  \emph{Group Testing} (GT) addresses the problem of identifying a small subset
of defective items from a large population, by grouping items into as few test
pools as possible. In \emph{Adaptive GT} (AGT), outcomes of previous tests can
influence the makeup of future tests. Using an information theoretic point of
view, Aldridge $2012$ showed that in the regime of a few defectives, adaptivity
does not help much, as the number of tests required is essentially the same as
for non-adaptive GT.
  \emph{Secure GT} considers a scenario where there is an eavesdropper who may
observe a fraction $\delta$ of the tests results, yet should not be able to
infer the status of the items. In the non-adaptive scenario, the number of
tests required is $1/(1-\delta)$ times the number of tests without the secrecy
constraint.
  In this paper, we consider \emph{Secure Adaptive GT}. Specifically, when
during the makeup of the pools one has access to a private feedback link from
the lab, of rate $R_f$. We prove that the number of tests required for both
correct reconstruction at the legitimate lab, with high probability, and
negligible mutual information at the eavesdropper is $1/min\{1,1-\delta+R_f\}$
times the number of tests required with no secrecy constraint. Thus, unlike
non-secure GT, where an adaptive algorithm has only a mild impact, under a
security constraint it can significantly boost performance. A key insight is
that not only the adaptive link should disregard the actual test results and
simply send keys, these keys should be enhanced through a "secret sharing"
scheme before usage. We drive sufficiency and necessity bounds that completely
characterizes the Secure Adaptive GT capacity.
