  We consider privacy in the context of streaming algorithms for cardinality
estimation. We show that a large class of algorithms all satisfy
$\epsilon$-differential privacy, so long as (a) the algorithm is combined with
a simple down-sampling procedure, and (b) the cardinality of the input stream
is $\Omega(k/\epsilon)$. Here, $k$ is a certain parameter of the sketch that is
always at most the sketch size in bits, but is typically much smaller. We also
show that, even with no modification, algorithms in our class satisfy
$(\epsilon, \delta)$-differential privacy, where $\delta$ falls exponentially
with the stream cardinality.
  Our analysis applies to essentially all popular cardinality estimation
algorithms, and substantially generalizes and tightens privacy bounds from
earlier works.
