We study the problem of secure communication in a multichannel, single-hop radio network with a malicious adversary that can cause collisions and spoof messages. We assume no pre-shared secrets or trusted-third-party infrastructure. The main contribution of this paper is f-AME: a randomized (f)ast-(A)uthenticated (M)essage (E)xchange protocol that enables nodes to exchange messages in a reliable and authenticated manner. It runs in O(|E|t 2 log n) time and has optimal resilience to disruption, where E is the set of pairs of nodes that need to swap messages, n is the total number of nodes, C the number of channels, and t < C the number of channels on which the adversary can participate in each round. We show how to use f-AME to establish a shared secret group key, which can be used to implement a secure, reliable and authenticated long-lived communication service. The resulting service requires O(nt 3 log n) rounds for the setup phase, and O(t log n) rounds for an arbitrary pair to communicate. By contrast, existing solutions rely on preshared secrets, trusted third-party infrastructure, and/or the assumption that all interference is non-malicious.

This paper presents an efficient protocol to reliably exchange information in a single-hop radio network with unpredictable interference. The devices can access C communication channels. We model the interference with an adversary that can disrupt up to t of these channels simultaneously. We assume no shared secret keys or third-party infrastructure. The running time of our protocol decreases as the gap between C and t increases. Two extreme cases prove particularly interesting: The running time is linear when the number of channels C = Ω(t 2), and exponential when only C = t + 1 channels are available. We prove that exponential-time is unavoidable in the latter case. At the core of our protocol lies a combinatorial function, of independent interest, and described for the first time in this paper: the multi-selector. This function determines a sequence of device channel assignments such that every sufficiently large subset of devices is partitioned, by at least one of these assignments, onto distinct channels.

Abstract. Many recommend planning for the worst and hoping for the best. In this paper we devise efficient indulgent consensus algorithms that can tolerate crash failures and arbitrarily long periods of asynchrony, and yet perform (asymptotically) optimally in well-behaved, synchronous executions with few failures. We present two such algorithms: In synchronous executions, the first has optimal message complexity, using only O(n) messages, but runs in superlinear time of O(n 1+ε). The second has a message complexity of O(n polylog(n)), but has an optimal running time, completing in O(f) rounds in synchronous executions with at most f failures. Both of these results improve significantly over the most message-efficient of previous indulgent consensus algorithms which have a message complexity of at least Ω(n 2) in well-behaved executions. 1

We consider bit communication complexity of binary consensus in synchronous message passing systems with processes prone to crashes. A distributed algorithm is locally scalable when each process contributes to the complexity measure an amount that is poly-logarithmic in the size n of the system, and it is globally scalable when the average contribution per process to the complexity measure is such. We show that consensus can be solved by a randomized algorithm that is locally scalable with respect to both time and bit communication complexities against oblivious adversaries. If a bound t on the number of crashes is a constant fraction of the number n of processes then our randomized consensus solution terminates in the expected O(log n) time while the expected number of bits that each process sends and receives is O(log n). Our solution uses overlay networks with topologies that are explicitly defined and have suitable connectivity and robustness properties related to graph expansion. To compare our results to deterministic consensus solutions, it is known [20] that consensus cannot be solved deterministically by an algorithm that is locally scalable with respect to message complexity and that deterministic solutions globally scalable with respect to bit communication complexity exist for any bound t < n on the number of crashes. We prove a lower bound relating the number of nonfaulty processes needed to obtain a specific message complexity of consensus of a randomized algorithm run against oblivious adversaries.

We study communication complexity of consensus in synchronous message-passing systems with processes prone to crashes. The goal in the consensus problem is to have all the nonfaulty processes agree on a common value from among the input ones, after each process has been initialized with a binary input value. The system consists of n processes and it is assumed that at most t < n processes crash in an execution. A consensus algorithm that tolerates up to t failures is called fast when its time complexity is O(t). All the previously known fast deterministic consensus solutions sent Ω(n 2) bits in messages. We give a fast deterministic consensus algorithm that has processes send only O(n log 4 n) bits. In our solution, processes exchange messages according to topologies of overlay graphs that have suitable robustness and connectivity properties related to graph expansion.

In this paper, we study the complexity of gossip in an asynchronous, message-passing fault-prone distributed system. In short, we show that an adaptive adversary can significantly hamper the spreading of a rumor, while an oblivious adversary cannot. This latter fact implies that there exist message-efficient asynchronous (randomized) consensus protocols, in the context of an oblivious adversary. In more detail, we summarize our results as follows. If the adversary is adaptive, we show that a randomized asynchronous gossip algorithm cannot terminate in fewer than O(f(d + δ)) time steps unless Ω(n + f 2) messages are exchanged, where n is the total number of processes, f is the number of tolerated crash failures, d is the maximum communication delay for the specific execution in question,

Abstract. Gossip, also known as epidemic dissemination, is becoming an increasingly popular technique in distributed systems. Yet, it has remained a partially open question: how robust are such protocols? We consider a natural extension of the random phone-call model (introduced by Karp et al. [1]), and we analyze two different notions of robustness: the ability to tolerate adaptive failures, and the ability to tolerate oblivious failures. For adaptive failures, we present a new gossip protocol, TrickleGossip, which achieves near-optimal O(n log 3 n) message complexity. To the best of our knowledge, this is the first epidemic-style protocol that can tolerate adaptive failures. We also show a direct relation between resilience and message complexity, demonstrating that gossip protocols which tolerate a large number of adaptive failures need to use a super-linear number of messages with high probability. For oblivious failures, we present a new gossip protocol, CoordinatedGossip, that achieves optimal O(n) message complexity. This protocol makes novel use of the universe reduction technique to limit the message complexity. 1