论文标题
关于私人单项计算的能力
On the Capacity of Private Monomial Computation
论文作者
论文摘要
在这项工作中，我们考虑用于复制的非集体数据库的私人单元计算（PMC）。在PMC中，用户希望从有限字段$ \ Mathbb f_q $上私下从$ f $消息中的候选单元中私下检索一个任意的多元单元，其中$ q = p^k $是prime $ p $ and $ p $ and $ k \ ge 1 $，复制了$ n $ n $ databases。我们在$ p $上的技术条件下得出PMC容量，对于渐近的$ Q $。满足$ P $的条件，例如，对于足够大的$ p $。此外，我们提出了一种新颖的PMC方案，用于任意$ Q $，在上面的渐近案例中具有能力实现的作用。此外，我们为多元单元和一组单一分布的随机变量的单元单元的熵提出了公式，该公式用于有限场上，这些变量用于衍生能力表达。
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.
