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scheme Instead of randomly selecting keys from a large key pool and assigning them to sensor nodes, this method randomly chooses polynomials from a random polynomial pool and assigns their polynomial shares to sensor nodes However, these two schemes also differ from each other In the basic probabilistic key predistribution scheme, the same key may be shared by multiple sensor nodes In contrast, in the random subset assignment scheme, there is a unique key for each pair of sensor nodes If no more than t shares on the same polynomial are disclosed, none of the pairwise keys constructed using this polynomial between two noncompromised sensor nodes is disclosed Now let us describe this scheme by instantiating the three components in the general framework 1 Subset Assignment The setup server randomly generates a set F of s bivariate t-degree polynomials over the nite eld Fq .



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Note in the gure an increased quantity of positive charge on the right caused by a shortfall of electrons on the right The result is the voltage termed Nernst voltage When the concentrations of ions are xed, it is fairly easy to compute the Nernst voltage across the membrane Transport of charge from a higher concentration of sodium, N1, through a membrane, to a lower concentration of sodium, N2 is modeled as on the left of Figure 2-12, where I represents Ben Franklin current from N1 to N2 and a script E (E) is an electric eld that resists this tendency In the Figure 1 mM/cm3 means that the total number of particles in a cubic centimeter is about 602 1020 Typical concentrations of ions in a neuron are indicated on the right of the gure.

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For each sensor node, the setup server randomly picks a subset of s0 polynomials from F and assigns shares as well as the IDs of these s0 polynomials to the sensor node 2 Polynomial Share Discovery Since the setup server does not predistribute enough information to the sensor nodes for polynomial share discovery, sensor nodes that need to establish a pairwise key have to discover a common polynomial with real-time discovery techniques To nd a common bivariate polynomial, the source node discloses a list of polynomial IDs to the destination node If the destination node nds that they have shares on the same polynomial, it informs the source node the ID of this polynomial; otherwise, it replies with a message that contains a list of its polynomial IDs, which also indicates that the direct key establishment has failed 3 Path Discovery.

The available tools you see in the Workspace window will depend upon, among other things, the implementation of this particular server. Tools and implementation vary so widely that I could not hope to cover them in this brief introductory chapter. As the saying goes, if you have questions, consult your site administrator. To open a SharePoint workspace later, right-click on the SharePoint Workspace 2010 icon in Windows noti cation area, and choose Open Workspace. Click the desired target, and then click OK.

If two sensor nodes fail to establish a direct key, they need to start the path-key establishment phase During this phase, the source node tries to nd another node that can help it set up a pairwise key with the destination node Basically, the source node broadcasts two lists of polynomial IDs One list includes the polynomial IDs at the source node, and the other includes the polynomial IDs at the destination node These two lists are available at both the source and the destination nodes after the polynomial share discovery.

To derive the voltage component across the membrane because of a particular ion, it is possible to model the membrane as a potential barrier assuming a potential DV that repels ions attempting to move from N1 to N2 Thus, only ions with higher speeds in the thermal distribution can enter the membrane and capture an electron The probability of charge transfer due to ions on the left is proportional to N2; the probability of charge transfer due to ions on the right is proportional to N1 Ludwig Boltzmann (1844 1906), famous for analyzing thermal energy, derived.

Discrete problem The discrete problem (2.5) reads: Find a function ut,.pE V F ~such] , ,~ that u( h,p, vh.p) = L ( o / L p ) for v/J.p KL,p. Consider some basis {vI, t i 2 , . . . t i r V } c V,,, , (a concrete basis will be presented in Paragraph 2.4.7). When expressing as usual

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