Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Capacity of Private Monomial Computation   In this work, we consider private monomial computation (PMC) for replicated
noncolluding databases. In PMC, a user wishes to privately retrieve an
arbitrary multivariate monomial from a candidate set of monomials in $f$
messages over a finite field $\mathbb F_q$, where $q=p^k$ is a power of a prime
$p$ and $k \ge 1$, replicated over $n$ databases. We derive the PMC capacity
under a technical condition on $p$ and for asymptotically large $q$. The
condition on $p$ is satisfied, e.g., for large enough $p$. Also, we present a
novel PMC scheme for arbitrary $q$ that is capacity-achieving in the asymptotic
case above. Moreover, we present formulas for the entropy of a multivariate
monomial and for a set of monomials in uniformly distributed random variables
over a finite field, which are used in the derivation of the capacity
expression.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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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: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: eess