Ilya Mironov, Omkant Pandey, Omer Reingold, and Salil Vadhan
The definition of differential privacy has recently emerged as a leading standard of privacy guarantees for algorithms on statistical databases. We offer several relaxations of the definition which require privacy guarantees to hold only against efficient — i.e., computationally bounded — adversaries. We establish various relationships among these notions, and in doing so, we observe their close connection with the theory of pseudodense sets by Reingold et al. (FOCS `08). We extend the dense model theorem of Reingold et al. to demonstrate equivalence between two definitions (indistinguishability- and simulatability-based) of computational differential privacy.
Our computational analogues of differential privacy seem to allow for more accurate constructions than the standard information-theoretic analogues. In particular, in the context of private approximation of the distance between two vectors, we present a differentially-private protocol for computing the approximation, and contrast it with a substantially more accurate protocol that is only computationally differentially private.