Secure Adaptive Group Testing

TL;DR

This paper introduces a secure adaptive group testing framework that leverages private feedback and secret sharing to significantly reduce the number of tests needed under secrecy constraints, outperforming non-adaptive methods.

Contribution

It develops a theoretical model for secure adaptive group testing with feedback, deriving bounds that characterize the capacity under secrecy constraints.

Findings

Adaptive testing with feedback can greatly improve efficiency under security constraints.

The number of tests is reduced by a factor of 1/min{1,1−δ+R_f} with security considerations.

Secret sharing schemes are essential for maintaining secrecy in adaptive group testing.

Abstract

\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.