of lattice problems based on the sieving technique due to Ajtai, Kumar, and Sivakumar (AKS01). Given a k-dimensional subspace M ⊆ Rn and a full rank integer lattice L ⊆ Qn, the subspace avoiding problem SAP, defined by Bl¨

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    ABSTRACT: We give a deterministic 2(o(n))algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This leads to a nearly optimal deterministic algorithm for estimating the volume of a convex body and improved deterministic algorithms for fundamental lattice problems under general norms.
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