Despite over 25 years of research on non-malleable commitments in the plain model, their round complexity has remained open. The goal of achieving non-malleable commitment protocols with only one or two rounds has been especially elusive. Pass (TCC 2013, CC 2016) captured this difficulty by proving important impossibility results regarding ... more >>>

We study multi-collision-resistant hash functions --- a natural relaxation of collision-resistant hashing that only guarantees the intractability of finding many (rather than two) inputs that map to the same image. An appealing feature of such hash functions is that unlike their collision-resistant counterparts, they do not necessarily require a key. ... more >>>

In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give the first-ever polynomial time (in the size of data) algorithm to train to global optimality a ReLU DNN with one hidden layer, assuming the input dimension and number ... more >>>