Searchable Encryption with Optimal Locality: Achieving Sublogarithmic Read Efficiency

Abstract

We propose the first linear-space searchable encryption scheme with constant locality and \emph{sublogarithmic} read efficiency, strictly improving the previously best known read efficiency bound (Asharov et al., STOC 2016) from $\Theta(\log N \log \log N)$ to $O(\log ^{\gamma} N)$ where $\gamma=\frac{2}{3}+\delta$ for any fixed $\delta>0$. 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 $\tilde{O}(n^{1/3})$ bandwidth overhead and zero failure probability, both of which can be of independent interest