The Locality of Searchable Symmetric Encryption.

This paper proves a lower bound on the trade-off between server storage size and the locality of memory accesses in searchable symmetric encryption (SSE). Namely, when encrypting an index of N identifier/keyword pairs, the encrypted index must have size omega(N) or the scheme must perform searching with omega(1) non-contiguous reads to memory or the scheme must read many more bits than is necessary to compute the results. Recent implementations have shown that nonlocality of server memory accesses create a throughput-bottleneck on very large databases. Our lower bound shows that this is due to the security notion and not a defect of the constructions. An upper bound is also given in the form of a new SSE construction with an O(N logN) size encrypted index that performs O(log N) reads during a search.