Polynomial Representation Is Tricky: Maliciously Secure Private Set Intersection Revisited

Private Set Intersection protocols (PSIs) allow parties to compute the intersection of their private sets, such that nothing about sets’ elements beyond is revealed. PSIs have a variety applications, primarily in efficiently supporting data sharing privacy-preserving manner. At Eurocrypt 2019, Ghosh and Nilges proposed three efficient based on polynomial representation sets proved security against active adversaries. In this work, we show these are susceptible several serious attacks. The attacks let an adversary (1) learn correct while making its victim believe empty, (2) certain element victim’s set intersection, (3) delete multiple input set. We explain why proofs did not identify propose mitigations.