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Sybil identities will allocate a channel to each of its neighbors The neighboring node is expected to transmit a message on the allocated channel The veri er node then picks random channels to listen to If no message is heard on the channel selected, then the corresponding node identity is assumed to be a Sybil identity Another approach [76] to detecting Sybil identities leverages the random key predistribution technique (explained in 3) When using random key management schemes, a node is loaded with a set of random keys before deployment This scheme can be leveraged to detect Sybil identities if the set of keys assigned to a node is related to the identity of the node As a result, a node claiming any identity will have to prove the claimed identity by also demonstrating that it has the keys corresponding to that identity The node does so by participating in encryption or decryption operations with the key In this case, an adversary will rst have to compromise many nodes, thereby getting access to the keys corresponding to each identity Following this, the adversary might be able to create fake identities Some other approaches proposed are based on verifying the location for each of the node identities or on registering the identities with a base station Another approach for detecting Sybil attacks is given in [77] In this scheme each node is provided a unique secret by a central authority A hash chain is derived from this secret by the node The node is also provided an identity certi cate by the central authority binding the node s identity to the secret information A node that claims a given identity is then expected to present the identity certi cate and prove that it possesses the unique information certi ed in the identity certi cate The proof might be needed during every interaction between two nodes The hashing property of pre-image resistance can be used to create the proof Thus, the identity certi cate might contain the authenticated value of the root of the hash chain, while every proof instance might require the node to expose the predecessor value in the hash chain.

Calculation of the optimal coef cients 1 and 2 and of the error is costly in terms of calculation time Saupe considers the orthonormal basis of the vector subspace of RB , spanned by 1 the normalized vectors b1 (b1 = B (1, , 1)) and (b2 ) The symbol represents the projection operator making (b2 ) orthonormal to b1 It is shown, in this case [SAU 95], that the error E( , r) is proportional to an increasing monotonic function r of distance D given by: D( , r) = min d (b2 ), (r) , d (b2 ), (r) r Minimizing E( , r) amounts to minimizing D( , r) and thus, to seeking for r r the closest neighbor of (r) among the 2Q vectors (b2 ) Different fast search algorithms of the nearest neighbor are proposed in the literature In [FRI 77], the authors build a tree of dimension B 2 and de ne a search method of complexity in O(log Q) The results presented in [SAU 95] show that it is possible to gain a factor 13 to 115 over the compression time, without degrading the quality of the reconstructed image signi cantly The gain depends of course on the nature of the image and on the number of source blocks considered 1036 Other optimization diagrams: hybrid methods Seminal work by Jacquin, based on the use of a local iterated contracting functions system, launched a great deal of research into the approximation or coding of real 1D, 2D and 3D signals by fractals [FIS 95a, JACQ 93, SAU 94, WOH 99] These mainly concern: the construction of an optimal partition to calculate the fractal transformation [DAVO 97, FIS 95b, FIS 95c, HURT 93c, NOV 93, REU 94, THO 95] They are composed of square, rectangular or polygonal surface blocks locally adapted to the texture of the images (see Figure 1014); the acceleration of the coding algorithm (see [DAVO 96, DUD 92, LEP 93, TRU 00]);.

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the use of constant vectors issued from a known dictionary, to approximate the destination blocks from the source blocks [GHA 93, VIN 93]; the use of non-af ne elementary functions n that allow for coding the spatial redundancy of the images [LIN 94, POP 97]; the acceleration of the decoding algorithm: iterative, non-iterative, hierarchical [BARA 95, CHAN 00, IE 93, IE 94a]; the theoretical study of the fractal transformation [VRS 99] and of the convergence of the decoder [HURT 93a, HURT 94, LUN 92, MUK 00]; the extension of the method to the coding of video sequences [BART 95, BEA 91, BOG 94, FIS 94, HURD 92, HURT 93b, LAZ 94, MON 95b, WIL 94]; the use of fractals in hybrid coding-decoding schemes, either based on a discrete cosine transform [BART 94a, BART 94b, BART 95b] or on a wavelet transform of the image [BEL 98, DAVI 98, KRU 95, RIN 95, SIM 95, WALLE 96] The fractal code is, in this case, calculated on another representation of the original image, which can be more favorable to the search of local similarities

Figure 1014 Illustration of different partitionings: quadtree (square), HV (rectangular) and Vorono (polygonal), used for the search of local similarities in the image and for the calculation of the fractal code

Figure 1015 compares the compression performances using fractal coding on square, rectangular and polygonal partitioning with those of a normalized JPEG compression [WALLA 91] It highlights the fact that beyond a reasonable compression rate, compression by fractals outperforms the JPEG compression, at least in terms of visual quality of the images

Risk refers to the degree of uncertainty that the client is willing to undertake in contracting to have a project implemented In simple terms, the forms of risk can be categorized as health, safety, and environmental (HSE) risks; schedule risks; cost risks; and other risks Risk results from several factors Among these are the lack of information about the project organization itself (How reliable are they Can I trust their estimates and promises ) and about the product concept due to technical complexity (Is it proven technology Will it work as anticipated If it doesn t, how much will

We conclude this chapter by summarizing the various secure routing protocols that we studied in this chapter in Figure 433 We consider several attributes and comment on these attributes with respect to each of the protocols

38 36 Reconstruction SNR 34 32 30 28 26 10 20 30 40 50 60 70 Compression rate 80 90 100 JPEG Delaunay fractal Voronoi fractal HV fractal Quadtree 1 fractal Quadtree 2 fractal

Figure 1015 Signal to noise ratios versus the compression rate, calculated on the 512 512 Lena image These ratios compare the quality of the reconstructed images, after fractal compression on blocks of variable geometries, and after a normalized JPEG compressor

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