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basis so that nodes receiving OLSR message can authenticate the node that generated the original message rather than just the node forwarding the message We will discuss both types of schemes in more detail next We rst discuss the scheme given in [62] The focus here is on authentication on a hop by hop basis Figure 418 shows the basic signature extension that is attached to each OLSR packet The scheme and algorithm elds shown in Figure 418 specify the algorithm that is used for creating the signature (Halfslund et al [62] use SHA-1 as an example) The signature is generated by applying the hash function (based on the scheme and algorithm de ned in the message) on the OLSR packet header, the OLSR routing messages contained in the OLSR packet, the elds in the signature extension shown in Figure 418 except for the signature eld, and the shared secret key The timestamp eld is needed in this scheme so that malicious nodes cannot launch replay attacks by just moving to a different neighborhood and replaying messages they recorded earlier In order for this scheme to work, nodes need to know the current time of their neighbors This does not require that nodes synchronize their clocks It only requires that the nodes know the approximate time difference between themselves and their neighbors It is also assumed that clocks move forward at about the same speed In order for neighbors to discover the relative time of their neighbors, Halfslund et al [62] propose the following scheme When node A needs to discover the relative time of its neighbor, it initiates the timestamp exchange process by sending a challenge message as shown in Figure 419 The destination eld contains the IP address of the node (say node B) that node A is trying to get the time value for The random value eld contains a random number to avoid replay attacks and the signature is created by applying the hash function as described earlier The destination node, that is, Node B, then veri es the authenticity of the challenge message and then responds with a challenge-response message with the format shown in Figure 420 The challenge-response message contains the IP address of node A, the random number, and its timestamp The response signature eld is created by applying the hash function to the IP address of node B, the random challenge, and the shared key The signature eld is produced by applying the hash function to the entire message and the shared key When node A receives the challenge-response from node B, it rst veri es its.

(910)

cn 2k+i (911)

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Page 200 respond rapidly to market opportunities rest with the project team rather than being retained at some highly centralized level Finally, as we have noted throughout this book, the shift in focus has begun to profoundly affect the manner in which the project organization, manager, and the team operate The new focus, on the external customer, becomes the driving force for operations, not simply one of several competing demands placed on the project team for them to satisfy as best they can

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for n = j0 + 2, , J 1 Formulae (98), (910) and (911) de ne the approximation of f by a WSA function NOTE 93 Obviously, it is possible to develop a similar algorithm for ordinary self-similar functions However, such an algorithm would restrict the search to a class of functions smaller than that of WSA functions Therefore, this would yield less precise representations in general Moreover, since ordinary self-similar functions are a particular case of WSA functions, the proposed algorithm is thus also able to model signals that are properly represented by ordinary self-similar functions Indeed, n i given by (911) would be equal for all n 98 Segmentation of signals by weak self-similar functions In many scenarios, a single WSA function cannot alone represent a signal A typical example is the concatenation of two IFS Consider a signal X on [0, 1] whose restrictions to [0, 1 ] and [ 1 , 1] consist of the attractors of two different IFS The 2 2 modeling of X by a single WSA function would result in a signi cant global L2 error, whereas two WSA functions would yield a perfect approximation (using a Schauder basis as wavelet decomposition) It is therefore important to design a procedure that segments a given signal into many parts, each one being appropriately represented by a WSA function As with the previous section, it is worth mentioning that constructing an optimal algorithm is a dif cult task In what follows, we present a segmentation method which yields good results in practice Let us consider the root node lives at each level j with l = 0, , 2j the dyadic tree of depth J for which, by convention, at level zero and the leaves at level J 1 The nodes, {0, , J 1}, are numbered from left to right by (l, j) 1 The coef cient cj is associated with each node (l, j) l.

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such that j > j0 The segmentation algorithm is based on the fact that the sub-tree extending from node (l, j) completely determines the restriction of f to I(l, j) = {l2J j , , (l + 1)2J j 1} The aim is to de ne and measure the error associated with each node (l, j) by the L2 distance between the restriction of the original signal f to I(l, j) and the representation of this restriction by a single WSA function In order to account for the fact that large scale errors have more impact than small scale ones, errors are weighted (see below) Starting from the root node, which obviously corresponds to a single WSA function for all the signal, we recursively divide the tree until the error falls, for each sub-tree, below a given threshold de ned a priori Each resulting sub-tree is appropriately represented by a (single) WSA function and the union of the corresponding I(l, j) de nes the segmentation of f More precisely, the set of integers I(l, j, n) = {l2n j , , (l + 1)2n j 1} is associated with each node (l, j) and each n > j Let n (l, j) denote the i ratio of sums similar to those in (911), but where the indices are determined by (k I(l, j, n 1), cn 2k+i < 1) Let us denote: en (l, j) = i 1 2n j

ei (l, j) =

and: e(l, j) = e0 (l, j) + e1 (l, j) (j)

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