Breaking and Fixing the Security Proof of Garbled Bloom Filters

We identify a flaw in the proof of security of Garbled Bloom Filters, a recent hash structure introduced by Dong et al. (ACM CCS 2013) that is used to design Private Set Intersection (PSI) protocols, a important family of protocols for secure cloud computing. We give counter-examples invalidating a claim that is central to the original proof and we show that variants of the GBF construction have the same issue in their security analysis. We then give a new proof of security that shows that Garbled Bloom Filters are secure nonetheless.