Irit Dinur

Revealing information while preserving privacy

We examine the tradeoff between privacy and usability of statistical databases. We model a statistical database by an <i>n</i>-bit string <i>d</i><inf>1</inf>,..,<i>d</i><inf><i>n</i></inf>, with a query being a subset <i>q</i> ⊆ [<i>n</i>] to be answered by Σ<inf><i>i</i>ε<i>q</i></inf> <i>d</i><inf><i>i</i></inf>. Our main result is a polynomial reconstruction algorithm of data from noisy (perturbed) subset sums. Applying this reconstruction algorithm to statistical databases we show that in order to achieve privacy one has to add perturbation of magnitude (Ω√<i>n</i>). That is, smaller perturbation always results in a strong violation of privacy. We show that this result is tight by exemplifying access algorithms for statistical databases that preserve privacy while adding perturbation of magnitude Õ(√<i>n</i>).For time-<i>T</i> bounded adversaries we demonstrate a privacypreserving access algorithm whose perturbation magnitude is ≈ √<i>T</i>.

The importance of being biased

(MATH) We show that the Minimum Vertex Cover problem is NP-hard to approximate to within any factor smaller than

Approximating-CVP to within almost-polynomial factors is NP-hard

10\sqrt{5}-21 \approx 1.36067

Analytical approach to parallel repetition

, improving on the previously known hardness result for a

A new multilayered PCP and the hardness of hypergraph vertex cover

\frac{7}{6}

Approximating SVPinfty to within Almost-Polynomial Factors Is NP-Hard

factor.

A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover

This paper shows the problem of finding the closest vector in an n-dimensional lattice to be NP-hard to approximate to within factor nc/log log n for some constant c > 0.

The hardness of 3-uniform hypergraph coloring

We propose an analytical framework for studying parallel repetition, a basic product operation for one-round twoplayer games. In this framework, we consider a relaxation of the value of projection games. We show that this relaxation is multiplicative with respect to parallel repetition and that it provides a good approximation to the game value. Based on this relaxation, we prove the following improved parallel repetition bound: For every projection game G with value at most ρ, the k-fold parallel repetition G⊗k has value at most [EQUATION] This statement implies a parallel repetition bound for projection games with low value ρ. Previously, it was not known whether parallel repetition decreases the value of such games. This result allows us to show that approximating set cover to within factor (1 --- ε) ln n is NP-hard for every ε > 0, strengthening Feiges quasi-NP-hardness and also building on previous work by Moshkovitz and Raz. In this framework, we also show improved bounds for few parallel repetitions of projection games, showing that Razs counterexample to strong parallel repetition is tight even for a small number of repetitions. Finally, we also give a short proof for the NP-hardness of label cover(1, δ) for all δ > 0, starting from the basic PCP theorem.

PCP characterizations of NP: towards a polynomially-small error-probability

Given a k-uniform hyper-graph, the Ek-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within factor (k-1-ε) for any k ≥ 3 and any ε>0. The result is essentially tight as this problem can be easily approximated within factor k. Our construction makes use of the biased Long-Code and is analyzed using combinatorial properties of s-wise t-intersecting families of subsets.

Robust local testability of tensor products of LDPC codes

We show SVP∞ and CVP∞ to be NP-hard to approximate to within nc/log log n for some constant c > 0. We show a direct reduction from SAT to these problems, that combines ideas from [ABSS93] and from [DKRS99], along with some modifications. Our result is obtained without relying on the PCP characterization of NP, although some of our techniques are derived from the proof of the PCP characterization itself [DFK+99].