Oblivious Decision Programs from Oblivious Transfer: Efficient Reductions

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In this paper, we design efficient protocols for a number of \emph{private database query} problems. Consider a general form of the problem where a client who holds a private input interacts with a server who holds a private decision program (e.g. a decision tree or a branching program) with the goal of evaluating his input on the decision program without learning any additional information. Many known private database queries such as Symmetric PIR, and Private Keyword Search can be formulated as special cases of this problem. We design \emph{computationally efficient} protocols for the above general problem, and a few of its special cases. In addition to being one-round and requiring a small amount of work by the client (in the RAM model), our protocols only require a small number of exponentiations (independent of the server's input) by both parties. Our constructions are, in essence, efficient and black-box reductions of the above problem to $1$-out-of-$2$ oblivious transfer. We prove our protocols secure (private) against \emph{malicious} adversaries in the standard ideal/real world simulation-based paradigm. The majority of the existing work on the same problems focus on optimizing communication. However, in some environments (supported by a few experimental studies), it is the computation and not the communication that may be the performance bottleneck. Our protocols are suitable alternatives for such scenarios.