Near-Optimal Oblivious Key-Value Stores for Efficient PSI, PSU and Volume-Hiding Multi-Maps

In this paper, we study oblivious key-value stores (OKVS) that enable encoding n key-value pairs into length m encodings while hiding the input keys. The goal is to obtain high rate, n/m, with efficient encoding and decoding algorithms. We present RB-OKVS built on random band matrices that obtains near-optimal rates as high as 0.97 whereas prior works could only achieve rates up to 0.81 with similar encoding times. Using RB-OKVS, we obtain state-of-the-art protocols for private set intersection (PSI) and union (PSU). Our semi-honest PSI has up to 12% smaller communication and 13% reductions in monetary cost with slightly larger computation. We also obtain similar improvements for both malicious and circuit PSI. For PSU, our protocol obtains improvements of up to 22% in communication, 40% in computation and 21% in monetary cost. In general, we obtain the most communication-and cost-efficient protocols for all the above primitives. Finally, we present the first connection between OKVS and volume-hiding encrypted multi-maps (VH-EMM) where the goal is to outsource storage of multi-maps while hiding the number of values associated with each key (i.e., volume). We present RB-MM with 16% smaller storage, 5x faster queries and 8x faster setup than prior works.