Private function evaluation (PFE) allows to obliviously evaluate a private function on private inputs. PFE has several applications such as privacy-preserving credit checking and user-specific insurance tariffs. Recently, PFE protocols based on universal circuits (UCs), that have an inevitable superlinear overhead, have been investigated thoroughly. Specialized public key-based protocols with linear complexity were believed to be less efficient than UC-based approaches. In this paper, we take another look at the linear-complexity PFE protocol by Katz and Malka (ASIACRYPT'11): We propose several optimizations and split the protocol in different phases that depend on the function and inputs respectively. We show that HE-based PFE is practical when instantiated with state-of-the-art ECC and RLWE-based homomorphic encryption. Our most efficient implementation outperforms the most recent UC-based PFE implementation of Alhassan et al. (JoC'20) in communication for all circuit sizes and in computation starting from circuits of a few thousand gates already.

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