Several well-known public key encryption schemes, including those of Alekhnovich (FOCS 2003), Regev (STOC 2005), and Gentry, Peikert and Vaikuntanathan (STOC 2008), rely on the conjectured intractability of inverting noisy linear encodings. These schemes are limited in that they either require the underlying field to grow with the security parameter, ... more >>>

We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions.

As corollaries, we also prove similar inapproximability results for Bayesian Nash equilibrium in a two-player incomplete ... more >>>

We show how to compress communication in distributed protocols in which parties do not have private inputs. More specifically, we present a generic method for converting any protocol in which parties do not have private inputs, into another protocol where each message is "short" while preserving the same number of ... more >>>