An official website of the United States government
Among the most challenging traffic-analysis attacks to confound are those leveraging the sizes of objects downloaded over the network, as the size of an object is often a powerful indicator of its identity. In this dissertation, we consider this challenge in both (i) the simplified setting where successive object retrievals are assumed to be independent and (ii) the setting where sequential object retrievals are dependent on one another. Furthermore, within the dependent retrievals setting, we address the scenario where enumerating all possible sequences is impractical. For each setting, we present algorithms by which a benevolent object store computes a memoryless padding scheme to pad objects before sending them, in a way that bounds the information gain that the padded sizes provide to the network observer about the objects being retrieved. Furthermore, all of our algorithms ensure that no object is padded to more than c× its original size, for a tunable factor c > 1. We compare each algorithm to recent contenders in the research literature and evaluate their performance on practical datasets.
more »
« less
Contention Resultion with Predictions
In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network sizes that predicts the likelihood of each size occurring. The goal is to leverage the predictive power of this distribution to improve on worst-case time complexity bounds. Using a novel connection between contention resolution and information theory, we prove lower bounds on the expected time complexity with respect to the Shannon entropy of the corresponding network size random variable, for both the collision detection and no collision detection assumptions. We then analyze upper bounds for these settings, assuming now that the distribution provided as input might differ from the actual distribution generating network sizes. We express their performance with respect to both entropy and the statistical divergence between the two distributions---allowing us to quantify the cost of poor predictions. Finally, we turn our attention to the related perfect advice setting, parameterized with a length b ≥ 0, in which all active processes in a given execution are provided the best possible b bits of information about their network. We provide tight bounds on the speed-up possible with respect to b for deterministic and randomized algorithms, with and without collision detection. These bounds provide a fundamental limit on the maximum power that can be provided by any predictive model with a bounded output size.
more »
« less
- Award ID(s):
- 1733872
- PAR ID:
- 10309767
- Editor(s):
- Miller, Avery
- Date Published:
- Journal Name:
- ACM Symposium on Principles of Distributed Computing
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution p, extensive research has established optimal bounds for uniformity testing, identity testing (goodness of fit), and closeness testing (equivalence or two-sample testing). We explore these problems in a setting where a predicted data distribution, possibly derived from historical data or predictive machine learning models, is available. We demonstrate that such a predictor can indeed reduce the number of samples required for all three property testing tasks. The reduction in sample complexity depends directly on the predictor’s quality, measured by its total variation distance from p. A key advantage of our algorithms is their adaptability to the precision of the prediction. Specifically, our algorithms can self-adjust their sample complexity based on the accuracy of the available prediction, operating without any prior knowledge of the estimation’s accuracy (i.e. they are consistent). Additionally, we never use more samples than the standard approaches require, even if the predictions provide no meaningful information (i.e. they are also robust). We provide lower bounds to indicate that the improvements in sample complexity achieved by our algorithms are information-theoretically optimal. Furthermore, experimental results show that the performance of our algorithms on real data significantly exceeds our worst-case guarantees for sample complexity, demonstrating the practicality of our approach.more » « less
-
Guruswami, Venkatesan (Ed.)Algorithms with predictions is a new research direction that leverages machine learned predictions for algorithm design. So far a plethora of recent works have incorporated predictions to improve on worst-case bounds for online problems. In this paper, we initiate the study of complexity of dynamic data structures with predictions, including dynamic graph algorithms. Unlike online algorithms, the goal in dynamic data structures is to maintain the solution efficiently with every update. We investigate three natural models of prediction: (1) δ-accurate predictions where each predicted request matches the true request with probability δ, (2) list-accurate predictions where a true request comes from a list of possible requests, and (3) bounded delay predictions where the true requests are a permutation of the predicted requests. We give general reductions among the prediction models, showing that bounded delay is the strongest prediction model, followed by list-accurate, and δ-accurate. Further, we identify two broad problem classes based on lower bounds due to the Online Matrix Vector (OMv) conjecture. Specifically, we show that locally correctable dynamic problems have strong conditional lower bounds for list-accurate predictions that are equivalent to the non-prediction setting, unless list-accurate predictions are perfect. Moreover, we show that locally reducible dynamic problems have time complexity that degrades gracefully with the quality of bounded delay predictions. We categorize problems with known OMv lower bounds accordingly and give several upper bounds in the delay model that show that our lower bounds are almost tight. We note that concurrent work by v.d.Brand et al. [SODA '24] and Liu and Srinivas [arXiv:2307.08890] independently study dynamic graph algorithms with predictions, but their work is mostly focused on showing upper bounds.more » « less
-
This paper considers the recently popular beyond-worst-case algorithm analysis model which integrates machine-learned predictions with online algorithm design. We consider the online Steiner tree problem in this model for both directed and undirected graphs. Steiner tree is known to have strong lower bounds in the online setting and any algorithm’s worst-case guarantee is far from desirable. This paper considers algorithms that predict which terminal arrives online. The predictions may be incorrect and the algorithms’ performance is parameterized by the number of incorrectly predicted terminals. These guarantees ensure that algorithms break through the online lower bounds with good predictions and the competitive ratio gracefully degrades as the prediction error grows. We then observe that the theory is predictive of what will occur empirically. We show on graphs where terminals are drawn from a distribution, the new online algorithms have strong performance even with modestly correct predictions.more » « less
-
null (Ed.)This paper explores some applications of a two-moment inequality for the integral of the rth power of a function, where 0<1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/https://doi.org/10.1145/3465084.3467911
