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Secure Communication over Radio Channels
 PODC'08
, 2008
"... We study the problem of secure communication in a multichannel, singlehop radio network with a malicious adversary that can cause collisions and spoof messages. We assume no preshared secrets or trustedthirdparty infrastructure. The main contribution of this paper is fAME: a randomized (f)ast( ..."
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Cited by 24 (9 self)
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We study the problem of secure communication in a multichannel, singlehop radio network with a malicious adversary that can cause collisions and spoof messages. We assume no preshared secrets or trustedthirdparty infrastructure. The main contribution of this paper is fAME: 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(Et 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 fAME to establish a shared secret group key, which can be used to implement a secure, reliable and authenticated longlived 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 thirdparty infrastructure, and/or the assumption that all interference is nonmalicious.
InterferenceResilient Information Exchange
"... This paper presents an efficient protocol to reliably exchange information in a singlehop 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 ..."
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Cited by 21 (7 self)
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This paper presents an efficient protocol to reliably exchange information in a singlehop 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 thirdparty 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 exponentialtime 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 multiselector. 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.
On the Message Complexity of Indulgent Consensus
"... 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 wellbehaved, synchronous executions wi ..."
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Cited by 3 (3 self)
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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 wellbehaved, 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 messageefficient of previous indulgent consensus algorithms which have a message complexity of at least Ω(n 2) in wellbehaved executions. 1
Locally scalable randomized consensus for synchronous crash failures
 in Proceedings of the 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA
, 2009
"... 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 polylogarithmic in the size n of the system, and ..."
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Cited by 3 (3 self)
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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 polylogarithmic 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.
Distributed agreement with optimal communication complexity
 In Proceedings of the 21st ACMSIAM Symposium on Discrete Algorithms (SODA
, 2010
"... We consider the problem of faulttolerant agreement in a crashprone synchronous system. We present a new randomized consensus algorithm that achieves optimal communication efficiency, using only O(n) bits of communication, and terminates in (almost optimal) time O(log n), with high probability. The ..."
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Cited by 3 (2 self)
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We consider the problem of faulttolerant agreement in a crashprone synchronous system. We present a new randomized consensus algorithm that achieves optimal communication efficiency, using only O(n) bits of communication, and terminates in (almost optimal) time O(log n), with high probability. The same protocol, with minor modifications, can also be used in partially synchronous networks, guaranteeing correct behavior even in asynchronous executions, while maintaining efficient performance in synchronous executions. Finally, the same techniques also yield a randomized, faulttolerant gossip protocol that terminates in O(log ∗ n) rounds using O(n) messages (with bit complexity that depends on the data being gossiped). 1
How Efficient Can Gossip Be? (On the Cost of Resilient Information Exchange)
"... 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 phonecall model (introduced by Karp et al. [1]), and we an ..."
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Cited by 2 (0 self)
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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 phonecall 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 nearoptimal O(n log 3 n) message complexity. To the best of our knowledge, this is the first epidemicstyle 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 superlinear 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.
Liverpool L69 3BX, U.K.
"... We study communication complexity of consensus in synchronous messagepassing 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 inp ..."
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We study communication complexity of consensus in synchronous messagepassing 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.
University of Cyprus, CY1048 Nicosia, Cyprus.
"... In this paper, we study the complexity of gossip in an asynchronous, messagepassing faultprone 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 ..."
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In this paper, we study the complexity of gossip in an asynchronous, messagepassing faultprone 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 messageefficient 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,
EarlyDeciding Consensus is Expensive
"... In consensus, the n nodes of a distributed system seek to take a consistent decision on some output, despite up to t of them crashing or even failing maliciously, i.e., behaving “Byzantine”. It is known that it is impossible to guarantee that synchronous, deterministic algorithms consistently decide ..."
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In consensus, the n nodes of a distributed system seek to take a consistent decision on some output, despite up to t of them crashing or even failing maliciously, i.e., behaving “Byzantine”. It is known that it is impossible to guarantee that synchronous, deterministic algorithms consistently decide on an output in fewer than f + 1 rounds in executions in which the actual number of faults is f ≤ t. This even holds if faults are crashonly, and in this case the bound can be matched precisely. However, the question of whether this can be done efficiently, i.e., with little communication, so far has not been addressed. In this work, we show that algorithms tolerating Byzantine faults and deciding within f + 2 rounds must send Ω(nt + t 2 f) messages; as a byproduct, our analysis shows that decision within f +1 rounds is impossible in this setting (unless f = t). Moreover, we prove that any crashresilient algorithm deciding in f + 1 rounds has worstcase message complexity Ω(n 2 f). Interestingly, this changes drastically if we restrict the fault model further. If crashes are orderly, i.e., in each round, each node picks an order in which its messages are sent, and crashing nodes successfully transmit a prefix of their sequence, deciding in f + 1 rounds can be guaranteed with O(nt) messages.