Assumption-Free Fuzzy PSI via Predicate Encryption

We present the first protocol for efficient Fuzzy Private Set Intersection (PSI) that achieves linear communication complexity, does not depend on restrictive assumptions on the distribution of party inputs, and abstains from inefficient fully homomorphic encryption. Specifically, our protocol enables two parties to compute all pairs of elements from their respective sets that are within a given Hamming distance, without constraints on how these sets are structured. Our key insight is that securely computing the (threshold) Hamming distance between two inputs can be reduced to securely computing their inner product. Leveraging this reduction, we construct a Fuzzy PSI protocol using recent techniques for inner-product predicate encryption. To enable the use of predicate encryption in our setting, we establish that these predicate encryption schemes only require a weak notion of simulation security. We also demonstrate how their internal key derivation can be efficiently distributed without a trusted third party. As a result, our Fuzzy PSI on top of predicate encryption achieves optimal linear communication complexity for arbitrary input distributions. Our implementation validates its feasibility and demonstrates improved performance over the most closely related work.