272 research outputs found
Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems
In this paper, we show that the protocol complex of a Byzantine synchronous
system can remain -connected for up to rounds,
where is the maximum number of Byzantine processes, and .
This topological property implies that rounds are
necessary to solve -set agreement in Byzantine synchronous systems, compared
to rounds in synchronous crash-failure systems. We
also show that our connectivity bound is tight as we indicate solutions to
Byzantine -set agreement in exactly synchronous
rounds, at least when is suitably large compared to . In conclusion, we
see how Byzantine failures can potentially require one extra round to solve
-set agreement, and, for suitably large compared to , at most that
Iterative Approximate Consensus in the presence of Byzantine Link Failures
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each directed link of the underlying
communication graph represents a communication channel between a pair of nodes.
We adopt the transient Byzantine link failure model [15, 16], where an
omniscient adversary controls a subset of the directed communication links, but
the nodes are assumed to be fault-free.
Recent work has addressed the problem of reaching approximate consen- sus in
incomplete graphs with Byzantine nodes using a restricted class of iterative
algorithms that maintain only a small amount of memory across iterations [22,
21, 23, 12]. However, to the best of our knowledge, we are the first to
consider approximate consensus in the presence of Byzan- tine links. We extend
our past work that provided exact characterization of graphs in which the
iterative approximate consensus problem in the presence of Byzantine node
failures is solvable [22, 21]. In particular, we prove a tight necessary and
sufficient condition on the underlying com- munication graph for the existence
of iterative approximate consensus algorithms under transient Byzantine link
model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609
On Byzantine Broadcast in Loosely Connected Networks
We consider the problem of reliably broadcasting information in a multihop
asynchronous network that is subject to Byzantine failures. Most existing
approaches give conditions for perfect reliable broadcast (all correct nodes
deliver the authentic message and nothing else), but they require a highly
connected network. An approach giving only probabilistic guarantees (correct
nodes deliver the authentic message with high probability) was recently
proposed for loosely connected networks, such as grids and tori. Yet, the
proposed solution requires a specific initialization (that includes global
knowledge) of each node, which may be difficult or impossible to guarantee in
self-organizing networks - for instance, a wireless sensor network, especially
if they are prone to Byzantine failures. In this paper, we propose a new
protocol offering guarantees for loosely connected networks that does not
require such global knowledge dependent initialization. In more details, we
give a methodology to determine whether a set of nodes will always deliver the
authentic message, in any execution. Then, we give conditions for perfect
reliable broadcast in a torus network. Finally, we provide experimental
evaluation for our solution, and determine the number of randomly distributed
Byzantine failures than can be tolerated, for a given correct broadcast
probability.Comment: 1
Parameterizable Byzantine Broadcast in Loosely Connected Networks
We consider the problem of reliably broadcasting information in a multihop
asynchronous network, despite the presence of Byzantine failures: some nodes
are malicious and behave arbitrarly. We focus on non-cryptographic solutions.
Most existing approaches give conditions for perfect reliable broadcast (all
correct nodes deliver the good information), but require a highly connected
network. A probabilistic approach was recently proposed for loosely connected
networks: the Byzantine failures are randomly distributed, and the correct
nodes deliver the good information with high probability. A first solution
require the nodes to initially know their position on the network, which may be
difficult or impossible in self-organizing or dynamic networks. A second
solution relaxed this hypothesis but has much weaker Byzantine tolerance
guarantees. In this paper, we propose a parameterizable broadcast protocol that
does not require nodes to have any knowledge about the network. We give a
deterministic technique to compute a set of nodes that always deliver authentic
information, for a given set of Byzantine failures. Then, we use this technique
to experimentally evaluate our protocol, and show that it significantely
outperforms previous solutions with the same hypotheses. Important disclaimer:
these results have NOT yet been published in an international conference or
journal. This is just a technical report presenting intermediary and incomplete
results. A generalized version of these results may be under submission
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