arXiv subjects

Negar Kiyavash

Publications and source records attributed to Negar Kiyavash.

108 records · Page 6Linked to original sources

arXiv2016

Improved Achievability and Converse Bounds for Erdős-Rényi Graph Matching

We consider the problem of perfectly recovering the vertex correspondence between two correlated Erdős-Rényi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. In some cases, the structural information in the graphs allow this correspondence to be recovered. We investigate the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources. Pedarsani and Grossglauser provided an achievability result of this type. Their result establishes the scaling dependence of the threshold on the number of vertices. We improve on their achievability bound. We also provide a converse bound, establishing conditions under which exact recovery is impossible. Together, these establish the scaling dependence of the threshold on the level of correlation between the two graphs. The converse and achievability bounds differ by a factor of two for sparse, significantly correlated graphs.

cs.IT↗

arXiv2015

Efficient Neighborhood Selection for Gaussian Graphical Models

This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a threshold-based algorithm for walk summable Gaussian graphical models. Both algorithms are shown to be structurally consistent, and efficient. Numerical results show that both algorithms work very well.

stat.ML↗

arXiv2015

Bounded Degree Approximations of Stochastic Networks

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with specified in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

cs.IT↗

arXiv2015

Generalized sphere-packing and sphere-covering bounds on the size of codes for combinatorial channels

Many of the classic problems of coding theory are highly symmetric, which makes it easy to derive sphere-packing upper bounds and sphere-covering lower bounds on the size of codes. We discuss the generalizations of sphere-packing and sphere-covering bounds to arbitrary error models. These generalizations become especially important when the sizes of the error spheres are nonuniform. The best possible sphere-packing and sphere-covering bounds are solutions to linear programs. We derive a series of bounds from approximations to packing and covering problems and study the relationships and trade-offs between them. We compare sphere-covering lower bounds with other graph theoretic lower bounds such as Turán's theorem. We show how to obtain upper bounds by optimizing across a family of channels that admit the same codes. We present a generalization of the local degree bound of Kulkarni and Kiyavash and use it to improve the best known upper bounds on the sizes of single deletion correcting codes and single grain error correcting codes.

cs.IT↗

arXiv2015

Directed Information Graphs

We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper-bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper-bounds are not valid, the resulting graph is nonetheless an optimal approximation. Another algorithm uses near-minimal dimension statistics when no bounds are known but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Lastly, we demonstrate the effectiveness of the proposed algorithms through analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times.

cs.IT↗

arXiv2014

Quantifying the Information Leakage in Timing Side Channels in Deterministic Work-Conserving Schedulers

When multiple job processes are served by a single scheduler, the queueing delays of one process are often affected by the others, resulting in a timing side channel that leaks the arrival pattern of one process to the others. In this work, we study such a timing side channel between a regular user and a malicious attacker. Utilizing Shannon's mutual information as a measure of information leakage between the user and attacker, we analyze privacy-preserving behaviors of common work-conserving schedulers. We find that the attacker can always learn perfectly the user's arrival process in a longest-queue-first (LQF) scheduler. When the user's job arrival rate is very low (near zero), first-come-first-serve (FCFS) and round robin schedulers both completely reveal the user's arrival pattern. The near-complete information leakage in the low-rate traffic region is proven to be reduced by half in a work-conserving version of TDMA (WC-TDMA) scheduler, which turns out to be privacy-optimal in the class of deterministic-working-conserving (det-WC) schedulers, according to a universal lower bound on information leakage we derive for all det-WC schedulers.

cs.IT↗

arXiv2013

An Improvement to Levenshtein's Upper Bound on the Cardinality of Deletion Correcting Codes

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code size, we apply a packing argument to channels that perform different mixtures of insertions and deletions. Even though the set of codes is identical for all of these channels, the bounds that we obtain vary. Prior to this work, only the bounds corresponding to the all insertion case and the all deletion case were known. We recover these as special cases. The bound from the all deletion case, due to Levenshtein, has been the best known for more than forty five years. Our generalized bound is better than Levenshtein's bound whenever the number of deletions to be corrected is larger than the alphabet size.

cs.IT↗

arXiv2013

Invisible Flow Watermarks for Channels with Dependent Substitution, Deletion, and Bursty Insertion Errors

Flow watermarks efficiently link packet flows in a network in order to thwart various attacks such as stepping stones. We study the problem of designing good flow watermarks. Earlier flow watermarking schemes mostly considered substitution errors, neglecting the effects of packet insertions and deletions that commonly happen within a network. More recent schemes consider packet deletions but often at the expense of the watermark visibility. We present an invisible flow watermarking scheme capable of enduring a large number of packet losses and insertions. To maintain invisibility, our scheme uses quantization index modulation (QIM) to embed the watermark into inter-packet delays, as opposed to time intervals including many packets. As the watermark is injected within individual packets, packet losses and insertions may lead to watermark desynchronization and substitution errors. To address this issue, we add a layer of error-correction coding to our scheme. Experimental results on both synthetic and real network traces demonstrate that our scheme is robust to network jitter, packet drops and splits, while remaining invisible to an attacker.

cs.CR↗

arXiv2013

An Information Theoretic Study of Timing Side Channels in Two-user Schedulers

Timing side channels in two-user schedulers are studied. When two users share a scheduler, one user may learn the other user's behavior from patterns of service timings. We measure the information leakage of the resulting timing side channel in schedulers serving a legitimate user and a malicious attacker, using a privacy metric defined as the Shannon equivocation of the user's job density. We show that the commonly used first-come-first-serve (FCFS) scheduler provides no privacy as the attacker is able to to learn the user's job pattern completely. Furthermore, we introduce an scheduling policy, accumulate-and-serve scheduler, which services jobs from the user and attacker in batches after buffering them. The information leakage in this scheduler is mitigated at the price of service delays, and the maximum privacy is achievable when large delays are added.

cs.IT↗

arXiv2013

Mitigating Timing Side Channel in Shared Schedulers

In this work, we study information leakage in timing side channels that arise in the context of shared event schedulers. Consider two processes, one of them an innocuous process (referred to as Alice) and the other a malicious one (referred to as Bob), using a common scheduler to process their jobs. Based on when his jobs get processed, Bob wishes to learn about the pattern (size and timing) of jobs of Alice. Depending on the context, knowledge of this pattern could have serious implications on Alice's privacy and security. For instance, shared routers can reveal traffic patterns, shared memory access can reveal cloud usage patterns, and suchlike. We present a formal framework to study the information leakage in shared resource schedulers using the pattern estimation error as a performance metric. The first-come-first-serve (FCFS) scheduling policy and time-division-multiple-access (TDMA) are identified as two extreme policies on the privacy metric, FCFS has the least, and TDMA has the highest. However, on performance based metrics, such as throughput and delay, it is well known that FCFS significantly outperforms TDMA. We then derive two parametrized policies, accumulate and serve, and proportional TDMA, which take two different approaches to offer a tunable trade-off between privacy and performance.

cs.CR↗

arXiv2012

Two Approaches to the Construction of Deletion Correcting Codes: Weight Partitioning and Optimal Colorings

We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a code by taking the union of many constant Hamming weight codes. This results in codes that have additional structure. Searching for codes in constant Hamming weight induced subgraphs is computationally easier than searching the original graph. We prove a lower bound on size of a codebook constructed this way for any number of deletions and show that it is only a small factor below the corresponding lower bound on unrestricted codes. In the single deletion case, we find optimal colorings of the constant Hamming weight induced subgraphs. We show that the resulting code is asymptotically optimal. We discuss the relationship between codes and colorings and observe that the VT codes are optimal in a coloring sense. We prove a new lower bound on the chromatic number of the deletion channel graphs. Colorings of the deletion channel graphs that match this bound do not necessarily produce asymptotically optimal codes.

cs.IT↗

arXiv2012

Non-asymptotic Upper Bounds for Deletion Correcting Codes

Explicit non-asymptotic upper bounds on the sizes of multiple-deletion correcting codes are presented. In particular, the largest single-deletion correcting code for $q$-ary alphabet and string length $n$ is shown to be of size at most $\frac{q^n-q}{(q-1)(n-1)}$. An improved bound on the asymptotic rate function is obtained as a corollary. Upper bounds are also derived on sizes of codes for a constrained source that does not necessarily comprise of all strings of a particular length, and this idea is demonstrated by application to sets of run-length limited strings. The problem of finding the largest deletion correcting code is modeled as a matching problem on a hypergraph. This problem is formulated as an integer linear program. The upper bound is obtained by the construction of a feasible point for the dual of the linear programming relaxation of this integer linear program. The non-asymptotic bounds derived imply the known asymptotic bounds of Levenshtein and Tenengolts and improve on known non-asymptotic bounds. Numerical results support the conjecture that in the binary case, the Varshamov-Tenengolts codes are the largest single-deletion correcting codes.

cs.IT↗

arXiv2012

Multi-Flow Attacks Against Network Flow Watermarks: Analysis and Countermeasures

In this paper, we analyze several recent schemes for watermarking network flows that are based on splitting the flow into timing intervals. We show that this approach creates time-dependent correlations that enable an attack that combines multiple watermarked flows. Such an attack can easily be mounted in nearly all applications of network flow watermarking, both in anonymous communication and stepping stone detection. The attack can be used to detect the presence of a watermark, recover the secret parameters, and remove the watermark from a flow. The attack can be effective even if different flows are marked with different values of a watermark. We analyze the efficacy of our attack using a probabilistic model and a Markov-Modulated Poisson Process (MMPP) model of interactive traffic. We also implement our attack and test it using both synthetic and real-world traces, showing that our attack is effective with as few as 10 watermarked flows. Finally, we propose possible countermeasures to defeat the multi-flow attack.

cs.CR↗

arXiv2012

Non-blind watermarking of network flows

Linking network flows is an important problem in intrusion detection as well as anonymity. Passive traffic analysis can link flows but requires long periods of observation to reduce errors. Active traffic analysis, also known as flow watermarking, allows for better precision and is more scalable. Previous flow watermarks introduce significant delays to the traffic flow as a side effect of using a blind detection scheme; this enables attacks that detect and remove the watermark, while at the same time slowing down legitimate traffic. We propose the first non-blind approach for flow watermarking, called RAINBOW, that improves watermark invisibility by inserting delays hundreds of times smaller than previous blind watermarks, hence reduces the watermark interference on network flows. We derive and analyze the optimum detectors for RAINBOW as well as the passive traffic analysis under different traffic models by using hypothesis testing. Comparing the detection performance of RAINBOW and the passive approach we observe that both RAINBOW and passive traffic analysis perform similarly good in the case of uncorrelated traffic, however, the RAINBOW detector drastically outperforms the optimum passive detector in the case of correlated network flows. This justifies the use of non-blind watermarks over passive traffic analysis even though both approaches have similar scalability constraints. We confirm our analysis by simulating the detectors and testing them against large traces of real network flows.

cs.CR↗

arXiv2011

Fingerprinting with Equiangular Tight Frames

Digital fingerprinting is a framework for marking media files, such as images, music, or movies, with user-specific signatures to deter illegal distribution. Multiple users can collude to produce a forgery that can potentially overcome a fingerprinting system. This paper proposes an equiangular tight frame fingerprint design which is robust to such collusion attacks. We motivate this design by considering digital fingerprinting in terms of compressed sensing. The attack is modeled as linear averaging of multiple marked copies before adding a Gaussian noise vector. The content owner can then determine guilt by exploiting correlation between each user's fingerprint and the forged copy. The worst-case error probability of this detection scheme is analyzed and bounded. Simulation results demonstrate the average-case performance is similar to the performance of orthogonal and simplex fingerprint designs, while accommodating several times as many users.

cs.IT↗

arXiv2011

Website Detection Using Remote Traffic Analysis

Recent work in traffic analysis has shown that traffic patterns leaked through side channels can be used to recover important semantic information. For instance, attackers can find out which website, or which page on a website, a user is accessing simply by monitoring the packet size distribution. We show that traffic analysis is even a greater threat to privacy than previously thought by introducing a new attack that can be carried out remotely. In particular, we show that, to perform traffic analysis, adversaries do not need to directly observe the traffic patterns. Instead, they can gain sufficient information by sending probes from a far-off vantage point that exploits a queuing side channel in routers. To demonstrate the threat of such remote traffic analysis, we study a remote website detection attack that works against home broadband users. Because the remotely observed traffic patterns are more noisy than those obtained using previous schemes based on direct local traffic monitoring, we take a dynamic time warping (DTW) based approach to detecting fingerprints from the same website. As a new twist on website fingerprinting, we consider a website detection attack, where the attacker aims to find out whether a user browses a particular web site, and its privacy implications. We show experimentally that, although the success of the attack is highly variable, depending on the target site, for some sites very low error rates. We also show how such website detection can be used to deanonymize message board users.

cs.CR↗

arXiv2011

Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes

We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among processes. By extending the results by Chow and Liu on dependence tree approximations, we show that the best causal dependence tree approximation is the one which maximizes the sum of directed informations on its edges, where best is defined in terms of minimizing the KL-divergence between the original and the approximate distribution. Moreover, we describe a low-complexity algorithm to efficiently pick this approximate distribution.

cs.IT↗

arXiv2005

On the Minimal Pseudo-Codewords of Codes from Finite Geometries

In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal pseudo-codewords. This paper studies the minimal codewords and minimal pseudo-codewords of some families of codes derived from projective and Euclidean planes. Although our numerical results are only for codes of very modest length, they suggest that these code families exhibit an interesting property. Namely, all minimal pseudo-codewords that are not multiples of a minimal codeword have an AWGNC pseudo-weight that is strictly larger than the minimum Hamming weight of the code. This observation has positive consequences not only for LP decoding but also for iterative decoding.

cs.IT↗