Secure Adaptive Group Testing

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Abstract

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 Adaptive GT (AGT), outcomes of previous tests can influence the makeup of future tests. This scenario has been studied from 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 for identification of the set of defectives is essentially the same as for non-adaptive GT. Secure GT considers a scenario where there is an eavesdropper who may observe a fraction δ of the outcomes, and should not be able to infer the status of the items. In the non-adaptive scenario, the number of tests required is 1/(1-δ) times the number of tests without the secrecy constraint. In this paper, we consider Secure Adaptive GT. Specifically, when an adaptive algorithm has access to a private feedback link of rate R- f, we prove that the number of tests required for both correct reconstruction at the legitimate user, with high probability, and negligible mutual information at the eavesdropper is 1/min 1,1-δ+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 test results and send keys, these keys should be enhanced through a 'secret sharing' scheme before usage.

Original languageEnglish
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
Pages2589-2593
Number of pages5
DOIs
StatePublished - 15 Aug 2018
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: 17 Jun 201822 Jun 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2018-June

Conference

Conference2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/TerritoryUnited States
CityVail
Period17/06/1822/06/18

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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