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Every intermediate node will check the seqnum eld of the incoming RREQ packet and will discard packets with previously seen sequence numbers Otherwise, the intermediate node checks to see if it can open the cryptographic trapdoor If it cannot open the cryptographic trapdoor, it is not the destination In this case, it determines a random nonce N as well as a random symmetric key K0 (different from the random symmetric key chosen by the other nodes) It appends the onion in the RREQ packet received to the random nonce N and encrypts the result using the key K0 Note that both K0 and N are not known to any entity other than the node itself These will be made use of later during the receipt of the RREP packets to ensure that it is the correct receiver for those packets Thus an onion is built by an intermediate node We show the steps involved in building the onion in Figure 424 Here node A is assumed to be the source which desires to determine a route to node E Node A creates the onion in step 1 and the other intermediate nodes keep on appending to this after performing the necessary checks This is one method of building the onion Other methods using the public key of each node as well as using symmetric keys without the help of nonces are also explained in [66] We do not explain those here On the other hand, if the node can open the cryptographic trapdoor, then it is indeed the destination and needs to create and send an RREP packet The RREP packet contains the following elds:

(1014)

Figure 104 Destination blocks rn and source blocks d (n) The source block transformed by n must resemble the smaller size destination block The set of destination blocks form a partition of the image

We call R the partition of the image support in destination blocks Each destination block is then put in correspondence with another transformed block n (d (n) ) that resembles it with respect to a gray-level based error measure The block d (n) , called a source block, is sought through a library made up of Q blocks belonging to the image: (n) is thus an application from [1 N ] to [1 Q] The Q blocks do not necessarily form a partition of the image but are representative of the entire image

The transformation of image A by W is formulated using the following equation:

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RREP this is a label that speci es that this is a route reply message; N this is a locally unique random route pseudonym; Pr_dest this is a proof of global trapdoor opening; onion this is the same cryptographic onion from the received RREQ packet

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W (A) =

n (d n ) =

(1015)

where n is the approximation of the destination block rn , obtained by transforming r r the source block d n by n (the mapping between block d n and block n is called a collage operation) The calculation of the transformation parameters n and the position of the blocks d n are detailed in the following section It should be noted that the problem described here is different from the inverse problem introduced in section 1026 since the spatial transformations considered do not apply to the whole image directly but to subparts of it, as it is not fractal Moreover, no probability pi is assigned to the transformation i de ning W We will see that, among the proposed methods, the Dudbridge method is that which comes closest to it 1032 Coding of natural images by fractals Jacquin [JACQ 92] proposed in 1989 an approach based on a regular partition R with square geometry The image is partitioned into square destination blocks4 of xed size equal to B 2 pixels (B = 8) The algorithm seeks, for each destination block r rn , the source block d (n) of size D2 (D = 2B) that minimizes the error d(rn , n ) where n is the approximation of rn calculated from the source block d (n) The error r measure d is given by:

The destination transmits the RREP packet after populating the above elds Note that the locally unique random route pseudonym will be used for data forwarding Any node that

r d(rn , n ) =

(667) (668)

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