Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Secure Distributed Matrix Computation with Discrete Fourier Transform   We consider the problem of secure distributed matrix computation (SDMC),
where a \textit{user} queries a function of data matrices generated at
distributed \textit{source} nodes. We assume the availability of $N$ honest but
curious computation servers, which are connected to the sources, the user, and
each other through orthogonal and reliable communication links. Our goal is to
minimize the amount of data that must be transmitted from the sources to the
servers, called the \textit{upload cost}, while guaranteeing that no $T$
colluding servers can learn any information about the source matrices, and the
user cannot learn any information beyond the computation result. We first focus
on secure distributed matrix multiplication (SDMM), considering two matrices,
and propose a novel polynomial coding scheme using the properties of finite
field discrete Fourier transform, which achieves an upload cost significantly
lower than the existing results in the literature. We then generalize the
proposed scheme to include straggler mitigation, and to the multiplication of
multiple matrices while keeping the input matrices, the intermediate
computation results, as well as the final result secure against any $T$
colluding servers. We also consider a special case, called computation with own
data, where the data matrices used for computation belong to the user. In this
case, we drop the security requirement against the user, and show that the
proposed scheme achieves the minimal upload cost. We then propose methods for
performing other common matrix computations securely on distributed servers,
including changing the parameters of secret sharing, matrix transpose, matrix
exponentiation, solving a linear system, and matrix inversion, which are then
used to show how arbitrary matrix polynomials can be computed securely on
distributed servers using the proposed procedure.

16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin