Motivated by the problem of data breaches, we formalize a notion of security for dynamic structured encryption (STE) schemes that guarantees security against a snapshot adversary; that is, an adversary that receives a copy of the encrypted structure at various times but does not see the transcripts related to any queries. In particular, we focus on the construction of dynamic encrypted multi-maps which are used to build efficient searchable symmetric encryption schemes, graph encryption schemes and encrypted relational databases. Interestingly, we show that a form of snapshot security we refer to as breach resistance implies previously-studied notions such as a (weaker version) of history independence and write-only obliviousness. Moreover, we initiate the study of dual-secure dynamic STE constructions: schemes that are forward-private against a persistent adversary and breach-resistant against a snapshot adversary. The notion of forward privacy guarantees that updates to the encrypted structure do not reveal their association to any query made in the past. As a concrete instantiation, we propose a new dual-secure dynamic multi-map encryption scheme that outperforms all existing constructions; including schemes that are not dual-secure. Our construction has query complexity that grows with the selectivity of the query and the number of deletes since the client executed a linear-time rebuild protocol which can be de-amortized. We implemented our scheme (with the de-amortized rebuild protocol) and evaluated its concrete efficiency empirically. Our experiments show that it is highly efficient with queries taking less than 1 microsecond per label/value pair.
The problem of privatizing statistical databases is a well-studied topic that has culminated with the notion of differential privacy. The complementary problem of securing these differentially private databases, however, has—as far as we know—not been considered in the past. While the security of private databases is in theory orthogonal to the problem of private statistical analysis (e.g., in the central model of differential privacy the curator is trusted) the recent real-world deployments of differentially-private systems suggest that it will become a problem of increasing importance. In this work, we consider the problem of designing encrypted databases (EDB) that support differentially-private statistical queries. More precisely, these EDBs should support a set of encrypted operations with which a curator can securely query and manage its data, and a set of private operations with which an analyst can privately analyze the data. Using such an EDB, a curator can securely outsource its database to an untrusted server (e.g., on-premise or in the cloud) while still allowing an analyst to privately query it. We show how to design an EDB that supports private histogram queries. As a building block, we introduce a differentially-private encrypted counter based on the binary mechanism of Chan et al. (ICALP, 2010). We then carefully combine multiple instances of this counter with a standard encrypted database scheme to support differentially-private histogram queries.