{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/135506"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/135506","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"On Privacy in Group Testing","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Liu, Shuqi"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Matthews, Gretchen L."],"committee_members":["McMillon, Emily","López, Hiram H.","LeGrow, Jason T."],"year":2025,"date_issued":"2025-05-06","date_published":"2025-05-06","updated_at":"2026-07-22T22:19:51Z","subjects":["non-adaptive group testing","eavesdropper interference","Hamming codes","d-disjunct matrices"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10919/135506","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Matthews, Gretchen L."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["McMillon, Emily","López, Hiram H.","LeGrow, Jason T."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Liu, Shuqi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-06-13T13:11:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-06-13T13:11:11Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-05-06"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["non-adaptive group testing","eavesdropper interference","Hamming codes","d-disjunct matrices"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/135506"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Group testing is a method in which samples from several individuals are tested together as a group to save time or reduce costs. This approach has been especially useful when large numbers of people need to be tested quickly, such as during the coronavirus pandemic. However, one major concern is about privacy: can someone viewing the group test results figure out who tested positive? This thesis considers how much information that an outside observer who can see only part of the test results might be able to determine. We explore two kinds of structures: one type from Hamming codes and another based on d-disjunct matrices. For each, we calculate the chance that the observer can correctly guess who is positive, under some reasonable assumptions. Our findings suggest that the way we group and structure the overall testing scheme can make a huge difference in how much can be learned by someone watching from the outside. By understanding and analyzing these risks, we can begin to design group testing methods that protect individual privacy more effectively, even when some of the test information is exposed."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On Privacy in Group Testing"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Matthews, Gretchen L."],"dc:contributor.committeemember":["McMillon, Emily","López, Hiram H.","LeGrow, Jason T."],"dc:contributor.department":["Mathematics"],"dc:creator":["Liu, Shuqi"],"dc:date.accessioned":["2025-06-13T13:11:11Z"],"dc:date.available":["2025-06-13T13:11:11Z"],"dc:date.issued":["2025-05-06"],"dc:description.abstract":["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."],"dc:description.abstractgeneral":["Group testing is a method in which samples from several individuals are tested together as a group to save time or reduce costs. This approach has been especially useful when large numbers of people need to be tested quickly, such as during the coronavirus pandemic. However, one major concern is about privacy: can someone viewing the group test results figure out who tested positive? This thesis considers how much information that an outside observer who can see only part of the test results might be able to determine. We explore two kinds of structures: one type from Hamming codes and another based on d-disjunct matrices. For each, we calculate the chance that the observer can correctly guess who is positive, under some reasonable assumptions. Our findings suggest that the way we group and structure the overall testing scheme can make a huge difference in how much can be learned by someone watching from the outside. By understanding and analyzing these risks, we can begin to design group testing methods that protect individual privacy more effectively, even when some of the test information is exposed."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/10919/135506"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["non-adaptive group testing","eavesdropper interference","Hamming codes","d-disjunct matrices"],"dc:title":["On Privacy in Group Testing"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:51Z"}