Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Systematic Approach towards Efficient Private Matrix Multiplication   We consider the problems of Private and Secure Matrix Multiplication (PSMM)
and Fully Private Matrix Multiplication (FPMM), for which matrices privately
selected by a master node are multiplied at distributed worker nodes without
revealing the indices of the selected matrices, even when a certain number of
workers collude with each other. We propose a novel systematic approach to
solve PSMM and FPMM with colluding workers, which leverages solutions to a
related Secure Matrix Multiplication (SMM) problem where the data (rather than
the indices) of the multiplied matrices are kept private from colluding
workers. Specifically, given an SMM strategy based on polynomial codes or
Lagrange codes, one can exploit the special structure inspired by the matrix
encoding function to design private coded queries for PSMM/FPMM, such that the
algebraic structure of the computation result at each worker resembles that of
the underlying SMM strategy. Adopting this systematic approach provides novel
insights in private query designs for private matrix multiplication,
substantially simplifying the processes of designing PSMM and FPMM strategies.
Furthermore, the PSMM and FPMM strategies constructed following the proposed
approach outperform the state-of-the-art strategies in one or more performance
metrics including recovery threshold (minimal number of workers the master
needs to wait for before correctly recovering the multiplication result),
communication cost, and computation complexity, demonstrating a more flexible
tradeoff in optimizing system efficiency.

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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph