We present a new protocol for computing a circuit which implements the private set intersection functionality (PSI). Using circuits for this task is advantageous over the usage of specific protocols for PSI, since many applications of PSI do not need to compute the intersection itself but rather functions based on the items in the intersection. Our protocol is the first circuit-based PSI protocol to achieve linear communication complexity. It is also concretely more efficient than all previous circuit-based PSI protocols. For example, for sets of size 2 20 it improves the communication of the recent work of Pinkas et al. (EURO-CRYPT'18) by more than 10 times, and improves the run time by a factor of 2.8x in the LAN setting, and by a factor of 5.8x in the WAN setting. Our protocol is based on the usage of a protocol for computing oblivious programmable pseudo-random functions (OPPRF), and more specifically on our technique to amortize the cost of batching together multiple invocations of OPPRF.

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We present a 2-party private set intersection (PSI) protocol which provides security against malicious participants, yet is almost as fast as the fastest known semi-honest PSI protocol of Kolesnikov et al. (CCS 2016). Our protocol is based on a new approach for two-party PSI, which can be instantiated to provide security against either malicious or semi-honest adversaries. The protocol is unique in that the only difference between the semi-honest and malicious versions is an instantiation with different parameters for a linear error-correction code. It is also the first PSI protocol which is concretely efficient while having linear communication and security against malicious adversaries, while running in the OT-hybrid model (assuming a non-programmable random oracle). State of the art semi-honest PSI protocols take advantage of cuckoo hashing, but it has proven a challenge to use cuckoo hashing for malicious security. Our protocol is the first to use cuckoo hashing for malicious-secure PSI. We do so via a new data structure, called a probe-and-XOR of strings ( ), which may be of independent interest. This abstraction captures important properties of previous data structures, most notably garbled Bloom filters. While an encoding by a garbled Bloom filter is larger by a factor of than the original data, we describe a significantly improved based on cuckoo hashing that achieves constant rate while being no worse in other relevant efficiency measures.

Recently, there has been huge progress in the field of concretely efficient secure computation, even while providing security in the presence of malicious adversaries. This is especially the case in the two-party setting, where constant-round protocols exist that remain fast even over slow networks. However, in the multi-party setting, all concretely efficient fully-secure protocols, such as SPDZ, require many rounds of communication. In this paper, we present a constant-round multiparty secure computation protocol that is fully-secure in the presence of malicious adversaries and for any number of corrupted parties. Our construction is based on the constant-round protocol of Beaver et al. (the BMR protocol), and is the first version of that protocol that is concretely efficient for the dishonest majority case. Our protocol includes an online phase that is extremely fast and mainly consists of each party locally evaluating a garbled circuit. For the offline phase we present both a generic construction (using any underlying MPC protocol), and a highly efficient instantiation based on the SPDZ protocol. Our estimates show the protocol to be considerably more efficient than previous fully-secure multi-party protocols.

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