Secure initialization in single-hop radio networks

We consider single-hop radio networks, where collisions in the shared channel cannot be detected (no-CD model). A radio channel can be accessed by an adversary trying to degrade functionality of the network, so we are interested in algorithms that work in the presence of an adversary, who knows the algorithm executed and may try make it faulty by injecting own messages. We also focus on algorithms that are time and energy efficient. We propose a randomized initialization algorithm for a single-hop no-CD radio network. The algorithm has time complexity O(N) and energy cost O(root logN). This is not much worse than the best fragile algorithms constructed so far (0(N) in time complexity and O(loglogN) energy cost). Our algorithm succeeds with probability 1 - 2(-Omega)(root logN) in presence of an adversary, who has energy cost Theta(logN).