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RREQ (ie node A) and contains the signature that can be used by an intermediary node for creating a RREP in response to an RREQ that has node A as the destination Figure 45 shows the format for the RREP message for the double signature scheme This RREP is created by the intermediary node The signature eld contains the signature for the RREP message provided by the destination of the RREQ message (ie node A) Since the lifetime of the route could have changed (since node A created the signed RREP elds earlier), the RREP double signature extension includes the old lifetime that was used by node A for creating the signature The RREP double signature extension also includes the signature of the intermediary node for the RREP message with the actual lifetime (shown as signature of the new lifetime in Fig 45) This way, when nodes receive a RREP message with the double signature extension, they can verify that the message is authentic since it has been signed by the intermediary node but also represents accurate information about the destination since it contains the signature of that node also 4212 Hash Chains for SAODV The second scheme in SAODV protects the mutable information such as the hop-count eld in the RREQ and RREP messages It does this by making use of the concept of hash chains This assures nodes receiving AODV messages that the hop-count values provided are accurate and have not been decremented by an adversary on the path Hash chains are created by applying a hash function (see 2) repeatedly to a seed number We describe this scheme in detail next When a node originates an SAODV message (eg RREQ, RREP) it selects a random number (ie seed) and a hash function to use The random seed is stored in the hash eld The max hop count eld is set to the TTL value of the IP packet The top Hash eld is also populated as described earlier The originator thereby completes the extension SAODV message Whenever a node receives an SAODV message it rst checks the digital signature on the message If the digital signature matches, then the node checks that the hop count (which has been incremented by nodes en route) has not been maliciously altered This is achieved as follows The node applies the hash function max hop count minus the value in the hop count eld times to the value of the hash eld The resulting value must equal the value of top hash as shown below: h(max.

where some of s possibly disappeared from the discrete sum on the indices in S n (this occurs very exactly when equation (747) does not have solutions such that e( s) > 0) In the diffusive part, = o( ) shows that in a certain way, the integral term is a perturbation of order NOTE 710 It should be noted that we observe here a generalization of the decomposition result (739), the only difference being the in nitely countable character of the poles For a detailed study of the family of diffusive representation ( ) indexed by , see 9 of [HEL 00] 7533 Fractional modal decomposition In (748), we carry out the decomposition of the meromorphic function in a series of normally convergent elementary meromorphic functions on every compact subset of the complex plane (see 5 of [CART 61]), by using: ( 1)n 1 = sinh(z) n= z in which gives us: 1 ( 1)n H(s) = 2 n= (s) + i(n + 0 ) Lastly, we break up each term of the series into rational fractions of the variable s: 1 1 1 1 = + + s + s s0 n n s n s n n

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then, we carry out a inverse Laplace transform, ie:

h(t) =

n=

(753)

hop count hop count)

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