International Association
for Cryptologic Research

Encrypted data structures have received a lot of attention due to their use as building blocks in the design of fast encrypted search algorithms and encrypted databases. An important design aspect that, as far as we know, has not been considered is that modern server architectures are concurrent in the sense that they support the execution of multiple operations simultaneously. In this work, we initiate the study of concurrent encrypted data structures. We identify new definitional and technical challenges posed by concurrency in the setting of encrypted search. In order to formalize the security of these schemes, we extend the standard framework of structured encryption to capture, among other things, fine-grained leakage which occurs at the instruction level as well as schedule-dependent leakage which changes as a function of the order in which instructions are executed. The latter is particularly challenging to handle when the scheduler is adversarial and adaptive. We provide security definitions in the ideal/real-world model which allows us to capture both security and consistency together. We combine techniques from structured encryption and concurrent data structures to design the first concurrent encrypted multi-map. We show that it is not only secure and efficient, but also satisfies a strong consistency guarantee called linearizability while supporting lock-free append operations and requiring no inter-client communication.

Recent work on dynamic structured and searchable symmetric encryption has focused on achieving the notion of forward-privacy. This is mainly motivated by the claim that forward privacy protects against adaptive file injection attacks (Zhang, Katz, Papamanthou, Usenix Security, 2016). In this work, we revisit the notion of forward-privacy in several respects. First, we observe that forward-privacy does not necessarily guarantee security against adaptive file injection attacks if a scheme reveals other leakage patterns like the query equality. We then propose a notion of security called correlation security which generalizes forward privacy. We then show how correlation security can be used to formally define security against different kinds of injection attacks. We then propose the first injection-secure multi-map encryption encryption scheme and use it as a building block to design the first injection-secure searchable symmetric encryption (SSE) scheme. Towards achieving this, we also propose a new fully-dynamic volume-hiding multi-map encryption scheme which may be of independent interest.

Structured encryption (STE) schemes encrypt data structures in such a way that they can be privately queried. Special cases ofSTE include searchable symmetric encryption (SSE) and graph encryption. Like all sub-linear encrypted search solutions, STE leaks information about queries against persistent adversaries. To address this, a line of work on leakage suppression was recently initiated that focuses on techniques to mitigate or completely remove the leakage of STE schemes (Kamara et al. CRYPTO’18 and Kamara and Moataz, Eurocrypt ’19). A notable example is the cache-based compiler which, when combined with the rebuild compiler, transforms any dynamic STE scheme that leaks the query equality into a new scheme that does not. Unfortunately, this compiler can only produce static schemes and it was left as an open problem to design a compiler that could yield dynamic constructions. In this work, we propose a dynamic variant of the cache-based compiler. Our compiler can transform any volume-hiding semi-dynamic or mutable STE scheme that leaks the query equality pattern into into a new fully-dynamic construction that does not. Using this compiler, we design three new fully-dynamic STE schemes that are “almost” and fully zero-leakage which, under natural assumptions about the data and query distributions, are asymptotically more efficient than using black-box ORAM simulation. These are the first constructions of their kind.

We initiate the study of structured encryption schemes with computationally-secure leakage. Specifically, we focus on the design of volume-hiding encrypted multi-maps; that is, of encrypted multi-maps that hide the response length to computationally-bounded adversaries. We describe the first volume-hiding STE schemes that do not rely on naïve padding; that is, padding all tuples to the same length. Our first construction has efficient query complexity and storage but can be lossy. We show, however, that the information loss can be bounded with overwhelming probability for a large class of multi-maps (i.e., with lengths distributed according to a Zipf distribution). Our second construction is not lossy and can achieve storage overhead that is asymptotically better than naïve padding for Zipf-distributed multi-maps. We also show how to further improve the storage when the multi-map is highly concentrated in the sense that it has a large number of tuples with a large intersection. We achieve these results by leveraging computational assumptions; not just for encryption but, more interestingly, to hide the volumes themselves. Our first construction achieves this using a pseudo-random function whereas our second construction achieves this by relying on the conjectured hardness of the planted densest subgraph problem which is a planted variant of the well-studied densest subgraph problem. This assumption was previously used to design public-key encryptions schemes (Applebaum et al., STOC ’10) and to study the computational complexity of financial products (Arora et al., ICS ’10).

Structured encryption (STE) schemes encrypt data structures in such a way that they can be privately queried. One aspect of STE that is still poorly understood is its leakage. In this work, we describe a general framework to design STE schemes that do not leak the query/search pattern (i.e., if and when a query was previously made).Our framework consists of two compilers. The first can be used to make any dynamic STE scheme rebuildable in the sense that the encrypted structures it produces can be rebuilt efficiently using only O(1) client storage. The second transforms any rebuildable scheme that leaks the query/search pattern into a new scheme that does not. Our second compiler is a generalization of Goldreich and Ostrovsky’s square root oblivious RAM (ORAM) solution but does not make use of black-box ORAM simulation. We show that our framework produces STE schemes with query complexity that is asymptotically better than ORAM simulation in certain (natural) settings and comparable to special-purpose oblivious data structures.We use our framework to design a new STE scheme that is “almost” zero-leakage in the sense that it reveals an, intuitively-speaking, small amount of information. We also show how the scheme can be used to achieve zero-leakage queries when one can tolerate a probabilistic guarantee of correctness. This construction results from applying our compilers to a new STE scheme we design called the piggyback scheme. This scheme is a general-purpose STE construction (in the sense that it can encrypt any data structure) that leaks the search/query pattern but hides the response length on non-repeating queries.

We show how to encrypt a relational database in such a way that it can efficiently support a large class of SQL queries. Our construction is based solely on structured encryption (STE) and does not make use of any property-preserving encryption (PPE) schemes such as deterministic and order-preserving encryption. As such, our approach leaks considerably less than PPE-based solutions which have recently been shown to reveal a lot of information in certain settings (Naveed et al., CCS ’15). Our construction is efficient and—under some conditions on the database and queries—can have asymptotically-optimal query complexity. We also show how to extend our solution to be dynamic while maintaining the scheme’s optimal query complexity.