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1 and L (the depth to hash each root key) The k keys preloaded on the node are such that the jth key is given by h aj (MAj) where h() denotes a one-way hash function Thus, the jth key corresponds to the Ajth root key hashed to a depth of a j This is done for each node by the TA Following this the nodes are deployed We would like to remark here that determining the keys deployed on a node as a function of the node identity will also make life easier for the adversary Using this information, the adversary can determine which nodes to compromise so as to increase his (the adversary s) knowledge of the keys from the key pool After deployment, every pair of neighboring nodes needs to gure out whether they have any common keys If the two nodes have common keys then they need to set up the session or link keys Both these steps are executed by the nodes based on information about their identities and then using the same public function F() from earlier The identity is hence the only information exchanged by the nodes We explain this again using an example Consider a node B which has to decide if it has any common keys with node A given earlier Let the identity of node B be IDB Both the nodes, A and B, exchange their identities Following this each node can calculate the sequence of k-length ordered pairs corresponding to the other Let this sequence for node B be given by F(IDB) which equals [(B1,b1), (B2,b2) , , (Bk,bk)] As in case of node A, (B1, , Bk) is a partial random permutation of integers between 1 and P (the number of root keys), while (b1, , bk) is a sequence of randomly distributed numbers between 1 and L (the depth to hash each root key) By comparing (A1 Ak) and (B1 , , Bk), the two nodes can determine the indices of the shared root keys that are present on both Let these indices of shared root keys be given as [s1, , sm] where m k Note that it is possible that m 0, which implies that the nodes do not have any common keys But otherwise if m 0, then the two nodes will have to decide the link key or the session key used to encrypt communication between themselves To do that the nodes determine di max(ai,bi) where the ai and bi values correspond to the depth of the hash for node A and node B, respectively, for the ith root key of the m shared root keys The session key between node A and node B is then obtained as K h hd1 (Ms1 )jhd2 (Ms2 )j jhdm (Msm ) We illustrate the above using a gure Consider Figure 39, where we assume that the TA has 10 root keys Further we assume that L 5 and there are three keys predeployed on every node In this gure, nodes A and C share root key indexes 5 and 10 For the key indexed 5, node A has to hash forward two times to reach the same depth as node C For the key indexed 10, node C has to hash forward one time Note that the scheme considered earlier in [17] is a special case of HARPs obtained when L 0 The authors in [18, 41] propose another probabilistic key distribution strategy The schemes here are based on the polynomial-based key predistribution protocol in [42] While the protocol in [42] was intended for group keys, the strategy has been enhanced in [18, 41] to make it feasible for a two-party case in sensor networks Consider the basic protocol in [42] applied to a two-party case In this case there exists a TA which generates a t-degree polynomial in two variables x and y denoted f(x,y) Further, this polynomial is symmetrical due to which f(x,y) f( y,x)4 The TA then computes the.

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The arrival of computers in educational and psychological testing has had a deep impact on the appearance of modern test items and the response modes possible in educational and psychological itesting As a result, we now have an enormous reservoir of types of item and response mode that can be used to increase the validity of our measurements At the same time, the use of computers in testing has enabled us to use their gigantic power to work operationally with the models and procedures necessary to score examinees taking different items on the same scale, for on-line assembly of tests in a xed or adaptive format, to increase the security of the item pools and to reduce the costs of item writing and pretesting It was the purpose of this chapter to illustrates some of these models and procedures

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We ignore some details for simplicity such as the fact that f(x,y) is over a nite eld corresponding to a large prime number

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