The 3SUM problem asks if there are three integers $a,b,c$ summing to $0$ in a given set of $n$ integers of magnitude poly($n$). Patrascu (STOC '10) reduces solving 3SUM in time $n^{2-\Omega(1)}$ to listing $m$ triangles in a graph with $m$ edges in time $m^{4/3-\Omega(1)}$.
In this note we present ... more >>>

In this paper we put forward a conjecture: an instantiation of the Sliding Scale Conjecture of Bellare, Goldwasser, Lund and Russell to projection games. We refer to this conjecture as the Projection Games Conjecture.

We further suggest the research agenda of establishing new hardness of approximation results based on the ... more >>>

We present a radically new approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), {\em without Gentry's bootstrapping procedure}.

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