Abstract not found

Abstract not found

We consider a statistical database in which a trusted administrator introduces noise to the query responses with the goal of maintaining privacy of individual database entries. In such a database, a query consists of a pair (S, f) where S is a set of rows in the database and f is a function mapping database rows to {0, 1}. The true answer is P i∈S f(di), and a noisy version is released as the response to the query. Results of Dinur, Dwork, and Nissim show that a strong form of privacy can be maintained using a surprisingly small amount of noise – much less than the sampling error – provided the total number of queries is sublinear in the number of database rows. We call this query and (slightly) noisy reply the SuLQ (Sub-Linear Queries) primitive. The assumption of sublinearity becomes reasonable as databases grow increasingly large. We extend this work in two ways. First, we modify the privacy analysis to real-valued functions f and arbitrary row types, as a consequence greatly improving the bounds on noise required for privacy. Second, we examine the computational power of the SuLQ primitive. We show that it is very powerful indeed, in that slightly noisy versions of the following computations can be carried out with very few invocations of the primitive: principal component analysis, k means clustering, the Perceptron Algorithm, the ID3 algorithm, and (apparently!) all algorithms that operate in the in the statistical query learning model [11].

A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely using polynomial resources" (where `resources' refers to communication and computation). This result follows by a general transformation from any circuit for f to a secure protocol that evaluates f . Although the resources used by protocols resulting from this transformation are polynomial in the circuit size, they are much higher (in general) than those required for an insecure computation of f . We propose a new methodology for designing secure protocols, utilizing the communication complexity tree (or branching program) representation of f . We start with an efficient (insecure) protocol for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". We show several simple applications of this new methodology resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the "millionaires problem ", where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation. 1.

Given two or more parties possessing large, confidential datasets, we consider the problem of securely computing the k of the datasets, e.g. the median of the values in the datasets. We investigate protocols with sublinear computation and communication costs. In the two-party case, we show that the k -ranked element can be computed in log k rounds, where the computation and communication costs of each round are O(log M), where log M is the number of bits needed to describe each element of the input data.

Motivated by the application of private statistical analysis of large databases, we consider the problem of selective private function evaluation (SPFE). In this problem, a client inter-acts with one or more servers holding copies of a database z = zt,...,z, in order to compute f(z~t,...,z~,,,) , for some function f and indices i = it,...,i, ~ chosen by the client. Ideally, the client must learn nothing more about the database than f(zit,..., zi,,~), and the servers should learn nothing. Generic solutions for this problem, based on standard techniques for secure function evaluation, incur communi-cation complexity that is at least linear in n, making them prohibitive for large databases even when f is relatively sim-ple and m is small. We present various approaches for con-structing sublinear-communication $PFE protocols, both for the general problem and for special cases of interest. Our so-lutions not only offer sublinear communication complexity, but are also practical in many scenarios. 1.

Mobile devices equipped with positioning capabilities (e.g., GPS) can ask location-dependent queries to Location Based Services (LBS). To protect privacy, the user location must not be disclosed. Existing solutions utilize a trusted anonymizer between the users and the LBS. This approach has several drawbacks: (i) All users must trust the third party anonymizer, which is a single point of attack. (ii) A large number of cooperating, trustworthy users is needed. (iii) Privacy is guaranteed only for a single snapshot of user locations; users are not protected against correlation attacks (e.g., history of user movement). We propose a novel framework to support private locationdependent queries, based on the theoretical work on Private Information Retrieval (PIR). Our framework does not require a trusted third party, since privacy is achieved via cryptographic techniques. Compared to existing work, our approach achieves stronger privacy for snapshots of user locations; moreover, it is the first to provide provable privacy guarantees against correlation attacks. We use our framework to implement approximate and exact algorithms for nearest-neighbor search. We optimize query execution by employing data mining techniques, which identify redundant computations. Contrary to common belief, the experimental results suggest that PIR approaches incur reasonable overhead and are applicable in practice.

Shmatikov z SRI International

Edit distance has been extensively studied for the past several years. Nevertheless, no linear-time algorithm is known to compute the edit distance between two strings, or even to approximate it to within a modest factor. Furthermore, for various natural algorithmic problems such as low-distortion embeddings into normed spaces, approximate nearest-neighbor schemes, and sketching algorithms, known results for the edit distance are rather weak. We develop algorithms that solve gap versions of the edit distance problem: given two strings of length n with the promise that their edit distance is either at most k or greater than ℓ, decide which of the two holds. We present two sketching algorithms for gap versions of edit distance. Our first algorithm solves the k vs. (kn) 2/3 gap problem, using a constant size sketch. A more involved algorithm solves the stronger k vs. ℓ gap problem, where ℓ can be as small as O(k 2)—still with a constant sketch—but works only for strings that are mildly “non-repetitive”. Finally, we develop an n 3/7-approximation quasi-linear time algorithm for edit distance, improving the previous best factor of n 3/4 [5]; if the input strings are assumed to be non-repetitive, then the approximation factor can be strengthened to n 1/3. 1.

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