Dynamic Local Searchable Symmetric Encryption

Abstract

In this article, we tackle for the first time the problem of dynamic memory-efficient Searchable Symmetric Encryption (SSE). In the term “memory-efficient” SSE, we encompass both the goals of local SSE, and page-efficient SSE. The centerpiece of our approach is a novel connection between those two goals. We introduce a map, called the Generic Local Transform, which takes as input a page-efficient SSE scheme with certain special features, and outputs an SSE scheme with strong locality properties. We obtain several results. (1) First, for page-efficient SSE with page size p, we build a dynamic scheme with storage efficiency $\mathcal {O}({1})$ and page efficiency $\widetilde{\mathcal {O}}\left( {\textrm{log}\, \textrm{log}\, (N/p)}\right)$, called $\textsf{LayeredSSE}$. The main technical innovation behind $\textsf{LayeredSSE}$ is a novel weighted extension of the two-choice allocation process, of independent interest. (2) Second, we introduce the Generic Local Transform, and combine it with $\textsf{LayeredSSE}$ to build a dynamic SSE scheme with storage efficiency $\mathcal {O}({1})$, locality $\mathcal {O}({1})$, and read efficiency $\widetilde{\mathcal {O}}\left( {\textrm{log}\,\textrm{log}\, N}\right)$, under the condition that the longest list is of size $\mathcal {O}({N^{1-1/\textrm{log}\, \textrm{log}\, \lambda }})$. This matches, in every respect, the purely static construction of Asharov et al. presented at STOC 2016: dynamism comes at no extra cost. (3) Finally, by applying the Generic Local Transform to a variant of the Tethys scheme by Bossuat et al. from Crypto 2021, we build an unconditional static SSE with storage efficiency $\mathcal {O}({1})$, locality $\mathcal {O}({1})$, and read efficiency $\mathcal {O}({\textrm{log}^\varepsilon N})$, for an arbitrarily small constant $\varepsilon > 0$. To our knowledge, this is the construction that comes closest to the lower bound presented by Cash and Tessaro at Eurocrypt 2014.