arXiv subjects

Osman Yagan

Publications and source records attributed to Osman Yagan.

33 records · Page 2Linked to original sources

arXiv2019

Secure Connectivity of Heterogeneous Wireless Sensor Networks Under a Heterogeneous On-Off Channel Model

In this paper, we investigate the secure connectivity of wireless sensor networks utilizing the heterogeneous random key predistribution scheme, where each sensor node is classified as class-$i$ with probability $μ_i$ for $i=1,\ldots,r$ with $μ_i>0$ and $\sum_{i=1}^r μ_i=1$. A class-$i$ sensor is given $K_i$ cryptographic keys selected uniformly at random from a key pool of size $P$. After deployment, two nodes can communicate securely if they share at least one cryptographic key. We consider the wireless connectivity of the network using a heterogeneous on-off channel model, where the channel between a class-$i$ node and a class-$j$ node is on (respectively, off) with probability $α_{ij}$ (respectively, $1-α_{ij}$) for $i,j=1,\ldots,r$. Collectively, two sensor nodes are adjacent if they i) share a cryptographic key and ii) have a wireless channel in between that is on. We model the overall network using a composite random graph obtained by the intersection of inhomogeneous random key graphs (IRKG) $\mathbb{K}(n;\pmbμ,\pmb{K},P)$ with inhomogeneous Erdős-Rényi graphs (IERG) $\mathbb{G}(n;\pmbμ, \pmbα)$. The former graph is naturally induced by the heterogeneous random key predistribution scheme, while the latter is induced by the heterogeneous on-off channel model. More specifically, two nodes are adjacent in the composite graph if they are i) adjacent in the IRKG i.e., share a cryptographic key and ii) adjacent in the IERG, i.e., have an available wireless channel. We investigate the connectivity of the composite random graph and present conditions (in the form of zero-one laws) on how to scale its parameters so that it i) has no secure node which is isolated and ii) is securely connected, both with high probability when the number of nodes gets large. We also present numerical results to support these zero-one laws in the finite-node regime.

eess.SP↗

arXiv2019

Optimizing Robustness against Cascading Failures under Max-Load Targeted Attack

Motivated by reliability of networks in critical infrastructures, we consider optimal robustness of a class of flow networks against a \textit{targeted} attack, namely max-load targeted attack, that triggers cascading failures due to removal of largest load carrying portion of lines. The setup involves a network of $N$ lines with initial loads $L_1, \ldots, L_N$, drawn from independent and identical uniform distribution, and free-spaces or redundancies $S_1, \ldots, S_N$ to be allocated. In the failure propagation mechanism, a line fails initially due to attack and later due to overloading. The load that was carried at the moment of failing gets redistributed equally among all remaining lines in the system. We analyze robustness of this network against the max-load targeted attack that removes the largest load carrying $p$-fraction of the lines from the system. The system designer allocates $S_i$ as a stochastic function of the load in each line. Assuming an average available resource budget, we show that allocating all lines the free-spaces equally among nodes is optimal under some regulatory assumptions. We provide numerical results verifying that equal free-space allocation to all lines perform optimally in more general targeted attack scenarios.

physics.soc-ph↗

arXiv2018

Robustness of flow networks against cascading failures under partial load redistribution

We study the robustness of flow networks against cascading failures under a partial load redistribution model. In particular, we consider a flow network of $N$ lines with initial loads $L_1, \ldots, L_N$ and free-spaces (i.e., redundant space) $S_1, \ldots, S_N$ that are independent and identically distributed with joint distribution $P_{LS}(x,y)=\mathbb{P}(L \leq x, S \leq y)$. The capacity $C_i$ is the maximum load allowed on line $i$, and is given by $C_i=L_i + S_i$. When a line fails due to overloading, it is removed from the system and $(1-\varepsilon)$-fraction of the load it was carrying (at the moment of failing) gets redistributed equally among all remaining lines in the system; hence we refer to this as the {\it partial} load redistribution model. The rest (i.e., $\varepsilon$-fraction) of the load is assumed to be lost or absorbed, e.g., due to advanced circuitry disconnecting overloaded power lines or an inter-connected network/material absorbing a fraction of the flow from overloaded lines. We analyze the robustness of this flow network against random attacks that remove a $p$-fraction of the lines. Our contributions include (i) deriving the final fraction of alive lines $n_{\infty}(p,\varepsilon)$ for all $p, \varepsilon \in (0,1)$ and confirming the results via extensive simulations; (ii) showing that partial redistribution might lead to (depending on the parameter $0<\varepsilon \leq 1$) the order of transition at the critical attack size $p^{*}$ changing from first to second-order; and (iii) proving analytically that flow networks achieve maximum robustness (quantified by the area $\int_{0}^{1} n_{\infty}(p,\varepsilon) \mathrm{d}p$) when all lines have the same free-space regardless of their initial load. The optimality of equal free-space allocation is also confirmed on real-world data from the UK National Power Grid.

physics.soc-ph↗

arXiv2018

Modeling and Analysis of Cascading Failures in Interdependent Cyber-Physical Systems

Integrated cyber-physical systems (CPSs), such as the smart grid, are increasingly becoming the underpinning technology for major industries. A major concern regarding such systems are the seemingly unexpected large-scale failures, which are often attributed to a small initial shock getting escalated due to intricate dependencies within and across the individual counterparts of the system. In this paper, we develop a novel interdependent system model to capture this phenomenon, also known as cascading failures. Our framework consists of two networks that have inherently different characteristics governing their intra-dependency: i) a cyber-network where a node is functional as long as it belongs to the largest connected (i.e., giant) component; and ii) a physical network where nodes are given an initial flow and a capacity, and failure of a node results with redistribution of its flow to the remaining nodes, upon which further failures might take place due to overloading (i.e., the flow of a node exceeding its capacity). Furthermore, it is assumed that these two networks are inter-dependent. For simplicity, we consider a one-to-one interdependency model where every node in the cyber-network is dependent upon and supports a single node in the physical network, and vice versa. We provide a thorough analysis of the dynamics of cascading failures in this interdependent system initiated with a random attack. The system robustness is quantified as the surviving fraction of nodes at the end of cascading failures, and is derived in terms of all network parameters involved (e.g., degree distribution, load/capacity distribution, failure size, etc.). Analytic results are supported through an extensive numerical study. Among other things, these results demonstrate the ability of our model to capture the unexpected nature of large-scale failures and provide insights on improving system robustness.

physics.soc-ph↗

arXiv2018

Attack vulnerability of power systems under an equal load redistribution model

This paper studies the vulnerability of flow networks against adversarial attacks. In particular, consider a power system (or, any system carrying a physical flow) consisting of $N$ transmission lines with initial loads $L_1, \ldots , L_N$ and capacities $C_1, \ldots, C_N$, respectively; the capacity $C_i$ defines the maximum flow allowed on line $i$. Under an equal load redistribution model, where load of failed lines is redistributed equally among all remaining lines, we study the {\em optimization} problem of finding the best $k$ lines to attack so as to minimize the number of {\em alive} lines at the steady-state (i.e., when cascades stop). This is done to reveal the worst-case attack vulnerability of the system as well as to reveal its most vulnerable lines. We derive optimal attack strategies in several special cases of load-capacity distributions that are practically relevant. We then consider a modified optimization problem where the adversary is also constrained by the {\em total} load (in addition to the number) of the initial attack set, and prove that this problem is NP-Hard. Finally, we develop heuristic algorithms for selecting the attack set for both the original and modified problems. Through extensive simulations, we show that these heuristics outperform benchmark algorithms under a wide range of settings.

physics.soc-ph↗

arXiv2016

Optimizing the robustness of electrical power systems against cascading failures

Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the robustness of power systems against cascading failures initiated by a random attack. This is done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a complete understanding of system robustness by i) deriving an expression for the final system size as a function of the size of initial attacks; ii) deriving the critical attack size after which system breaks down completely; iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is the same for all lines; i.e., when all lines have the same redundant space regardless of their initial load. This is in contrast with the intuitive and commonly used setting where capacity of a line is a fixed factor of its initial load.

physics.soc-ph↗

arXiv2015

Zero-one laws for connectivity in inhomogeneous random key graphs

We introduce a new random key predistribution scheme for securing heterogeneous wireless sensor networks. Each of the n sensors in the network is classified into r classes according to some probability distribution μ = {μ_1 , . . . , μ_r }. Before deployment, a class-i sensor is assigned K_i cryptographic keys that are selected uniformly at random from a common pool of P keys. Once deployed, a pair of sensors can communicate securely if and only if they have a key in common. We model the communication topology of this network by a newly defined inhomogeneous random key graph. We establish scaling conditions on the parameters P and {K_1 , . . . , K_r } so that this graph i) has no isolated nodes; and ii) is connected, both with high probability. The results are given in the form of zero-one laws with the number of sensors n growing unboundedly large; critical scalings are identified and shown to coincide for both graph properties. Our results are shown to complement and improve those given by Godehardt et al. and Zhao et al. for the same model, therein referred to as the general random intersection graph.

math.PR↗

arXiv2012

Conjoining Speeds up Information Diffusion in Overlaying Social-Physical Networks

We study the diffusion of information in an overlaying social-physical network. Specifically, we consider the following set-up: There is a physical information network where information spreads amongst people through conventional communication media (e.g., face-to-face communication, phone calls), and conjoint to this physical network, there are online social networks where information spreads via web sites such as Facebook, Twitter, FriendFeed, YouTube, etc. We quantify the size and the critical threshold of information epidemics in this conjoint social-physical network by assuming that information diffuses according to the SIR epidemic model. One interesting finding is that even if there is no percolation in the individual networks, percolation (i.e., information epidemics) can take place in the conjoint social-physical network. We also show, both analytically and experimentally, that the fraction of individuals who receive an item of information (started from an arbitrary node) is significantly larger in the conjoint social-physical network case, as compared to the case where the networks are disjoint. These findings reveal that conjoining the physical network with online social networks can have a dramatic impact on the speed and scale of information diffusion.

cs.SI↗

arXiv2012

Analysis of complex contagions in random multiplex networks

We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter $c_i$ in $[0,\infty]$ that measures the relative bias type-$i$ links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold τ. Namely, a node connected to $m_i$ active neighbors and $k_i-m_i$ inactive neighbors via type-$i$ links will turn active if $\sum{c_i m_i}/\sum{c_i k_i}$ exceeds its threshold τ. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.

physics.soc-ph↗

arXiv2012

Zero-one laws for connectivity in random key graphs

The random key graph is a random graph naturally associated with the random key predistribution scheme of Eschenauer and Gligor for wireless sensor networks. For this class of random graphs we establish a new version of a conjectured zero-one law for graph connectivity as the number of nodes becomes unboundedly large. The results reported here complement and strengthen recent work on this conjecture by Blackburn and Gerke. In particular, the results are given under conditions which are more realistic for applications to wireless sensor networks.

math.CO↗

arXiv2012

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures and Robustness

We consider a cyber-physical system consisting of two interacting networks, i.e., a cyber-network overlaying a physical-network. It is envisioned that these systems are more vulnerable to attacks since node failures in one network may result in (due to the interdependence) failures in the other network, causing a cascade of failures that would potentially lead to the collapse of the entire infrastructure. The robustness of interdependent systems against this sort of catastrophic failure hinges heavily on the allocation of the (interconnecting) links that connect nodes in one network to nodes in the other network. In this paper, we characterize the optimum inter-link allocation strategy against random attacks in the case where the topology of each individual network is unknown. In particular, we analyze the "regular" allocation strategy that allots exactly the same number of bi-directional inter-network links to all nodes in the system. We show, both analytically and experimentally, that this strategy yields better performance (from a network resilience perspective) compared to all possible strategies, including strategies using random allocation, unidirectional inter-links, etc.

physics.data-an↗

arXiv2011

Performance of the Eschenauer-Gligor key distribution scheme under an ON/OFF channel

We investigate the secure connectivity of wireless sensor networks under the random key distribution scheme of Eschenauer and Gligor. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on/off channels. We present conditions on how to scale the model parameters so that the network i) has no secure node which is isolated and ii) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of full zero-one laws, and constitute the first complete analysis of the EG scheme under non-full visibility. Through simulations these zero-one laws are shown to be valid also under a more realistic communication model, i.e., the disk model. The relations to the Gupta and Kumar's conjecture on the connectivity of geometric random graphs with randomly deleted edges are also discussed.

cs.IT↗

arXiv2011

On the gradual deployment of random pairwise key distribution schemes (Extended Version)

In the context of wireless sensor networks, the pairwise key distribution scheme of Chan et al. has several advantages over other key distribution schemes including the original scheme of Eschenauer and Gligor. However, this offline pairwise key distribution mechanism requires that the network size be set in advance, and involves all sensor nodes simultaneously. Here, we address this issue by describing an implementation of the pairwise scheme that supports the gradual deployment of sensor nodes in several consecutive phases. We discuss the key ring size needed to maintain the secure connectivity throughout all the deployment phases. In particular we show that the number of keys at each sensor node can be taken to be $O(\log n)$ in order to achieve secure connectivity (with high probability).

cs.CR↗

arXiv2011

Modeling the pairwise key distribution scheme in the presence of unreliable links

We investigate the secure connectivity of wireless sensor networks under the pairwise key distribution scheme of Chan et al.. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on/off channels. We present conditions on how to scale the model parameters so that the network i) has no secure node which is isolated and ii) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of zero-one laws, and exhibit significant differences with corresponding results in the full visibility case. Through simulations these zero-one laws are shown to be valid also under a more realistic communication model, i.e., the disk model.

cs.IT↗

arXiv2009

A zero-one law for the existence of triangles in random key graphs

Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the appearance of triangles, and identify the corresponding critical scaling. This is done by applying the method of first and second moments to the number of triangles in the graph.

math.CO↗