BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lucia Moura and Thaís Bardini Idalino (University of Ottawa and F ederal University of Santa Catarina) DTSTART:20210804T171500Z DTEND:20210804T181500Z DTSTAMP:20260416T224449Z UID:CCM2021/4 DESCRIPTION:Title: Cover-free families\, constructions and cryptographical applications\n by Lucia Moura and Thaís Bardini Idalino (University of Ottawa and Federa l University of Santa Catarina) as part of Carleton Combinatorics Meeting 2021\n\n\nAbstract\nCover-free families have been investigated under diffe rent names such as disjunct matrices\, superimposed codes and strongly sel ective families. They are interesting combinatorial objects used in combin atorial group testing as well as various applications in communications.\n \nA $d$-cover-free family $d$-$\\mathrm{CFF}(t\,n)$ is a set system consis ting of n subsets of a $t$-set\, where the union of any $d$ subsets does n ot contain any other. In combinatorial group testing\, a $d$-$\\mathrm{CFF }(t\, n)$ allows for the identification of up to $d$ defective elements in a set of $n$ elements by performing only $t$ tests (typically $t ≪ n$). \n\nThis talk begins with an introduction of cover-free families\, constru ctions and applications. We then focus on applications in cryptography and in particular discuss our work in the use of cover-free families to add f ault-tolerance to classical problems in cryptography. In order to add faul t-tolerance in aggregation of signatures\, we construct infinite sequences of cover-free families with desired properties such as high compression r atio. In the context of malleable digital signatures\, we propose a method that uses cover-free families to locate modifications in signed documents . Works by the authors on this topic can be found in the proceedings of IW OCA2018 and Indocrypt2019\, and in Advances in Mathematics of Communicatio ns (2019) and Theoretical Computer Science (2021).\n LOCATION:https://researchseminars.org/talk/CCM2021/4/ END:VEVENT END:VCALENDAR