On Privacy in Group Testing

Group testing is a method of designing collections of samples of individual items and assessing them as collections (rather than individuals) with the goal of revealing individuals who are positive for some attribute. It has been used to test for highly contagious diseases, such as coronavirus in recent years, often with the goal of minimizing processing time or the number of tests. Privacy of personal information is important, particularly when it comes to medical history or test results for diseases. Our research studies group testing designed with parity-check matrices of Hamming codes and constant row weight d-disjunct matrices. We consider partial knowledge that an eavesdropper needs to know from the group testing matrix to obtain personal medical data. We also evaluate the leakage risk of the information under certain assumptions of the eavesdropper's abilities. The thesis concludes by proposing future directions such as handling noise, correlated individuals, and decentralized testing designs.