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.
Encrypted search algorithms (ESA) are cryptographic algorithms that support search over encrypted data. ESAs can be designed with various primitives including searchable/structured symmetric encryption (SSE/STE) and oblivious RAM (ORAM). Leakage abuse attacks attempt to recover client queries using knowledge of the client’s data. An important parameter for any leakage-abuse attack is its known-data rate; that is, the fraction of client data that must be known to the adversary.
In this work, we revisit leakage abuse attacks in several ways. We first highlight some practical limitations and assumptions underlying the well-known IKK (Islam et al. NDSS ’12) and Count (Cash et al., CCS ’15) attacks. We then design four new leakage-abuse attacks that rely on much weaker assumptions. Three of these attacks are volumetric in the sense that they only exploit leakage related to document sizes. In particular, this means that they work not only on SSE/STE-based ESAs but also against ORAM-based solutions. We also introduce two volumetric injection attack which use adversarial file additions to recover queries even from ORAM-based solutions. As far as we know, these are the first attacks of their kind.
We evaluated all our attacks empirically and considered many experimental settings including different data collections, query selectivities, known-data rates, query space size and composition. From our experiments, we observed that the only setting that resulted in reasonable recovery rates under practical assumptions was the case of high-selectivity queries with a leakage profile that includes the response identity pattern (i.e., the identifiers of the matching documents) and the volume pattern (i.e., the size of the matching documents). All other attack scenarios either failed or relied on unrealistic assumptions (e.g., very high known-data rates). For this specific setting, we propose several suggestions and countermeasures including the use of schemes like PBS (Kamara et al, CRYPTO ’18), VLH/AVLH (Kamara and Moataz, Eurocrypt ’19 ), or the use of padding techniques like the ones recently proposed by Bost and Fouque (Bost and Fouque, IACR ePrint 2017/1060).
Recent foundational work on leakage-abuse attacks on encrypted databases has broadened our understanding of what an adversary can accomplish with a standard leakage profile. Nevertheless, all known value reconstruction attacks succeed under strong assumptions that may not hold in the real world. The most prevalent assumption is that queries are issued uniformly at random by the client. We present the first value reconstruction attacks that succeed without any knowledge about the query or data distribution. Our approach uses the search-pattern leakage, which exists in all known structured encryption schemes but has not been fully exploited so far. At the core of our method lies a support size estimator, a technique that utilizes the repetition of search tokens with the same response to estimate distances between encrypted values without any assumptions about the underlying distribution. We develop distribution-agnostic reconstruction attacks for both range queries and k-nearest neighbor (k-NN) queries based on information extracted from the search-pattern leakage. Our new range attack follows a different algorithmic approach than state-of-the-art attacks, which are fine-tuned to succeed under the uniformly distributed queries. Instead, we reconstruct plaintext values under a variety of skewed query distributions and even outperform the accuracy of previous approaches under the uniform query distribution. Our new k-NN attack succeeds with far fewer samples than previous attacks and scales to much larger values of k. We demonstrate the effectiveness of our attacks by experimentally testing them on a wide range of query distributions and database densities, both unknown to the adversary.
In the model of “no-dictionary” verifiable searchable symmetric encryption (SSE) scheme, a client does not need to keep the set of keywords W in the search phase, where W is called a dictionary. Still a malicious server cannot cheat the client by saying that ``your search word w does not exist in the dictionary W” when it exists. In the previous such schemes, it takes O(logm) time for the server to prove that w∉W, where m=|W| is the number of keywords. In this paper, we show a generic method to transform any SSE scheme (that is only secure against passive adversaries) to a no-dictionary verifiable SSE scheme. In the transformed scheme, it takes only O(1) time for the server to prove that w∉W.
We study the problem of dynamic symmetric searchable encryption. In that setting, it is crucial to minimize the information revealed to the server as a result of update operations (insertions and deletions). Two relevant privacy properties have been defined in that context: forward and backward privacy. The first makes it hard for the server to link an update operation with previous queries and has been extensively studied in the literature. The second limits what the server can learn about entries that were deleted from the database, from queries that happen after the deletion. Backward privacy was formally studied only recently (Bost et al., CCS 2017) in a work that introduced a formal definition with three variable types of leakage (Type-I to Type-III ordered from most to least secure), as well as the only existing schemes that satisfy this property. In this work, we introduce three novel constructions that improve previous results in multiple ways. The first scheme achieves Type-II backward privacy and our experimental evaluation shows it has 145-253X faster search computation times than previous constructions with the same leakage. Surprisingly, it is faster even than schemes with Type-III leakage which makes it the most efficient implementation of a forward and backward private scheme so far. The second one has search time that is asymptotically within a polylogarithmic multiplicative factor of the theoretical optimal (i.e., the result size of a search), and it achieves the strongest level of backward privacy (Type-I). All previous Type-I constructions require time that is at least linear in the total number of updates for the requested keywords, even the (arbitrarily many) previously deleted ones. Our final scheme improves upon the second one by reducing the number of roundtrips for a search at the cost of extra leakage (Type-III).
Secure search is the problem of securely retrieving from a database table (or any unsorted array) the records matching specified attributes, as in SQL ``SELECT…WHERE…’’ queries, but where the database and the query are encrypted. Secure search has been the leading example for practical applications of Fully Homomorphic Encryption (FHE) since Gentry’s seminal work in 2009, attaining the desired properties of a single-round low-communication protocol with semantic security for database and query (even during search). Nevertheless, the wide belief was that the high computational overhead of current FHE candidates is too prohibitive in practice for secure search solutions (except for the restricted case of searching for a uniquely identified record as in SQL UNIQUE constrain and Private Information Retrieval). This is due to the high degree in existing solutions that is proportional at least to the number of database records m.
We present the first algorithm for secure search that is realized by a polynomial of logarithmic degree (log m)^c for a small constant c>0. We implemented our algorithm in an open source library based on HElib, and ran experiments on Amazon’s EC2 cloud with up to 100 processors. Our experiments show that we can securely search to retrieve database records in a rate of searching in millions of database records in less than an hour on a single machine.
We achieve our result by: (1) Designing a novel sketch that returns the first strictly-positive entry in a (not necessarily sparse) array of non-negative real numbers; this sketch may be of independent interest. (2) Suggesting a multi-ring evaluation of FHE – instead of a single ring as in prior works – and leveraging this to achieve an exponential reduction in the degree.
Recent work on searchable symmetric encryption (SSE) has focused on increasing its expressiveness. A notable example is the OXT construction (Cash et al., CRYPTO ’13 ) which is the first SSE scheme to support conjunctive keyword queries with sub-linear search complexity. While OXT efficiently supports disjunctive and boolean queries that can be expressed in searchable normal form, it can only handle arbitrary disjunctive and boolean queries in linear time. This motivates the problem of designing expressive SSE schemes with worst-case sub-linear search; that is, schemes that remain highly efficient for any keyword query.
In this work, we address this problem and propose non-interactive highly efficient SSE schemes that handle arbitrary disjunctive and boolean queries with worst-case sub-linear search and optimal communication complexity. Our main construction, called IEX, makes black-box use of an underlying single keyword SSE scheme which we can instantiate in various ways. Our first instantiation, IEX-2Lev, makes use of the recent 2Lev construction (Cash et al., NDSS ’14 ) and is optimized for search at the expense of storage overhead. Our second instantiation, IEX-ZMF, relies on a new single keyword SSE scheme we introduce called ZMF and is optimized for storage overhead at the expense of efficiency (while still achieving asymptotically sub-linear search). Our ZMF construction is the first adaptively-secure highly compact SSE scheme and may be of independent interest. At a very high level, it can be viewed as an encrypted version of a new Bloom filter variant we refer to as a Matryoshka filter. In addition, we show how to extend IEX to be dynamic and forward-secure.
To evaluate the practicality of our schemes, we designed and implemented a new encrypted search framework called Clusion. Our experimental results demonstrate the practicality of IEX and of its instantiations with respect to either search (for IEX-2Lev) and storage overhead (for IEX-ZMF).
In the era of big data, graph databases have become in-creasingly important for NoSQL technologies, and many systems (e.g.,online social networks, world-wide web and electrical grids, etc.) can be modeled as graphs for semantic queries. Meanwhile, with the advent of cloud computing, data owners are highly motivated to outsource and s-tore their massive potentially-sensitive graph data on remote untrusted servers in an encrypted form, expecting to retain the ability to query over the encrypted graphs.To allow e↵ective and private queries over encrypted data, the most well-studied class of structured encryption schemes are searchable symmetric encryption (SSE) designs, which encrypt search structures (e.g., inverted indexes based on keyword-file pairs) for retrieving data files of interestfrom remote servers. So far, however, the problem of graph data encryption that supports customized queries has received limited attention inthe literature. In this paper, we tackle the challenge of designing a Se-cure Graph DataBase encryption scheme (SecGDB) to encrypt graph structures and enforce private graph queries over the encrypted graph database. Specifically, our construction strategically makes use of e�cient additively homomorphic encryption and garbled circuits to support the shortest distance queries with optimal time and storage complexities. Toachieve better amortized time complexity over multiple queries, we further propose an auxiliary data structure called query historyand storeit on the remote server to act as a “caching” resource. Compared with the state-of-the-art solutions, our design returns exact shortest distancequery results instead of approximate ones and allows e�cient graph up-date queries over large-scale encrypted graphs. We prove that our construction is adaptively semantically-secure in the random oracle model and finally implement and evaluate it on various representative real-world datasets, showing that our approach is practically efficient in terms of both storage and computation.
Symmetric Searchable Encryption (SSE) has received wide attention due to its practical application in searching on encrypted data. Beyond search, data addition and deletion are also supported in dynamic SSE schemes. Unfortunately, these update operations leak some information of updated data. To address this issue, forward-secure SSE is actively explored to protect the relations of newly updated data and previously searched keywords. On the contrary, little work has been done in backward security, which enforces that search should not reveal information of deleted data. In this paper, we propose the first practical and non-interactive backward-secure SSE scheme. In particular, we introduce a new form of symmetric encryption, named symmetric puncturable encryption (SPE), and construct a generic primitive from simple cryptographic tools. Based on this primitive, we then present a backward-secure SSE scheme that can revoke a server’s searching ability on deleted data. We instantiate our scheme with a practical puncturable pseudorandom function and implement it on a large dataset. The experimental results demonstrate its efficiency and scalability. Compared to the state-of-the-art, our scheme achieves a speedup of almost 50x in search latency, and a saving of 62% in server storage consumption.
The recently proposed Oblivious Cross-Tags (OXT) protocol (CRYPTO 2013) has broken new ground in designing efficient searchable symmetric encryption (SSE) protocol with support for conjunctive keyword search in a single-writer single-reader framework. While the OXT protocol offers high performance by adopting a number of specialised data-structures, it also trades-off security by leaking ‘partial’ database information to the server. Recent attacks have exploited similar partial information leakage to breach database confidentiality. Consequently, it is an open problem to design SSE protocols that plug such leakages while retaining similar efficiency. In this paper, we propose a new SSE protocol, called Hidden Cross-Tags (HXT), that removes ‘Keyword Pair Result Pattern’ (KPRP) leakage for conjunctive keyword search. We avoid this leakage by adopting two additional cryptographic primitives - Hidden Vector Encryption (HVE) and probabilistic (Bloom filter) indexing into the HXT protocol. We propose a ‘lightweight’ HVE scheme that only uses efficient symmetric-key building blocks, and entirely avoids elliptic curve-based operations. At the same time, it affords selective simulation-security against an unbounded number of secret-key queries. Adopting this efficient HVE scheme, the overall practical storage and computational overheads of HXT over OXT are relatively small (no more than 10% for two keywords query, and 21% for six keywords query), while providing a higher level of security.
Free cloud-based services are powerful candidates for deploying ubiquitous encryption for messaging. In the case of email and increasingly chat, users expect the ability to store and search their messages persistently. Using data from a major mail provider, we confirm that for a searchable encryption scheme to scale to millions of users, it should be highly IO-efficient (locality) and handle a very dynamic message corpi. We observe that existing solutions fail to achieve both properties simultaneously. We then design, build, and evaluate a provably secure Dynamic Searchable Symmetric Encryption (DSSE) scheme with significant reduction in IO cost compared to preceding works when used for email or other highly dynamic material.