Searchable Encryption with Optimal Locality: Achieving Sublogarithmic Read Efficiency.

We propose the first linear-space searchable encryption scheme with constant locality and sublogarithmic read efficiency, strictly improving the previously best known read efficiency bound (Asharov et al., STOC 2016) from Theta(logN log logN) to O(log(gamma) N) where gamma = 2/3 + delta for any fixed delta > 0 and where N is the number of keyword-document pairs. Our scheme employs four different allocation algorithms for storing the keyword lists, depending on the size of the list considered each time. For our construction we develop (i) new probability bounds for the offline two-choice allocation problem; (ii) and a new I/O-efficient oblivious RAM with (O) over tilde (n(1/3)) bandwidth overhead and zero failure probability, both of which can be of independent interest.