Of Malicious Motes and Suspicious Sensors
Author(s)Gilbert, Seth; Guerraoui, Rachid; Newport, Calvin
Theory of Computation
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How much damage can a malicious tiny device cause in a single-hopwireless network? Imagine two players, Alice and Bob, who want toexchange information. Collin, a malicious adversary, wants to preventthem from communicating. By broadcasting at the same time as Alice orBob, Collin can destroy their messages or overwhelm them with his ownmalicious data. Being a tiny device, however, Collin can onlybroadcast up to B times. Given that Alice and Bob do not knowB, and cannot distinguish honest from malicious messages, howlong can Collin prevent them from communicating? We show the answerto be 2B + Theta(lg|V|) communication rounds, where V is theset of values that Alice and Bob may transmit. We prove this resultto be optimal by deriving an algorithm that matches our lowerbound---even in the stronger case where Alice and Bob do not start thegame at the same time.We then argue that this specific 3-player game captures the generalextent to which a malicious adversary can disrupt coordination in asingle-hop wireless network. We support this claim by deriving---via reduction from the 3-player game---round complexity lower boundsfor several classical n-player problems: 2B + Theta(lg|V|) for reliable broadcast,2B + Omega(lg(n/k)) for leader election among k contenders,and 2B + Omega(k*lg(|V|/k)) for static k-selection. We then consider an extension of our adversary model that also includes up to t crash failures. We study binary consensus as the archetypal problem for this environment and show a bound of 2B + Theta(t) rounds. We conclude by providing tight, or nearly tight, upper bounds for all four problems. The new upper and lower bounds in this paper represent the first such results for a wireless network in which the adversary has the ability to disrupt communication.
Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory
wireless ad hoc networks, byzantine, reliable broadcast, leader election, k-selection, consensus, collision detection