Dynamic Local Searchable Symmetric Encryption

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. • First, for page-efficient SSE, we build a dynamic scheme with page efficiency O(log logN) and storage efficiency O(1), called LayeredSSE. The main technical innovation behind LayeredSSE is a new weighted extension of the two-choice allocation process, of independent interest. • Second, we introduce the Generic Local Transform, and combine it with LayeredSSE to build a dynamic SSE scheme with storage efficiency O(1), locality O(1), and read efficiency Õ (log logN), under the condition that the longest list is of size O ( N 1−1/ log log λ ) . This matches, in every respect, the purely static construction of Asharov et al. presented at STOC 2016: dynamism comes at no extra cost. • 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 O(1), locality O(1), and read efficiency O(log N), for an arbitrarily small constant ε > 0. To our knowledge, this is the construction that comes closest to the lower bound presented by Cash and Tessaro at Eurocrypt 2014.