Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sieving for closest lattice vectors (with preprocessing)   Lattice-based cryptography has recently emerged as a prime candidate for
efficient and secure post-quantum cryptography. The two main hard problems
underlying its security are the shortest vector problem (SVP) and the closest
vector problem (CVP). Various algorithms have been studied for solving these
problems, and for SVP, lattice sieving currently dominates in terms of the
asymptotic time complexity: one can heuristically solve SVP in time
$2^{0.292d}$ in high dimensions $d$ [BDGL'16]. Although several SVP algorithms
can also be used to solve CVP, it is not clear whether this also holds for
heuristic lattice sieving methods. The best time complexity for CVP is
currently $2^{0.377d}$ [BGJ'14].
  In this paper we revisit sieving algorithms for solving SVP, and study how
these algorithms can be modified to solve CVP and its variants as well. Our
first method is aimed at solving one problem instance and minimizes the overall
time complexity for a single CVP instance with a time complexity of
$2^{0.292d}$. Our second method minimizes the amortized time complexity for
several instances on the same lattice, at the cost of a larger preprocessing
cost. We can solve the closest vector problem with preprocessing (CVPP) with
$2^{0.636d}$ space and preprocessing, in $2^{0.136d}$ time, while the query
complexity can even be reduced to $2^{\epsilon d}$ at the cost of preprocessing
time and memory complexities of $(1/\epsilon)^{O(d)}$.
  For easier variants of CVP, such as approximate CVP and bounded distance
decoding (BDD), we further show how the preprocessing method achieves even
better complexities. For instance, we can solve approximate CVPP with large
approximation factors $k$ with polynomial-sized advice in polynomial time if $k
= \Omega(\sqrt{d/\log d})$, heuristically closing the gap between the
decision-CVPP result of [AR'04] and the search-CVPP result of [DRS'14].

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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn