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Among the most challenging traffic-analysis attacks to confound are those leveraging the sizes of objects downloaded over the network. In this paper we systematically analyze this problem under realistic constraints regarding the padding overhead that the object store is willing to incur. We give algorithms to compute privacy-optimal padding schemes—specifically that minimize the network observer’s information gain from a downloaded object’s padded size—in several scenarios of interest: per-object padding, in which the object store responds to each request for an object with the same padded copy; per-request padding, in which the object store pads an object anew each time it serves that object; and a scenario unlike the previous ones in that the object store is unable to leverage a known distribution over the object queries. We provide constructions for privacy-optimal padding in each case, compare them to recent contenders in the research literature, and evaluate their performance on practical datasets. 

Neural networks have enabled learning over examples that contain thousands of dimensions. However, most of these models are limited to training and evaluating on a finite collection of points and do not consider the hypervolume in which the data resides. Any analysis of the model’s local or global behavior is therefore limited to very expensive or imprecise estimators. We propose to formulate neural networks as a composition of a bijective (flow) network followed by a learnable, separable network. This construction allows for learning (or assessing) over full hypervolumes with precise estimators at tractable computational cost via integration over the input space. We develop the necessary machinery, propose several practical integrals to use during training, and demonstrate their utility.