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- W1566571341 abstract "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 $Msubseteq R^n$ and a full rank integer lattice $Lsubseteq Q^n$, the emph{subspace avoiding problem} SAP, defined by Blomer and Naewe cite{blomer}, is to find a shortest vector in $Lsetminus M$. 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 results.begin{enumerate}item We give a $2^{O(n)}$ time algorithm to compute $i^{th}$ successive minima of a full rank lattice $Lsubset Q^n$ if $i$ is $O(frac{n}{log n})$. item We give a $2^{O(n)}$ time algorithm to solve a restricted emph{closest vector problem CVP} where the inputs fulfil a promise about the distance of the input vector from the lattice.item We also show that unrestricted CVP has a $2^{O(n)}$ exact algorithm if there is a $2^{O(n)}$ time exact algorithm for solving CVP with additional input $v_iin L, 1leq ileq n$, where $|v_i|_p$ is the $i^{th}$ successive minima of $L$ for each $i$. end{enumerate}We also give a new approximation algorithm for SAP and theemph{Convex Body Avoiding problem} which is a generalization of SAP.Several of our algorithms work for emph{gauge} functions as metric,where the gauge function has a natural restriction and is accessed byan oracle." @default.
- W1566571341 created "2016-06-24" @default.
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- W1566571341 date "2008-01-01" @default.
- W1566571341 modified "2023-09-25" @default.
- W1566571341 title "Some Sieving Algorithms for Lattice Problems" @default.
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- W1566571341 doi "https://doi.org/10.4230/lipics.fsttcs.2008.1738" @default.
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