This paper studies nonadaptive Mastermind algorithms for attacking the privacy of string and vector databases like DNA strings, movie ratings, and social network data. The algorithms can take advantage of minimal privacy leaks, like whether two people share any genetic mutations or common friends. The attacks are analyzed theoretically and experimentally on genomic, recommendation, and social network data. Relatively few nonadaptive queries are shown to recover a large portion of each database by exploiting the inherent sparsity of real-world data and modulating query sparsity.

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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