Some Sieving Algorithms for Lattice Problems

V. Arvind & Pushkar S. Joglekar
We study the algorithmic complexity of lattice problems based on the sieving technique due to Ajtai, Kumar, and Sivakumar~\cite{aks}. Given a $k$-dimensional subspace $M\subseteq \R^n$ and a full rank integer lattice $\L\subseteq \Q^n$, the \emph{subspace avoiding problem} SAP, defined by Bl\"omer and Naewe \cite{blomer}, is to find a shortest vector in $\L\setminus M$. We first give a $2^{O(n+k \log k)}$ time algorithm to solve \emph{the subspace avoiding problem}. Applying this algorithm we obtain the following...