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ensure that two nodes share a key with a higher probability, thereby leading to greater chances of ensuring connectivity On the other hand, this could also increase the susceptibility of the network since, by compromising fewer nodes, the adversary would be able to eavesdrop successfully on a larger number of communications amongst the noncompromised nodes in the network For example, consider one extreme when the size of the key pool is 1 In this case, this scheme reduces to the simple deterministic case of a single key being used in the entire network While this scheme ensures high connectivity, it suffers from no resilience against node compromise since capture of a single node compromises the communication in the entire network Having a very large key pool causes the opposite behavior in terms of connectivity and resilience In such a case connectivity will be very low but resilience will be very high Several proposals have been developed based on this idea of random key predistribution The various proposals in this family of probabilistic key sharing approach differ in terms of the structure of the key pool, the number of common keys required, their applicability to a dynamic deployment scenario and the method of determining the common keys These schemes offer network resilience against capture of nodes since a node has very few keys deployed on it Thus, there is no need to consider tamper resistant nodes (though note that nontamper-resistant nodes might not be acceptable in some situations such as military deployments) This is an advantage given the problems such as cost and complexity associated with tamper-resistant nodes In addition this approach is more scalable for large-scale, dense deployments of sensor networks The drawbacks of these schemes are that the key setup is based on probabilistic arguments Additionally, setting up of a secure channel between nodes which do not share common keys might require communication over multiple hops This increases the workload and the latency associated with setting up secure links We next look at several solutions based on this idea of probabilistic key sharing In [39] the authors focus on very large, dense sensor networks The authors propose three random key predistribution schemes for such networks They are:.

equipped with the Hermitian product: Z1 , Z2 HX ,

hZ1 , hZ2 = E(Z1 Z2 )

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Page 44 project teams are formed in most organizations that possess functional structures, they are staffed on an ad hoc basis from members of the various departments These personnel are assigned to project teams through one of several ways: their services are expressly requested by a project manager who values their competence, they are exiled to the project team by a functional boss who is dissatisfied with their work, or they are assigned simply because they are available The key, however, is that these assignments, like the projects themselves, are temporary Personnel who staff the vast majority of project teams serve on those teams while maintaining links back to their functional departments In fact, it is quite common for these individuals to split their time between their project and functional duties Not surprisingly, this arrangement can lead to a great deal of internal conflict when each member of the project team seeks to create a workable balance between the competing demands of functional and project team superiors The temporary nature of projects, coupled with the very real limitations on their power and discretion that most project managers face, constitutes the core challenge of managing projects effectively Table 21 gives a comparative breakdown of some of the important distinctions between project-based work and more common department activities It is clear that the very issues that characterize projects as distinct from department work also illustrate the added complexity and difficulties they create for project managers For example, within a department, it is common to find people with a more homogenous background; that is, the finance department is staffed with finance people, the marketing department is made up of marketers, and so on On the other hand, most projects are constructed from special, cross-functional teams These teams are composed of representatives from each of the relevant departments and they each bring their own attitudes, time frames, learning, past experiences, and biases to the team.

(62)

is the reproducing kernel Hilbert space associated with the eld X It is veri ed, according to (62), that the application: h : HX HX Z hZ (63)

the q-composite random key predistribution scheme two nodes need to share more than one common key in order to set up a secure link; the multipath key reinforcement scheme An attacker has to compromise many more nodes to achieve a high probability of compromising any communication the random-pairwise key scheme enables node-to-node mutual authentication whereby any node can determine the identity of the other node it is communicating with

is an isometry between Gaussian space and the reproducing kernel Hilbert space, while the Hermitian product on HX is ad hoc In particular, this application is bijective, meaning that for all the functions h HX there is only one corresponding random variable Z of HX Moreover, HX contains the functions of y: hXx (y) = R(x, y) resulting from the covariance of X:

R(x, y) = E(Xx Xy )

and we can describe the reproducing kernel Hilbert space as the closure of the nite linear combinations of functions R(x, ) for HX Lastly, the name reproducing kernel Hilbert space comes from the property veri ed by its scalar product: R(x, ), R(y, )

= R(x, y)

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