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In 2-party Circuit-based Private Set Intersection (Circuit-PSI), P 0 and P 1 hold sets S0 and S1 respectively and wish to securely compute a function f over the set S0 ∩ S1 (e.g., cardinality, sum over associated attributes, or threshold intersection). Following a long line of work, Pinkas et al. (PSTY, Eurocrypt 2019) showed how to construct a concretely efficient Circuit-PSI protocol with linear communication complexity. However, their protocol requires super-linear computation. In this work, we construct concretely efficient Circuit-PSI protocols with linear computational and communication cost. Further, our protocols are more performant than the state-of-the-art, PSTY – we are ≈ 2.3× more communication efficient and are up to 2.8× faster. We obtain our improvements through a new primitive called Relaxed Batch Oblivious Programmable Pseudorandom Functions (RB-OPPRF) that can be seen as a strict generalization of Batch OPPRFs that were used in PSTY. This primitive could be of independent interest.

We present two Secure Two Party Computation (STPC) protocols for piecewise function approximation on private data. The protocols rely on a piecewise approximation of the to-be-computed function easing the implementation in a STPC setting. The first protocol relies entirely on Garbled Circuit (GC) theory, while the second one exploits a hybrid construction where GC and Homomorphic Encryption (HE) are used together. In addition to piecewise constant and linear approximation, polynomial interpolation is also considered. From a communication complexity perspective, the full-GC implementation is preferable when the input and output variables can be represented with a small number of bits, while the hybrid solution is preferable otherwise. With regard to computational complexity, the full-GC solution is generally more convenient., Comment: Draft of paper that will be soon submitted to IEEE Transaction on Information Forensic and Security