Efficient, Oblivious Data Structures for MPC

We present oblivious implementations of several data structures for secure multiparty computation (MPC) such as arrays, dictionaries, and priority queues. The resulting oblivious data structures have only polylogarithmic overhead compared with their classical counterparts. To achieve this, we give secure multiparty protocols for the ORAM of Shi et al. (Asiacrypt ‘11) and the Path ORAM scheme of Stefanov et al. (CCS ‘13), and we compare the resulting implementations. We subsequently use our oblivious priority queue for secure computation of Dijkstra’s shortest path algorithm on general graphs, where the graph structure is secret. To the best of our knowledge, this is the first implementation of a non-trivial graph algorithm in multiparty computation with polylogarithmic overhead. We implemented and benchmarked all of our protocols using the SPDZ protocol of Damg̊ard et al. (Crypto ‘12), which works in the preprocessing model and ensures active security against an adversary corrupting all but one players. For two parties, the online access time for an oblivious array of size 1 million is under 250 ms.