Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

Preventing Replay Attacks for Secure Routing in Ad Hoc Networks 147Fig. 3. Measuring RTTHello messages periodically to assure neighbors that the links between them arestill alive. We use a slightly modified Hello message (RTT REQ) by includinga flag to request for an immediate reply (RTT REP). By sending such a specialHello after every n Hello’s, each node should get the RTT to each trustedneighbor by subtracting the receiving time of RTT REP by the sending time ofRTT REQ. Trusted neighbors are those neighbors that have passed verification.At the beginning all neighbors are set as trusted because we assume there is noreplay due to the spontaneous nature of the ad-hoc network. The RTT thresholdis calculated by averaging the RTT’s to all trusted neighbors and adding amargin depending on the stringency of security. RTT REP messages also needto be slightly different to be distinguished from other common Hello’s. To reduceoverhead, RTT Hello’s do not need to be encrypted or signed because neitherconfidentiality nor integrity is required (it is only within one-hop range). But arandom number or time-stamp should be added to each RTT REQ to be embeddedin the RTT REP to prevent fake replies.For the nodes that currently do not have any route to maintain and thus arenot broadcasting Hello’s, RTT Hello’s are required to maintain RTT thresholdsfor themselves. Since RTT Hello’s have much longer interval, the overhead willbe minimum.5 AnalysisIn this section, we give a mathematical analysis of the overhead caused by neighborverification procedures. The overhead caused by RTT Hello is ignored sincethey are just Hello packets that need immediate responses.Suppose in a network of N nodes, each node has neighbor change rate X,i.e., after a specific period of time, X percent new neighbors need to be verified.Also, we suppose during this period of time M RREQ’s are processed.We can deem X as the probability of the verification being launched inone-hop range. If the average length of routes in the network is Y hops, thenaccording to Binomial distribution the probability of the verification being heldin only one hop is:P 1 = ( )Y1 X 1 (1 − X) (Y −1) (1)The probability of i hops being verified is:P i = ( )Yi X i (1 − X) (Y −i) (2)where 0 ≤ i ≤ Y . Suppose the time consumed at each hop is t if no verificationis needed, 3t if the verification is applied (one RREQ(t) and one RTT(2t)), then