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Figure 1013 Illustration of Dudbridge algorithm for decoding at resolution m = 3, a 8 8 image The four values gk1 k2 (k1 = 1 4) at resolution 2 depend on the value gk2 at resolution 1 and on their respective position in the image

with a nally contracting transformation G in the luminance space The expression of G (equation (1032)) is comparable with that of the mass transformation suggested by Jacquin, since it also relies on a scale factor sk1 and on a shift factor tk1 It also contains two additional coef cients ak1 and bk1 which act on the coordinates of the approximated elements inside the block: a rst order approximation, in that case Equation (1032) shares similarities with equation (1026): the coef cients ak1 and bk1 de ne weights associated with two inclined planes, in the luminance space The reason why this method is not as ef cient as the basic diagram of Jacquin is because a block is approximated from itself and not from another block of the image Then, the transformation G must be suf ciently complex to achieve a good block approximation That is why Dudbridge added two more parameters to the mass transformation expression However, saving these extra parameters results in a lower compression ratio Nonetheless, the method has the advantage of being very fast Moreover, the coding-decoding algorithm is evenly balanced regarding calculation time Initially, Dudbridge presented this coding technique in his thesis in 1992 [DUD 92] Since then, the approach has been generalized on square blocks issued from a quadtree partitioning [DUD 95a] The additional weights of the terms x2 , y 2 , x3 and y 3 in the expression of G, were studied by Monro et al [MON 93a, MON 93b, MON 94, WOO 94] The authors also extended this approach to the compression of video sequences [WIL 94] 10352 Decoding simpli cation by collage space orthogonalization We now consider that vector , an approximation of the destination vector r, reads: r = 2 b2 + 1 b1 r (1037)

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The vector belongs to the vector subspace spanned by b1 and b2 , where b1 is a r constant basis vector (b1 = [1, 1, , 1]T ) and b2 a vector extracted from the image to be coded Each vector , r, b1 and b2 is of dimension B 2 r

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We next describe the rushing attack [74] This attack impacts a reactive routing protocol Note that, in the case of a reactive routing protocol, a node that needs a path to a destination oods the network with route request packets Such route request packets are ooded in a controlled fashion in the network Thus, every node only forwards the rst route recovery packet that it receives and drops the rest The adversary can exploit this feature of reactive routing protocols It does so by rushing the route request packets towards the destination As a result, the nodes that receive this rushed request

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