An oblivious key-value store is a data structure that can encode and decode key-value pairs in a table of size obliviously. After encoding, one cannot distinguish the encoded key-value pairs from other key-value pairs in the input domain. In this paper, we first propose a data structure called Peelable Garbled Bloom Filter (PGBF), which encodes the key-value pairs in a similar way to peeling and unpeeling an \emph{onion}. Specifically, it can divide the key-value pair set (i.e., onion) as multiple subsets (i.e., peels) and order them from the outermost peel to the innermost peel by using a counting Bloom filter. However, using a small expansion rate (i.e., ) in PGBF will result in a non-empty core issue with non-negligible probability. To handle this issue, we propose Multi-PGBF by combining multiple PGBFs to do the peelings and unpeelings recursively. In addition, we propose a variant C-Multi-PGBF by clustering a large set into small sets to achieve faster encoding efficiency.
Our experiments show that Multi-PGBF and C-Multi-PGBF obtain the best encoding and decoding efficiency. Multi-PGBF improves the encoding time of RR (CCS’22) by , while C-Multi-PGBF improves the encoding time of the clustered RR variant by . For decoding, Multi-PGBF is faster than RR (CCS'22) and faster than RB-OKVS (Usenix'23). When integrated into the state-of-the-art two-party and multi-party private set intersection protocols (Eurocrypt'21, Usenix'24), Multi-PGBF and C-Multi-PGBF lead to faster protocols than those using existing OKVS constructions in most settings.