Ciphertexts of an order-preserving encryption (OPE) scheme preserve the order
of their corresponding plaintexts. However, OPEs are vulnerable to inference
attacks that exploit this preserved order. At another end, differential privacy
has become the de-facto standard for achieving data privacy. One of the most
attractive properties of DP is that any post-processing (inferential)
computation performed on the noisy output of a DP algorithm does not degrade
its privacy guarantee. In this paper, we intertwine the two approaches and
propose a novel differentially private order preserving encryption scheme,
OP$epsilon$. Under OP$epsilon$, the leakage of order from the ciphertexts is
differentially private. As a result, in the least, OP$epsilon$ ensures a
formal guarantee (specifically, a relaxed DP guarantee) even in the face of
inference attacks. To the best of our knowledge, this is the first work to
intertwine DP with a property-preserving encryption scheme. We demonstrate
OP$epsilon$’s practical utility in answering range queries via extensive
empirical evaluation on four real-world datasets. For instance, OP$epsilon$
misses only around $4$ in every $10K$ correct records on average for a dataset
of size $sim732K$ with an attribute of domain size $sim18K$ and $epsilon=
1$.

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