How to Hide Circuits in MPC: An Efficient Framework for Private Function Evaluation.

We revisit the problem of general-purpose private function evaluation (PFE) wherein a single party P-1 holds a circuit C, while each P-i for 1 <= i <= n holds a private input x(i), and the goal is for a subset (or all) of the parties to learn C(x(1), ..., x(n)) but nothing else. We put forth a general framework for designing PFE where the task of hiding the circuit and securely evaluating its gates are addressed independently: First, we reduce the task of hiding the circuit topology to oblivious evaluation of a mapping that encodes the topology of the circuit, which we refer to as oblivious extended permutation (OEP) since the mapping is a generalization of the permutation mapping. Second, we design a subprotocol for private evaluation of a single gate (PFE for one gate), which we refer to as private gate evaluation (PGE). Finally, we show how to naturally combine the two components to obtain efficient and secure PFE. We apply our framework to several well-known general-purpose MPC constructions, in each case, obtaining the most efficient PFE construction to date, for the considered setting. Similar to the previous work we only consider semi-honest adversaries in this paper.