Perfectly Secure Oblivious RAM with Sublinear Bandwidth Overhead

Oblivious RAM (ORAM) has established itself as a fundamental cryptographic building block. Understanding which bandwidth overheads are possible under which assumptions has been the topic of a vast amount of previous works. In this work, we focus on perfectly secure ORAM and we present the first construction with sublinear bandwidth overhead in the worst-case. All prior constructions with perfect security require linear communication overhead in the worst-case and only achieve sublinear bandwidth overheads in the amortized sense. We present a fundamentally new approach for construction ORAM and our results significantly advance our understanding of what is possible with perfect security. Our main construction, Lookahead ORAM, is perfectly secure, has a worst-case bandwidth overhead of $\mathcal{O}(\sqrt{n})$, and a total storage cost of $\mathcal{O}(n)$ on the server-side, where $n$ is the maximum number of stored data elements. In terms of concrete server-side storage costs, our construction has the smallest storage overhead among all perfectly and statistically secure ORAMs and is only a factor 3 worse than the most storage efficient computationally secure ORAM. Assuming a client-side position map, our construction is the first, among all ORAMs with worst-case sublinear overhead, that allows for a $\mathcal{O}(1)$ online bandwidth overhead without server-side computation. Along the way, we construct a conceptually extremely simple statistically secure ORAM with a worst-case bandwidth overhead of $\mathcal{O}(\sqrt{n}\frac{\log{n}}{\log{\log{n}}})$, which may be of independent interest

Two-server distributed ORAM with sublinear computation and constant rounds

First author draf

What Storage Access Privacy is Achievable with Small Overhead?

Oblivious RAM (ORAM) and private information retrieval (PIR) are classic cryptographic primitives used to hide the access pattern to data whose storage has been outsourced to an untrusted server. Unfortunately, both primitives require considerable overhead compared to plaintext access. For large-scale storage infrastructure with highly frequent access requests, the degradation in response time and the exorbitant increase in resource costs incurred by either ORAM or PIR prevent their usage. In an ideal scenario, a privacy-preserving storage protocols with small overhead would be implemented for these heavily trafficked storage systems to avoid negatively impacting either performance and/or costs. In this work, we study the problem of the best $\mathit{storage\ access\ privacy}$that is achievable with only$\mathit{small\ overhead}$over plaintext access. To answer this question, we consider$\mathit{differential\ privacy\ access}$which is a generalization of the$\mathit{oblivious\ access}$security notion that are considered by ORAM and PIR. Quite surprisingly, we present strong evidence that constant overhead storage schemes may only be achieved with privacy budgets of$\epsilon = \Omega(\log n)$. We present asymptotically optimal constructions for differentially private variants of both ORAM and PIR with privacy budgets$\epsilon = \Theta(\log n)$with only$O(1)$overhead. In addition, we consider a more complex storage primitive called key-value storage in which data is indexed by keys from a large universe (as opposed to consecutive integers in ORAM and PIR). We present a differentially private key-value storage scheme with$\epsilon = \Theta(\log n)$and$O(\log\log n)$ overhead. This construction uses a new oblivious, two-choice hashing scheme that may be of independent interest.Comment: To appear at PODS'1

Verifiable Oblivious Storage

We formalize the notion of Verifiable Oblivious Storage (VOS), where a client outsources the storage of data to a server while ensuring data confidentiality, access pattern privacy, and integrity and freshness of data accesses. VOS generalizes the notion of Oblivious RAM (ORAM) in that it allows the server to perform computation, and also explicitly considers data integrity and freshness. We show that allowing server-side computation enables us to construct asymptotically more efficient VOS schemes whose bandwidth overhead cannot be matched by any ORAM scheme, due to a known lower bound by Goldreich and Ostrovsky. Specifically, for large block sizes we can construct a VOS scheme with constant bandwidth per query; further, answering queries requires only poly-logarithmic server computation. We describe applications of VOS to Dynamic Proofs of Retrievability, and RAM-model secure multi-party computation

MPC for MPC: Secure Computation on a Massively Parallel Computing Architecture

Massively Parallel Computation (MPC) is a model of computation widely believed to best capture realistic parallel computing architectures such as large-scale MapReduce and Hadoop clusters. Motivated by the fact that many data analytics tasks performed on these platforms involve sensitive user data, we initiate the theoretical exploration of how to leverage MPC architectures to enable efficient, privacy-preserving computation over massive data. Clearly if a computation task does not lend itself to an efficient implementation on MPC even without security, then we cannot hope to compute it efficiently on MPC with security. We show, on the other hand, that any task that can be efficiently computed on MPC can also be securely computed with comparable efficiency. Specifically, we show the following results: - any MPC algorithm can be compiled to a communication-oblivious counterpart while asymptotically preserving its round and space complexity, where communication-obliviousness ensures that any network intermediary observing the communication patterns learn no information about the secret inputs; - assuming the existence of Fully Homomorphic Encryption with a suitable notion of compactness and other standard cryptographic assumptions, any MPC algorithm can be compiled to a secure counterpart that defends against an adversary who controls not only intermediate network routers but additionally up to 1/3 - ? fraction of machines (for an arbitrarily small constant ?) - moreover, this compilation preserves the round complexity tightly, and preserves the space complexity upto a multiplicative security parameter related blowup. As an initial exploration of this important direction, our work suggests new definitions and proposes novel protocols that blend algorithmic and cryptographic techniques

Sub-logarithmic Distributed Oblivious RAM with Small Block Size

Oblivious RAM (ORAM) is a cryptographic primitive that allows a client to securely execute RAM programs over data that is stored in an untrusted server. Distributed Oblivious RAM is a variant of ORAM, where the data is stored in $m>1$ servers. Extensive research over the last few decades have succeeded to reduce the bandwidth overhead of ORAM schemes, both in the single-server and the multi-server setting, from $O(\sqrt{N})$ to $O(1)$. However, all known protocols that achieve a sub-logarithmic overhead either require heavy server-side computation (e.g. homomorphic encryption), or a large block size of at least $\Omega(\log^3 N)$. In this paper, we present a family of distributed ORAM constructions that follow the hierarchical approach of Goldreich and Ostrovsky [GO96]. We enhance known techniques, and develop new ones, to take better advantage of the existence of multiple servers. By plugging efficient known hashing schemes in our constructions, we get the following results: 1. For any $m\geq 2$, we show an $m$-server ORAM scheme with $O(\log N/\log\log N)$ overhead, and block size $\Omega(\log^2 N)$. This scheme is private even against an $(m-1)$-server collusion. 2. A 3-server ORAM construction with $O(\omega(1)\log N/\log\log N)$ overhead and a block size almost logarithmic, i.e. $\Omega(\log^{1+\epsilon}N)$. We also investigate a model where the servers are allowed to perform a linear amount of light local computations, and show that constant overhead is achievable in this model, through a simple four-server ORAM protocol

Lower Bounds for Multi-Server Oblivious RAMs

In this work, we consider the construction of oblivious RAMs (ORAM) in a setting with multiple servers and the adversary may corrupt a subset of the servers. We present an $\Omega(\log n)$ overhead lower bound for any $k$-server ORAM that limits any PPT adversary to distinguishing advantage at most $1/4k$ when only one server is corrupted. In other words, if one insists on negligible distinguishing advantage, then multi-server ORAMs cannot be faster than single-server ORAMs even with polynomially many servers of which only one unknown server is corrupted. Our results apply to ORAMs that may err with probability at most $1/128$ as well as scenarios where the adversary corrupts larger subsets of servers. We also extend our lower bounds to other important data structures including oblivious stacks, queues, deques, priority queues and search trees

Privacy-Preserving Regular Expression Matching using Nondeterministic Finite Automata

Motivated by the privacy requirements in network intrusion detection and DNS policy checking, we have developed a suite of protocols and algorithms for regular expression matching with enhanced privacy: - A new regular expression matching algorithm that is oblivious to the input strings, of which the complexity is only $O(mn)$ where $m$ and $n$ are the length of strings and the regular expression respectively. It is achieved by exploiting the structure of the Thompson nondeterministic automata. - A zero-knowledge proof of regular expression pattern matching in which a prover generates a proof to demonstrate that a public regular expression matches her input string without revealing the string itself. -Two secure-regex protocols that ensure the privacy of both the string and regular expression. The first protocol is based on the oblivious stack and reduces the complexity of the state-of-the-art from $O(mn^2)$ to $O(mn\log n)$. The second protocol relies on the oblivious transfer and performs better empirically when the size of regular expressions is smaller than $2^{12}$. We also evaluated our protocols in the context of encrypted DNS policy checking and intrusion detection and achieved 4.5X improvements over the state-of-the-art. These results also indicate the practicality of our approach in real-world applications

Batched differentially private information retrieval

Private Information Retrieval (PIR) allows several clients to query a database held by one or more servers, such that the contents of their queries remain private. Prior PIR schemes have achieved sublinear communication and computation by leveraging computational assumptions, federating trust among many servers, relaxing security to permit differentially private leakage, refactoring effort into an offline stage to reduce online costs, or amortizing costs over a large batch of queries. In this work, we present an efficient PIR protocol that combines all of the above techniques to achieve constant amortized communication and computation complexity in the size of the database and constant client work. We leverage differentially private leakage in order to provide better trade-offs between privacy and efficiency. Our protocol achieves speed-ups up to and exceeding 10x in practical settings compared to state of the art PIR protocols, and can scale to batches with hundreds of millions of queries on cheap commodity AWS machines. Our protocol builds upon a new secret sharing scheme that is both incremental and non-malleable, which may be of interest to a wider audience. Our protocol provides security up to abort against malicious adversaries that can corrupt all but one party.1414119 - National Science Foundation; CNS-1718135 - National Science Foundation; CNS-1931714 - National Science Foundation; HR00112020021 - Department of Defense/DARPA; 000000000000000000000000000000000000000000000000000000037211 - SRI Internationalhttps://www.usenix.org/system/files/sec22-albab.pdfPublished versio

Secure Computation Towards Practical Applications

Secure multi-party computation (MPC) is a central area of research in cryptography. Its goal is to allow a set of players to jointly compute a function on their inputs while protecting and preserving the privacy of each player's input. Motivated by the huge growth of data available and the rise of global privacy concerns of entities using this data, we study the feasibility of using secure computation techniques on large scale data sets to address these concerns. An important limitation of generic secure computation protocols is that they require at least linear time complexity. This seems to rule out applications involving big amounts of data. On the other hand, specific applications may have particular properties that allow for ad-hoc secure protocols overcoming the linear time barrier. In addition, in some settings the full level of security guaranteed by MPC protocols may not be required, and some controlled amount of privacy leakage can be acceptable. Towards this end, we first take a theoretical point of view, and study whether sublinear time RAM programs can be computed securely with sublinear time complexity in the two party setting. We then take a more practical approach, and study the specific scenario of private database querying, where both the server's data and the client's query need to be protected. In this last setting we provide two private database management systems achieving different levels of efficiency, functionality, and security. These three results provide an overview of this three-dimensional trade-off space. For the above systems, we describe formal security definitions and stablish mathematical proofs of security. We also take a practical approach roviding an implementation of the systems and experimental analysis of their efficiency