Theory Seminar: Trapdoors for Hard Lattices, and New Lattice-based Cryptography

Vinod Vaikuntanathan, MIT
יום ראשון, 27.1.2008, 11:00
חדר 337, בניין טאוב למדעי המחשב

We show that disjointness requires randomized communication Omega(n^{1/2k} / (k-1)2^{k-1}2^{2^{k-1}}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound was Omega (\log n / k-1). By results of Beame, Pitassi, and Segerlind, this implies 2^{n^{Omega(1)}} lower bounds on the size of tree-like Lovasz-Schrijver proof systems needed to refute certain unsatisfiable CNFs, and super-polynomial lower bounds on the size of any tree-like proof system whose terms are degree-d polynomial inequalities for d = loglog n -O(logloglog n).

Joint work with Troy Lee from Rutgers University and Chris Peikert (SRI International).

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