Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Algorithms for Variants of Average-Case Lattice Problems via
  Filtering   We show polynomial-time quantum algorithms for the following problems:
  (*) Short integer solution (SIS) problem under the infinity norm, where the
public matrix is very wide, the modulus is a polynomially large prime, and the
bound of infinity norm is set to be half of the modulus minus a constant.
  (*) Learning with errors (LWE) problem given LWE-like quantum states with
polynomially large moduli and certain error distributions, including bounded
uniform distributions and Laplace distributions.
  (*) Extrapolated dihedral coset problem (EDCP) with certain parameters.
  The SIS, LWE, and EDCP problems in their standard forms are as hard as
solving lattice problems in the worst case. However, the variants that we can
solve are not in the parameter regimes known to be as hard as solving
worst-case lattice problems. Still, no classical or quantum polynomial-time
algorithms were known for the variants of SIS and LWE we consider. For EDCP,
our quantum algorithm slightly extends the result of Ivanyos et al. (2018).
  Our algorithms for variants of SIS and EDCP use the existing quantum
reductions from those problems to LWE, or more precisely, to the problem of
solving LWE given LWE-like quantum states. Our main contribution is solving LWE
given LWE-like quantum states with interesting parameters using a filtering
technique.

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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex