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The corresponding fourth-order submodel is [6,9] SUBMODEL DDx(n$, bb$, v, vx) Vector vx = (2 * v{ 2} 16 * v{-1} + 16 * v{1} 2 * v{2}) * bb$ vx[1] = ( 50 * v[1] + 96 * v[2] 72 * v[3] + 32 * v[4] 6 * v[5]) * bb$ vx[2] = ( 6 * v[1] 20 * v[2] + 36 * v[3] 12 * v[4] + 2 * v[5]) * bb$ vx[n$-1] = ( 2 * v[n$-4] + 12 * v[n$-3] - 36 * v[n$-2] + 20 * v[n$-1] + 6 * v[n$]) * bb$ vx[n$] = (6 * v[n$-4] 32 * v[n$-3] + 72 * v[n$ 2] 96 * v[n$ 1] + 50 * v[n$]) * bb$ end [SET bb$ = 1/(24 DX)] The end-value assignments again overwrite part of the vector assignment

Following this Bob determines its own nonce n2 He then calculates a ticket (denoted as ticketB) as a hash of the common shared key, pseudonym of Alice (PSA), Bob s own pseudonym (PSB), as well as the two nonces n1 and n2 The ticket is calculated as H2(KBA kPSAkPSBkn1kn2k0), where H2 is another hash function Bob then transmits a message to Alice The message includes Bob s own pseudonym, which is Bellcor in this case, the ticket and the nonce n2 Alice on receiving this message can also calculate the common key KAB as f[H1(Bob s pseudonym], Alice s secret point) The properties of function f() ensure that this key is the same as KBA calculated by Bob (assuming that both Bob and Alice are given the corresponding pseudonyms and secret points by the TA accurately) Alice also calculates if ticketB provided by Bob is valid by computing H2(KABkPSAkPSBkn1kn2k0) If the ticket is valid, then Alice calculates another ticket (denoted as ticketA below) as H2(KABkPSAkPSBkn1kn2k1) Alice then transmits a message with this ticket to Bob, who can then verify it As a result of the veri cation of these tickets, both Alice and Bob are convinced that they both belong to the same group Note that the identity of either party is not known to the other This completes the anonymous neighborhood authentication phase To summarize, the following message exchange is used in this phase: 1 Alice ! Bob: ,Alice s pseudonym (PSA), n1 2 Bob ! Alice: ,Bob s pseudonym (PSB), ticketB, n2 3 Alice ! Bob: ,ticketA Alice and Bob then calculate L pairs of link identi ers to be used for the link between them and the shared session keys to be used with each link identi er Each pair of neighboring nodes thereby shares multiple link identi ers uniquely, that is, no two links have the same link identi er, while the same link has multiple link identi ers Hence, when one node broadcasts a packet identi ed by the link identi er, only the neighboring node which shares this link identi er can interpret and accept the packet These link identi ers (linkIDs) and the shared session keys are used in the routing process The anonymous route discovery in MASK is similar to that in AODV The difference, though, is in the use of the anonymity property Each node maintains four tables:.

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The initial temperature u(x, 0) has to be 8000 K for all x along the rod At x = 0, the rod is insulated, but at x = L it radiates according to a fourth-power law, so that we have mixed-type boundary conditions at the ends of the rod:

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Test Series 1221 - Two Servers Test 12211 - 200 Users Test 12212 - 280 Users Test 12213 - 320 Users Test Series 1222 - Three Servers Test 12221 - 280 Users Test 12222 - 320 Users Test 12223 - 400 Users Conclusion

ux = 0 (for x = 0, all t) ux = E[UA4 u(L)4] (for x = L, all t)

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