tailieunhanh - Wireless Network Security phần 5

nếu kênh được biết là có rất nhiều va chạm hoặc nếu chúng ta cho phép di chuyển nút trong hệ thống, fmax có thể được sử dụng để chịu đựng những yếu tố này. Ví dụ, nếu chúng tôi ước tính rằng một kênh sẽ có một tỷ lệ va chạm của 2 gói / giây; | EURASIP Journal on Wireless Communications and Networking 3 This information can be acquired from any secure link-state routing protocol for example 10 . These assumptions allow us to concentrate on the essential theoretical properties of the multipath routing problem and the resulting solutions. In the case where link reliability factors and network topology change frequently the update of the multipath set should be performed periodically or triggered by the change. 3. Multipath Routing with Minimum Worst-Case Security Risk In this section we study the multipath routing solution minimizing the worst-case security risk. We quantify the worst-case security risk by the percentage of packets captured by the attackers under the condition that the attackers make all their efforts to maximize this percentage or equivalently the probability that a packet is captured by the attackers under the condition that the attackers make all their efforts to maximize this probability . We start with the case of single attacker M. In such a routing problem the objective of s is to calculate q qfl to minimize the maximum security risk caused by M. Mathematically the multipath routing problem can be formulated as the following minimaximization problem MP1 min max q p veV r q P T P v p P v veP PeP Subject to pv 1 pv 0 Vv E V VE V pv 2 s q P 1 q P 0 VP E P PeP where T P v ĩ eEP e vre p P v ribEP b v 1 -pb . a b denotes that packets encounter node edge a before node edge b when routed along P. r ILveV SveP PeP q P T P v p P v pv is the expected probability that the packet is captured by M. Let r ĩ vEV SveP PeP q P T P v pv. If M attacks at most one node per path then r r .In general case it always holds that r r . Noticing that MP1 is a nonlinear optimization problem we focus on solving MPp r minmax r q p 3 which is a linear optimization problem. Later in Section we will show that r r . Consider the inner maximization problem of MP1 for fixed q max s T P v q P P vEV vEP PEP pv 4 .

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