Various cryptographic techniques are used in outsourced database systems to
ensure data privacy while allowing for efficient querying. This work proposes a
definition and components of a new secure and efficient outsourced database
system, which answers various types of queries, with different privacy
guarantees in different security models. This work starts with the survey of
five order-revealing encryption schemes that can be used directly in many
database indices and five range query protocols with various security /
efficiency tradeoffs. The survey systematizes the state-of-the-art range query
solutions in a snapshot adversary setting and offers some non-obvious
observations regarding the efficiency of the constructions. In
$mathcal{E}text{psolute}$, a secure range query engine, security is achieved
in a setting with a much stronger adversary where she can continuously observe
everything on the server, and leaking even the result size can enable a
reconstruction attack. $mathcal{E}text{psolute}$ proposes a definition,
construction, analysis, and experimental evaluation of a system that provably
hides both access pattern and communication volume while remaining efficient.
The work concludes with $ktext{-a}ntext{o}n$ — a secure similarity search
engine in a snapshot adversary model. The work presents a construction in which
the security of $ktext{NN}$ queries is achieved similarly to OPE / ORE
solutions — encrypting the input with an approximate Distance Comparison
Preserving Encryption scheme so that the inputs, the points in a hyperspace,
are perturbed, but the query algorithm still produces accurate results. We use
TREC datasets and queries for the search, and track the rank quality metrics
such as MRR and nDCG. For the attacks, we build an LSTM model that trains on
the correlation between a sentence and its embedding and then predicts words
from the embedding.

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