Some Sieving Algorithms for Lattice Problems

ABSTRACT. We study the algorithmic complexity of lattice problems based on Ajtai-Kumar-Sivakumar sieving technique [AKS01]. Given a k-dimensional subspace M ⊆ Rn and a full rank integer lattice L ⊆ Qn, the subspace avoiding problem SAP, defined by Bl¨omer and Naewe [BN07], is to find a shortest vector in L \ M. We first give a 2O(n+k log k) time algorithm to solve the subspace avoiding problem. Then, applying this algorithm we obtain the following results:

• Type: Conference
• Year: 2008
• Where: FSTTCS
• Authors: Vikraman Arvind, Pushkar S. Joglekar
• Keywords: Ajtai-Kumar-Sivakumar Sieving Technique, FSTTCS 2008, Rank Integer Lattice, Software Engineering, Subspace Avoiding Problem