Fundamental limits of failure identifiability by Boolean Network Tomography

Boolean network tomography is a powerful tool to infer the state (working/failed) of individual nodes from path-level measurements obtained by egde-nodes. We consider the problem of optimizing the capability of identifying network failures through the design of monitoring schemes. Finding an optimal solution is NP-hard and a large body of work has been devoted to heuristic approaches providing lower bounds. Unlike previous works, we provide upper bounds on the maximum number of identifiable nodes, given the number of monitoring paths and different constraints on the network topology, the routing scheme, and the maximum path length. The proposed upper bounds represent a fundamental limit on the identifiability of failures via Boolean network tomography. This analysis provides insights on how to design topologies and related monitoring schemes to achieve the maximum identifiability under various network settings. Through analysis and experiments we demonstrate the tightness of the bounds and efficacy of the design insights for engineered as well as real network

Anonymous Networking amidst Eavesdroppers

The problem of security against timing based traffic analysis in wireless networks is considered in this work. An analytical measure of anonymity in eavesdropped networks is proposed using the information theoretic concept of equivocation. For a physical layer with orthogonal transmitter directed signaling, scheduling and relaying techniques are designed to maximize achievable network performance for any given level of anonymity. The network performance is measured by the achievable relay rates from the sources to destinations under latency and medium access constraints. In particular, analytical results are presented for two scenarios: For a two-hop network with maximum anonymity, achievable rate regions for a general m x 1 relay are characterized when nodes generate independent Poisson transmission schedules. The rate regions are presented for both strict and average delay constraints on traffic flow through the relay. For a multihop network with an arbitrary anonymity requirement, the problem of maximizing the sum-rate of flows (network throughput) is considered. A selective independent scheduling strategy is designed for this purpose, and using the analytical results for the two-hop network, the achievable throughput is characterized as a function of the anonymity level. The throughput-anonymity relation for the proposed strategy is shown to be equivalent to an information theoretic rate-distortion function

Efficient Two-Step Adversarial Defense for Deep Neural Networks

In recent years, deep neural networks have demonstrated outstanding performance in many machine learning tasks. However, researchers have discovered that these state-of-the-art models are vulnerable to adversarial examples: legitimate examples added by small perturbations which are unnoticeable to human eyes. Adversarial training, which augments the training data with adversarial examples during the training process, is a well known defense to improve the robustness of the model against adversarial attacks. However, this robustness is only effective to the same attack method used for adversarial training. Madry et al.(2017) suggest that effectiveness of iterative multi-step adversarial attacks and particularly that projected gradient descent (PGD) may be considered the universal first order adversary and applying the adversarial training with PGD implies resistance against many other first order attacks. However, the computational cost of the adversarial training with PGD and other multi-step adversarial examples is much higher than that of the adversarial training with other simpler attack techniques. In this paper, we show how strong adversarial examples can be generated only at a cost similar to that of two runs of the fast gradient sign method (FGSM), allowing defense against adversarial attacks with a robustness level comparable to that of the adversarial training with multi-step adversarial examples. We empirically demonstrate the effectiveness of the proposed two-step defense approach against different attack methods and its improvements over existing defense strategies.Comment: 12 page

The Embedding Capacity of Information Flows Under Renewal Traffic

Given two independent point processes and a certain rule for matching points between them, what is the fraction of matched points over infinitely long streams? In many application contexts, e.g., secure networking, a meaningful matching rule is that of a maximum causal delay, and the problem is related to embedding a flow of packets in cover traffic such that no traffic analysis can detect it. We study the best undetectable embedding policy and the corresponding maximum flow rate ---that we call the embedding capacity--- under the assumption that the cover traffic can be modeled as arbitrary renewal processes. We find that computing the embedding capacity requires the inversion of very structured linear systems that, for a broad range of renewal models encountered in practice, admits a fully analytical expression in terms of the renewal function of the processes. Our main theoretical contribution is a simple closed form of such relationship. This result enables us to explore properties of the embedding capacity, obtaining closed-form solutions for selected distribution families and a suite of sufficient conditions on the capacity ordering. We evaluate our solution on real network traces, which shows a noticeable match for tight delay constraints. A gap between the predicted and the actual embedding capacities appears for looser constraints, and further investigation reveals that it is caused by inaccuracy of the renewal traffic model rather than of the solution itself.Comment: Sumbitted to IEEE Trans. on Information Theory on March 10, 201