Data-Oblivious Graph Algorithms in Outsourced External Memory

Motivated by privacy preservation for outsourced data, data-oblivious external memory is a computational framework where a client performs computations on data stored at a semi-trusted server in a way that does not reveal her data to the server. This approach facilitates collaboration and reliability over traditional frameworks, and it provides privacy protection, even though the server has full access to the data and he can monitor how it is accessed by the client. The challenge is that even if data is encrypted, the server can learn information based on the client data access pattern; hence, access patterns must also be obfuscated. We investigate privacy-preserving algorithms for outsourced external memory that are based on the use of data-oblivious algorithms, that is, algorithms where each possible sequence of data accesses is independent of the data values. We give new efficient data-oblivious algorithms in the outsourced external memory model for a number of fundamental graph problems. Our results include new data-oblivious external-memory methods for constructing minimum spanning trees, performing various traversals on rooted trees, answering least common ancestor queries on trees, computing biconnected components, and forming open ear decompositions. None of our algorithms make use of constant-time random oracles.Comment: 20 page

Cloud Data Auditing Using Proofs of Retrievability

Cloud servers offer data outsourcing facility to their clients. A client outsources her data without having any copy at her end. Therefore, she needs a guarantee that her data are not modified by the server which may be malicious. Data auditing is performed on the outsourced data to resolve this issue. Moreover, the client may want all her data to be stored untampered. In this chapter, we describe proofs of retrievability (POR) that convince the client about the integrity of all her data.Comment: A version has been published as a book chapter in Guide to Security Assurance for Cloud Computing (Springer International Publishing Switzerland 2015

Lower Bounds for Oblivious Near-Neighbor Search

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search ($\mathsf{ANN}$) over the $d$-dimensional Hamming cube. For the natural setting of $d = \Theta(\log n)$, our result implies an $\tilde{\Omega}(\lg^2 n)$ lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for $\mathsf{ANN}$. This is the first super-logarithmic $\mathit{unconditional}$ lower bound for $\mathsf{ANN}$ against general (non black-box) data structures. We also show that any oblivious $\mathit{static}$ data structure for decomposable search problems (like $\mathsf{ANN}$) can be obliviously dynamized with $O(\log n)$ overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page

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

The Melbourne Shuffle: Improving Oblivious Storage in the Cloud

We present a simple, efficient, and secure data-oblivious randomized shuffle algorithm. This is the first secure data-oblivious shuffle that is not based on sorting. Our method can be used to improve previous oblivious storage solutions for network-based outsourcing of data