BLOOM: BLoom filter based oblivious outsourced matchings

Whole genome sequencing has become fast, accurate, and cheap, paving the way towards the large-scale collection and processing of human genome data. Unfortunately, this dawning genome era does not only promise tremendous advances in biomedical research but also causes unprecedented privacy risks for the many. Handling storage and processing of large genome datasets through cloud services greatly aggravates these concerns. Current research efforts thus investigate the use of strong cryptographic methods and protocols to implement privacy-preserving genomic computations.

We propose FHE-BLOOM and PHE-BLOOM, two efficient approaches for genetic disease testing using homomorphically encrypted Bloom filters. Both approaches allow the data owner to securely outsource storage and computation to an untrusted cloud. FHE-BLOOM is fully secure in the semi-honest model while PHE-BLOOM slightly relaxes security guarantees in a trade-off for highly improved performance.

We implement and evaluate both approaches on a large dataset of up to 50 patient genomes each with up to 1000000 variations (single nucleotide polymorphisms). For both implementations, overheads scale linearly in the number of patients and variations, while PHE-BLOOM is faster by at least three orders of magnitude. For example, testing disease susceptibility of 50 patients with 100000 variations requires only a total of 308.31 s (σ=8.73 s) with our first approach and a mere 0.07 s (σ=0.00 s) with the second. We additionally discuss security guarantees of both approaches and their limitations as well as possible extensions towards more complex query types, e.g., fuzzy or range queries.

Both approaches handle practical problem sizes efficiently and are easily parallelized to scale with the elastic resources available in the cloud. The fully homomorphic scheme, FHE-BLOOM, realizes a comprehensive outsourcing to the cloud, while the partially homomorphic scheme, PHE-BLOOM, trades a slight relaxation of security guarantees against performance improvements by at least three orders of magnitude.