1. NONADAPTIVE MASTERMIND ALGORITHMS FOR STRING AND VECTOR
DATABASES, WITH CASE STUDIES
ABSTRACT:
In this paper, we study sparsity-exploiting Mastermind algorithms for attacking the privacy of an
entire database of character strings or vectors, such as DNA strings, movie ratings, or social
network friendship data. Based on reductions to nonadaptive group testing, our methods are able
to take advantage of minimal amounts of privacy leakage, such as contained in a single bit that
indicates if two people in a medical database have any common genetic mutations, or if two
people have any common friends in an online social network.
We analyze our Mastermind attack algorithms using theoretical characterizations that provide
sublinear bounds on the number of queries needed to clone the database, as well as experimental
tests on genomic information, collaborative filtering data, and online social networks. By taking
advantage of the generally sparse nature of these real-world databases and modulating a
parameter that controls query sparsity, we demonstrate that relatively few nonadaptive queries
are needed to recover a large majority of each database.
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