Labeled PSI from Homomorphic Encryption with Reduced Computation and Communication

It is known that fully homomorphic encryption (FHE) can be used to build efficient (labeled) Private Set Intersection protocols in the unbalanced setting, where one of the sets is much larger than the other~(Chen et al. (CCS'17, CCS'18)). In this paper we demonstrate multiple algorithmic improvements upon these works. In particular, our protocol has an asymptotically better computation cost, requiring only O(√|X| ) homomorphic multiplications, and communication complexity sublinear in the larger set size|X|. We demonstrate that our protocol is significantly better than that of Chen et al. (CCS'18) for many practical parameters, especially in terms of online communication cost. For example, when intersecting $228 and 2048 item sets, our protocol reduces the online computation time by more than 71% and communication by more than 63%. When intersecting 224 and 4096 item sets, our protocol reduces the online computation time by 27% and communication by 63%. Our comparison to other state-of-the-art unbalanced PSI protocols shows that our protocol has the best total communication complexity when |X| ≥ 224. For labeled PSI our protocol also outperforms Chen et al. (CCS'18). When intersecting 220 and 256 item sets, with the larger set having associated 288-byte labels, our protocol reduces the online computation time by more than 67% and communication by 34%. Finally, we demonstrate a modification that results in nearly constant communication cost in the larger set size |X|, but impractically high computation complexity on today's CPUs. For example, to intersect a 210-item set with sets of size 222, 224, or 226, our proof-of-concept implementation requires only 0.76 MB of online communication, which is more than a 24-fold improvement over Chen et al. (CCS'18).