  There exists an absolute constant $C$ with the following property. Let $A
\subseteq \mathbb{F}_p$ be a set in the prime order finite field with $p$
elements. Suppose that $|A| > C p^{5/8}$. The set \[ (A \pm A)(A \pm A) =
\{(a_1 \pm a_2)(a_3 \pm a_4) : a_1,a_2,a_3,a_4 \in A\} \] contains at least
$p/2$ elements.
