On the capacity of private monomial computation
arXiv preprint arXiv:2001.06320, 2020•arxiv.org
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, eg, for large enough $ p $. Also, we present a …
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, eg, for large enough $ p $. Also, we present a …
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 messages over a finite field , where is a power of a prime and , replicated over databases. We derive the PMC capacity under a technical condition on and for asymptotically large . The condition on is satisfied, e.g., for large enough . Also, we present a novel PMC scheme for arbitrary 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.
arxiv.org
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