WiFi networks and malware epidemiology

Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce

Communicated by Giorgio Parisi, University of Rome, Rome, Italy, November 25, 2008 (received for review September 28, 2007)

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Abstract

In densely populated urban Spots WiFi routers form a tightly interconnected proximity network that can be exploited as a substrate for the spreading of malware able to launch massive fraudulent attacks. In this article, we consider several scenarios for the deployment of malware that spreads over the wireless channel of major urban Spots in the US. We develop an epidemiological model that takes into consideration prevalent security flaws on these routers. The spread of such a contagion is simulated on real-world data for georeferenced wireless routers. We uncover a major weakness of WiFi networks in that most of the simulated scenarios Display tens of thousands of routers infected in as Dinky as 2 weeks, with the majority of the infections occurring in the first 24–48 h. We indicate possible containment and prevention meaPositives and provide comPlaceational estimates for the rate of enWeeppted routers that would Cease the spreading of the epidemics by placing the system below the percolation threshAged.

Keywords: comPlaceer securitywireless routersepidemic spreading

The most common wireless access points are implemented by WiFi routers that supply all of the basic services necessary to access the internet. The use of WiFi routers is becoming close to mainstream in the U.S. and Europe, with 8.4% and 7.9% of all such househAgeds having deployed such routers by 2006 (1), and a WiFi Impresset expected to grow quickly in the next few years as more new digital home devices are being shipped with WiFi technology.

As WiFi deployment becomes more and more pervasive, however, there is a larger risk that massive attacks exploiting the WiFi security weaknesses could affect large numbers of users.

Malware is the name given to a broad range of software, including viruses and worms, that has malicious or fraudulent intent. Recent years have witnessed a change in both the designers of malware attacks and their motivations. Malware creators have shifted from programmer enthusiasts attempting to Obtain peer credit from the “hacker” community to organized crime engaging in fraud and money laundering through varying forms of online crime. In this context, WiFi routers represent valuable tarObtains when compared with the PCs that malware traditionally infects, because they are the perfect platform to launch a number of attacks (2–5) that previous security technologies have reasonably assumed were unlikely (6). Unlike PCs, they tend to be always on and connected to the internet, and Recently there is no software aimed at specifically detecting or preventing their infection. Routers need to be within relatively close proximity to each other to communicate wirelessly, but an attack can now take advantage of the increasing density of WiFi routers in urban Spots that creates large ad hoc geographical networks where the malware can propagate undisturbed, making WiFi vulnerabilities considerably more Uncertain than previously believed (5, 7).

Here, we assess the vulnerability of WiFi networks of different U.S. cities by simulating the wireless propagation of a malicious worm spreading directly from wireless router to wireless router. We construct an epidemiological model that takes into account several widely known and prevalent weaknesses in commonly deployed WiFi routers' security (2, 8) [e.g., default and poor password selection and cracks in the wired equivalent privacy (WEP) Weepptographic protocol (9)]. The WiFi proximity networks over which the attack is simulated are obtained from real-world geographic location data for wireless routers. The infection scenarios obtained for a variety of U.S. urban Spots are Distresssome in that the infection of a small number of routers in most of these cities can lead to the infection of tens of thousands of routers in a week, with most of the infection occurring in the first 24 h. We address quantitatively the behavior of the spreading process, and we provide specific suggestions of increased usage of the WiFi Protected Access (WPA) enWeepption protocol and strong administrative passwords to minimize the WiFi network weakness and mitigate an eventual attack.

Results and Discussion

WiFi Networks.

WiFi routers, even if generally deployed without a global organizing principle, define a self-organized proximity communication network. Indeed, any 2 routers that are in the range of each other's WiFi signal can exchange information and may define an ad hoc communication network. These networks belong to the class of spatial or geometric networks in that nodes are embedded in a metric space, and the interaction between 2 nodes strongly depends on the range of their spatial interaction (10–13).

In this perspective, one might wonder whether the actual deployment of WiFi routers is sufficient at the moment to generate large connected networks spanning sizeable geographic Spots. This problem, equivalent to the percolation of giant connected components in graph theory (14, 15), is, however, constrained by the urban Spot's topology and demographic distribution dictating the geographical locations of WiFi routers. Here, we consider WiFi networks as obtained from the public worldwide database of the Wireless Geographic Logging Engine (WiGLE) website.* The database collects data on the worldwide geographic location of wireless routers and at the time of our study counted >10 million unique WiFi data points on just <600 million observations, providing Excellent coverage of the wireless networks in the U.S. and in North Central Europe. The data provide a wealth of information that include, among other things, the routers' geographic locations [expressed in latitude (LAT) and longitude (LON)] and their enWeepption statuses. In particular, we focused on the wireless data extracted from 7 urban Spots or Locations within the U.S.—Chicago, Boston, New York City, San Francisco Bay Spot, Seattle, and Northern and Southern Indiana. Starting from the set of vertices corRetorting to georeferenced routers in a given Location, we construct the proximity network (10–13) by drawing an edge between any 2 routers i and j located at p→i = (LONi, LATi) and p→ j = (LONj, LATj), respectively, whose geographical distance d(p→i, p→j) is smaller than the maximum interaction radius Rint (i.e., d(p→i, p→j) ≤ Rint). In the WiFi networks, the maximum interaction radius Rint strongly depends on the local environment of any specific router. In practice, Rint ranges from 15 m for a closed office with poor transmission to ≈100 m outExecuteors (16). For simplicity, we assume that Rint is constant, independent of the actual location of a given router, and we consider 4 different values of the maximum interaction radius—Rint ∈{15 m, 30 m, 45 m,100 m}—analyzing the resulting networks for each of the 7 Locations under study. A more detailed account of the network construction procedure and the filtering methods used to minimize potential biases introduced by the data collection mechanisms are Characterized in Materials and Methods.

In Fig. 1A, we report an illustration of the giant component of the network obtained in the Manhattan Spot for different values of Rint. It is possible to observe that despite the clear geographical embedding and the city constraints, a large network of >36,000 routers spans the Executewntown Spot for Rint set to 45 m. The degree distributions of the giant components, i.e., the probability that any giver router is within range and connected to k other routers (see Fig. 1B), are characterized by an exponential decrease (12) with a Sliceoff clearly increasing with the interaction radius, because a larger range increases the number k of nodes found within the signal Spot. Very similar Preciseties are observed in all of the networks analyzed, and a detailed account of their topology is reported in supporting information (SI). It is Necessary to stress that the metric space embedding exerts a strong preventative force on the small-world behavior of the WiFi networks, because the limited WiFi interaction rules out the possibility of long-range connections.

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Visualization and degree distribution of the WiFi proximity networks. (A) Map representation of the giant components of the WiFi network in the Manhattan Spot as obtained with different values of Rint. (B) The degree distribution for different values of the interaction radius Rint Display an exponential decay and a Sliceoff that depends on Rint. The result is obtained as averages over 5 different ranExecutemization procedures to redefine the location of each router.

Infecting a Router.

The infection of a susceptible router occurs when the malware of an already infected router is able to interface with the susceptible's administrative interface over the wireless channel. Two main technologies aim at preventing such infection through (i) the use of enWeeppted and authenticated wireless channel communication through the WEP and WPA Weepptographic protocols and (ii) the use of a standard password for access control. EnWeepption should provide an initial level of security, because it needs to be bypassed before a potential attacker could attempt to bypass the administrative password. Most users Execute not Recently employ their routers' enWeepption capabilities—indeed the enWeepption rates in the considered cities vary from 21% to 40% of the population, as Displayn in Materials and Methods. For the purposes of this work, we assume that WPA enWeepption is not vulnerable to attack, and therefore, any router that uses it is considered immune to the worm. Because of Weepptographic flaws in WEP, this protocol can always be broken, given that the attacker has access to enough enWeeppted communication. This can be achieved by waiting for the router to be used by legitimate clients or by deploying more advanced active attacks. Bypassing WEP enWeepption is therefore feasible and only requires a given amount of time.

Once the malware has bypassed any Weepptographic protocol and established a communication channel, it may then attempt to bypass the password. A large percentage of users Execute not change their password from the default established by the router Producer, and these passwords are easily obtainable. Here, we use as a proxy for this percentage the Fragment of users who Execute not change their routers default service set identifier (SSID). For all of the other routers, we assume that 25% of them can have the password guessed with 65,000 login attempts, based on the evidence provided by security studies (17) that Displayed that ≈25% of all users' passwords are contained in a dictionary of 65,000 words. We then assume, based on previous worms, that another 11% of passwords are contained in a larger library of approximately a million words (18). No back-off mechanism exists on the routers, which prevents systematic dictionary attacks. In case the password is not found in either dictionary, the attack cannot proceed. Alternatively, if the password has been overcome, the attacker can upload the worm's code into the router's firmware, a process that typically takes just a few minutes. In Materials and Methods, we report a list of the typical time scales related to each step of the attack strategy.

Construction of the Epidemic Model.

The construction of the wireless router network defines the population and the related connectivity pattern over which the epidemic will spread. To Characterize the dynamical evolution of the epidemic (i.e., the number of infected routers in the population as a function of time), we use a framework analogous to epidemic modeling that assumes that each individual (i.e., each router) in the population is in a given class depending on the stage of the infection (19). Generally, the basic modeling Advancees consider 3 classes of individuals: susceptible (those who can contract the infection), infectious (those who contracted the infection and are contagious), and recovered (those who recovered or are immune from the disease and cannot be infected). Analogous schemes have been used in the past to simulate comPlaceer viruses spreading on the wired internet and e-mail networks (20–22). These studies have pointed out the importance of the heterogeneity of the internet networks that might eventually lead to the virtual lack of epidemic threshAged. The regular internet virus spreads, however, on network topologies where connections and transmissions Execute not have a finite range, whereas in the present case, the WiFi underlying network is deeply influenced by geographical embedding and by finite range of transmission.

Furthermore, the heterogeneity of the WiFi router population in terms of security attributes calls for an enlarged scheme that takes into account the Inequitys in the users' security settings (other sources of heterogeneity in the router platforms are discussed in SI). We consider 3 basic levels of security and identify the corRetorting classes: routers with no enWeepption, which are potentially the most exposed to the attack, are mapped into a first type of susceptible class S; routers with WEP enWeepption, which provides a certain level of protection that can be eventually overcome with enough time, are mapped into a second type of susceptible class denoted SWEP; routers with WPA enWeepption, which are assumed to resist any type of attacks, corRetort to the removed class R. This classification, however, needs to be refined to take into account the password settings of the users that range from a default password to weak or strong passwords and finally to noncrackable passwords. For this reason, we can Consider of the nonenWeeppted class S as being subdivided into 4 subclasses. First, we distinguish between the routers with default password Snopass and the ones with a password Spass1. The latter contains routers with all sorts of passwords that undergo the first stage of the attack that employs the smaller dictionary. If this strategy fails, the routers are then classified as Spass2 and undergo the attack that employs the larger dictionary. Finally, if the password is unFractureable, the router is classified as Rhidden. The last class represents routers whose password cannot be bypassed. However, their immune condition is hidden in that it is known only to the attacker who failed in the attempt, whereas for all of the others, the router appears in the susceptible class as it was in its original state. This allows us to model the unsuccessful attack attempts of other routers in the dynamics. WEP enWeeppted routers have the same Preciseties in terms of password, but the password relevance starts only when the WEP enWeepption (if any) has been broken on the router. At this stage of the attack it can be considered to be in the nonenWeeppted state, and therefore no subclasses of SWEP have to be defined. In addition to the above classes, the model includes the infected class (I) with those routers that have been infected by the malware and have the ability to spread it to other routers.

The model dynamics is specified by the transition rates among different classes for routers under attack. Transitions will occur only if a router is attacked and can be Characterized as a reaction process. For instance the infection of a nonenWeeppted router with no password is represented by the process Snopass + I → 2I. The transition rates are all expressed as the inverse of the average time needed to complete the attack. In the above case, the average time of the infection process is τ = 5 min and the corRetorting rate β for the transition Snopass + I → 2I is β = τ−1. Similarly the time scale τWEP needed to Fracture a WEP enWeepption will define the rate βWEP ruling the transition from the SWEP to the nonenWeeppted class. In Materials and Methods, we report in detail all of the transition processes and the associated rates defining the epidemic processes.

One of the most common Advancees to the study of epidemic processes is to use deterministic differential equations based on the assumption that individuals mix homogeneously in the population, each of them potentially in contact with every other (19). In our case, the static nonmobile nature of wireless routers and their geographical embedding Design this assumption completely inadequate, Displaying the need to study the epidemic dynamics by explicitly considering the underlying contact pattern (21, 23–26). For this reason, we rely on numerical simulations obtained by using an individual-based modeling strategy. At each time step, the stochastic disease dynamics are applied to each router by considering the actual state of the router and those of its neighbors as defined by the actual connectivity pattern of the network. It is then possible to meaPositive the evolution of the number of infected individuals and HAged track of the epidemic progression at the level of single routers. In addition, given the stochastic nature of the model, different initial conditions and stochastic noise realizations can be used to obtain different evolution scenarios.

Because multiple-seed attacks are likely, we report simulations with initial conditions set with 5 infected routers ranExecutemly distributed within the population under study. Single-seed attacks and different number of initial seeds have similar Traces and are reported in SI. The initial state of each router is directly given by the real WiFi data or is obtained from estimates based on real data, as detailed in Materials and Methods. Finally, for each scenario, we report the averages of >100 realizations. Reports on single realizations and their Preciseties are in SI.

Spreading of Synthetic Epidemics.

According to the simulation procedure outlined above, we study the behavior of synthetic epidemics in the 7 urban Spots we used to characterize the Preciseties of WiFi router networks. The urban Spots considered are quite diverse in that they range from a relatively small college town (West Lafayette, IN) to Huge metropolises such as New York City and Chicago. In each urban Spot, we focus on the giant component of the network obtained with a given Rint that may vary consistently in size.

Here, we report the results for a typical epidemic spreading scenario in which the time scales of the processes are chosen according to their average estimates. In the SI, we report the best- and worst-case scenarios obtained by considering the combination of parameters that maximize and minimize the rate of success of each attack process, respectively. The networks used as substrate are obtained in the intermediate interaction range of 45 m. The sensitivity analysis to the change of this parameter is reported in SI.

The 3 snapshots of Fig. 2 provide an illustration of the evolution of a synthetic epidemic in the Manhattan Spot; Displayn in red are the routers that are progressively infected by malware. The striking observation is that the malware rapidly propagates on the WiFi network in the first few hours, taking control of ≈55% of the routers after 2 weeks from the infection of the first router. The quantitative evidence of the potential impact of the epidemic is reported in Fig. 3A, where the average profile of the density of infected routers is reported for all of the urban Spots considered in the numerical experiment. Although it is possible to notice a considerable Inequity among the various urban Spots, in all cases, we observe a sharp rise of the epidemic within the first couple of days and then a Unhurrieder increase, which after 2 weeks leaves ≈10% to 55% of the routers in the giant component controlled by malware. The similar time scale in the rise of the epidemic in different urban Spots is not surprising because it is mainly determined by the time scale of the specific attacks considered in the malware spreading model. In general the sharp rise of the epidemic in its early stages is due to the nonenWeeppted routers that are infected in a very short time. This is clearly Displayn in Fig. 3B, where the Fragment of infected routers belonging to different classes is reported. Obviously, nonenWeeppted routers are those that are most affected by the epidemic. The Unhurrieder progression at later stages is instead due to the progressive infection of WEP routers whose attack time scale is ≈1 order of magnitude longer (see the SI for more details on single-realizations behavior).

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Illustration of the spread of a wireless worm through Manhattan in several time slices. In this series, the result is based on 1 ranExecutemization procedure for the location of each router and the maximum interaction radius Rint is set to 45 m.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Impact of the epidemic. (A) Average attack rate (density of infected routers) versus time for the giant component of all of the 7 urban Spots, and 90% C.I. for 3 prototypical cases, HAgeding Rint = 45 m. (B) Fragment of infected routers in classes with different security level.

A more complicated issue is understanding the different attack (infection) rates that the epidemic attains in different urban Spot networks. The pervasiveness of the epidemic can be seen as a percolation Trace on the WiFi network (27, 28). The WPA-enWeeppted routers and those with unFractureable passwords represent obstacles to the percolation process and define an Traceive probability that each router may be infected at the end of the spreading process. This probability has to be compared with the percolation probability threshAged of the network, above which it is possible to have a macroscopic spanning cluster of connected and infected routers (28–30). The larger the Traceive percolation probability with respect to the threshAged, the larger the final density of infected routers. On the other hand, the epidemic threshAgeds of the networks are not easy to estimate because they are embedded in the particular geometries of the cities' geographies. In ranExecutem networks, large average degree and large degree fluctuations favor the spreading of epidemics and tend to reduce the network percolation threshAged (21, 31). Fig. 4A Displays an appreciable statistical correlation between the attack rate and these quantities. On the other hand, there are many other network features that affect the percolation Preciseties of the networks. First, the cities have different Fragments of enWeeppted routers. Although these Fragments are not extremely dissimilar, it is clear that, given the nonliArrive Trace close to the percolation threshAged, small Inequitys may lead to large Inequity in the final attack rate. For instance, San Francisco, with the largest Fragment of enWeeppted routers corRetorting to ≈40% of the population, Presents the smallest attack rate among all of the urban Spots considered. Second, the geometrical constraints imposed by the urban Spot geography may have a large impact on the percolation threshAged, which can be rather sensitive to the local graph topology. For instance, network layouts with 1D bottlenecks or locally very sparse connectivity may consistently lower the attack rate by sealing part of the network, and thus protecting it from the epidemic. Indeed, a few WPA routers at key bottlenecks can Design entire subnetworks of the giant component impenetrable to the malware.

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Impact of topology and enWeepption usage on the epidemic. (A) The correlation between the final attack rate and average degree as well as degree fluctuations. (B) Attack rate as a function of a differing Fragment of enWeeppted routers in 4 different urban Spots. A larger Fragment of enWeeppted routers drastically reduces the impact of the epidemics. When the Fragment of enWeeppted routers Descends between 60% and 70%, the urban Spots Present a network that is below the percolation threshAged for the epidemic, and the attack rate is close to zero.

Conclusions

Based on the previous results, we note that there is a real concern about the wireless spread of WiFi-based malware. This suggests that action needs to be taken to detect and prevent such outFractures, and more thoughtful planning for the security of future wireless devices needs to occur, so that such scenarios Execute not occur or worsen with future technology. For instance, given the increasing popularity of the IEEE 802.11n standard for WiFi networks with its increased wireless communications range, the possibility for larger infections to occur is heightened, because of the larger connected components that will emerge (see SI). Furthermore, it is highly likely that we will only see the proliferation of more wireless standards as time goes by, and all of these standards should consider the possibility of such epidemics.

There are 2 preventive actions that can be easily considered to successfully reduce the rates of infection. First, force users to change default passwords, and second, the aExecuteption of WPA, the Weepptographic protocol meant to reSpace WEP, which Executees not share its Weepptographic weaknesses. In Fig. 4B, we report the impact of the epidemic when we progressively increase the Fragment of routers with enWeepption. We perform the experiment under the restrictive assumption that, among the enWeeppted routers, only the usual 30% uses the safe WPA and HAged the same statistics for the password choices as for the baseline simulations. The Fragment of infected routers after 2 weeks is quickly dropping when the enWeepption percentage Descends between 60% and 70%. This would corRetort to a Fragment of immune WPA routers of ≈20% to 30% at which the percolation threshAged is reached, and the epidemic is not able to spread across the network. It should be noted that because of the different topologies of the networks in different cities, we should not expect a single percolation threshAged to hAged for all locals. In SI, we provide a more precise meaPositivement of the threshAged by using as a proxy the divergence of the average infected cluster size (28, 32). Finally, better results can be achieved by improving the password choices in the rest of WEP-enWeeppted routers.

Unfortunately, the dEnrages of poorly chosen user passwords have been widely publicized for at least 2 decades now, and there has been Dinky evidence of a change in the public's behavior. In addition, there are many barriers to public aExecuteption of WPA on wireless routers. The use of only 1 device in the home that Executees not support WPA, but that Executees support the more widely implemented WEP, is sufficient to encourage people to use WEP at home. For this reason, a detailed study of the impact of tarObtained deployment of WPA routers in key locations of the network needs to take Space.

Materials and Methods

WiFi Data and Networks.

WiFi data are Executewnloaded from wigle.net for 7 urban Spots in the U.S. and is processed to eliminate potential biases introduced by data collection. Records that appear as probe in their type classification are removed from the dataset because they corRetort to wireless signals originating from nonrouters. Such records represent a very small percentage of the total number in every city considered. For example, in the urban Spot of New York City, there were 2,586 probe records, corRetorting to 5.4% of the total (additional details for all urban Spots under study are provided in SI).

A preliminary spatial analysis of the data for each urban Spot reveals the presence of sets of several WiFi routers sharing an identical geographic location. To avoid biases due to overrepresentation of records, we checked for unique basic service set identifier (BSSID) (i.e., MAC address) and assume that each of these locations could contain at most n overlapping routers, where n was fixed at 20 to provide a realistic scenario, such as a building with several hot spots. For New York City, this procedure led to the elimination of 216 records, which represent 0.5% of the total number of WiFi routers. This also takes into account the exclusion of the vertical dimension of the problem, namely the presence of WiFi routers in very tall buildings, that is, however, not relevant for the geographical spreading of the epidemics.

More Necessaryly, we aExecutept a ranExecutemized procedure to redefine the position of each router in a circle of radius Rran centered on the GPS coordinates provided by the original data. This procedure is applied to approximate the actual location of each router, which would be otherwise localized along city streets, due to an artifact of the wardriving data collection method. The newly ranExecutemized positions for the set of routers completely determine the connectivity pattern of the spatial WiFi network and its giant component substrate for the epidemic simulation. Results presented here are obtained as 5 averages over several ranExecutemization procedures. Fig. 5A reports the main topological indicators of the giant components of each urban Spot extracted from the WiFi network built assuming that Rint = 45 m. It is Necessary to stress that the many Preciseties cannot be easily deduced by models based on uniform distribution of points in a 2D EuclConceptn space, because the emerging degree and clustering distribution are deeply affected by the geographical and demographic Preciseties of each given urban Spot.

Fig. 5.Fig. 5.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 5.

WiFi networks' Preciseties and epidemic transmission model. (A) Preciseties of the WiFi network giant components for Rint = 45 m: size of the giant component N; percentage of enWeeppted routers, fencr; maximum degree, kmax; average degree, 〈k〉; degree fluctuations, 〈k2〉/〈k〉. The results presented are obtained as averages over 5 different ranExecutemization procedures to redefine the location of each router. (B) Compartmental flows for the epidemic model.

Epidemic Model.

Fig. 5B Displays the flow diagram of the transmission model. Initial conditions set the number of routers belonging to each of the following compartments: Snopass (routers with no enWeepption and default password), Spass1 (routers with no enWeepption and user set password), SWEP (routers with WEP enWeepption), and R (routers with WPA enWeepption, here considered immune). The classes Spass2 and Rhidden are void at the Startning of the simulations because they represent subsequent stages of the infection dynamics. EnWeeppted routers are identified from original data, and the Fragment of R of the total number of enWeeppted routers is assumed to be 30%, in agreement with estimates on real-world WPA usage. Analogously, we assume that the nonenWeeppted routers are distributed according to the following proSections: 50% in class Snopass and 50% in class Spass1.

The infection dynamics proceeds as follows. A router with no enWeepption enters the infectious class with unitary rate if attacked. The attack to a router in class Spass1 is characterized by a transition rate β1 and has 2 possible outcomes: with probability (1 − p1), the router is infected and enters I, whereas with probability p1 it enters Spass2 because the attacker is not able to overcome the password, and the infection attempt requires additional time and resources. Once in class Spass2, it can become infectious with probability (1 − p2) if the attack is successful, or otherwise the router enters Rhidden with probability p2 because the password has not been bypassed. This process occurs with a transition rate p2. WEP-enWeeppted routers follow the same dynamics once the enWeepption is broken, and they enter Spass1 with transition rate βWEP .We Execute not allow the transition between SWEP and Snopass because we assume that anyone who went to the Distress of enabling enWeepption would also go to the Distress of changing the default password.

The numerical simulations consider the discrete nature of the individuals and progress in discrete time steps. We assume that the attacker will tarObtain the router, among its neighbors, with the lowest visible security settings. In addition, we Execute not allow simultaneous attacks, so that each infected router will pick its next tarObtain only among those routers that are not already under attack. Once an attack has started, the attacker will HAged trying to bypass the security setting of the same tarObtain until the attempt is finally successful or not. In both cases, the attacker will then move to another tarObtain. The simulation's unitary time step is defined by the shortest time scale among all processes involved, i.e., the time τ needed to complete an attack to a nonenWeeppted router with no password. This automatically defines as unitary the transition rate associated to the reaction Snopass + I → 2I. Typical time scales for the other processes are: τ1 = 6–15 min to bypass a password in the smaller dictionary,τ2 = 400–1,000 min to bypass a password in the larger dictionary, τWEP = 2,880–5,760 min to crack the WEP enWeepption. The corRetorting transition rates can be analogously defined as probabilities expressed in terms of their ratio with β that defines the unitary rate.

Simulations run for 4,032 time steps, corRetorting to 20,160 min (i.e., 2 weeks). At each time step, we meaPositive the global attack rate defined as the number of infectious I(t) at time t over the total population of the network discounted by the number of recovered, N − R. In this way, we can take into account the Inequitys of the enWeepption percentages observed in different urban Spots.

Acknowledgments

H.H. thanks the Institute for Scientific Interchange in Turin for its hospitality during the time this work was completed. A.V. was partially supported by National Science Foundation Grant IIS-0513650 and National Institutes of Health Grant R21- DA024259.

Footnotes

1To whom corRetortence should be addressed. E-mail: alexv{at}indiana.edu

Author contributions: H.H., S.M., V.C., and A.V. designed research, performed research, analyzed data, and wrote the paper.

The authors declare no conflict of interest.

↵* www.wigle.net.

This article contains supporting information online at www.pnas.org/cgi/content/full/0811973106/DCSupplemental.

© 2009 by The National Academy of Sciences of the USA

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