625 research outputs found
Towards Optimal Synchronous Counting
Consider a complete communication network of nodes, where the nodes
receive a common clock pulse. We study the synchronous -counting problem:
given any starting state and up to faulty nodes with arbitrary behaviour,
the task is to eventually have all correct nodes counting modulo in
agreement. Thus, we are considering algorithms that are self-stabilizing
despite Byzantine failures. In this work, we give new algorithms for the
synchronous counting problem that (1) are deterministic, (2) have linear
stabilisation time in , (3) use a small number of states, and (4) achieve
almost-optimal resilience. Prior algorithms either resort to randomisation, use
a large number of states, or have poor resilience. In particular, we achieve an
exponential improvement in the space complexity of deterministic algorithms,
while still achieving linear stabilisation time and almost-linear resilience.Comment: 17 pages, 2 figure
Optimal byzantine resilient convergence in oblivious robot networks
Given a set of robots with arbitrary initial location and no agreement on a
global coordinate system, convergence requires that all robots asymptotically
approach the exact same, but unknown beforehand, location. Robots are
oblivious-- they do not recall the past computations -- and are allowed to move
in a one-dimensional space. Additionally, robots cannot communicate directly,
instead they obtain system related information only via visual sensors. We draw
a connection between the convergence problem in robot networks, and the
distributed \emph{approximate agreement} problem (that requires correct
processes to decide, for some constant , values distance
apart and within the range of initial proposed values). Surprisingly, even
though specifications are similar, the convergence implementation in robot
networks requires specific assumptions about synchrony and Byzantine
resilience. In more details, we prove necessary and sufficient conditions for
the convergence of mobile robots despite a subset of them being Byzantine (i.e.
they can exhibit arbitrary behavior). Additionally, we propose a deterministic
convergence algorithm for robot networks and analyze its correctness and
complexity in various synchrony settings. The proposed algorithm tolerates f
Byzantine robots for (2f+1)-sized robot networks in fully synchronous networks,
(3f+1)-sized in semi-synchronous networks. These bounds are optimal for the
class of cautious algorithms, which guarantee that correct robots always move
inside the range of positions of the correct robots
self-stabilizing
Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given C>1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input. We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience f<n/3, asymptotically optimal stabilisation and response time O(f), and message size O(log f). As our framework does not restrict the type of consensus routines used, we also obtain efficient randomised solutions
Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries
We propose an efficient framework for enabling secure multi-party numerical
computations in a Peer-to-Peer network. This problem arises in a range of
applications such as collaborative filtering, distributed computation of trust
and reputation, monitoring and other tasks, where the computing nodes is
expected to preserve the privacy of their inputs while performing a joint
computation of a certain function. Although there is a rich literature in the
field of distributed systems security concerning secure multi-party
computation, in practice it is hard to deploy those methods in very large scale
Peer-to-Peer networks. In this work, we try to bridge the gap between
theoretical algorithms in the security domain, and a practical Peer-to-Peer
deployment.
We consider two security models. The first is the semi-honest model where
peers correctly follow the protocol, but try to reveal private information. We
provide three possible schemes for secure multi-party numerical computation for
this model and identify a single light-weight scheme which outperforms the
others. Using extensive simulation results over real Internet topologies, we
demonstrate that our scheme is scalable to very large networks, with up to
millions of nodes. The second model we consider is the malicious peers model,
where peers can behave arbitrarily, deliberately trying to affect the results
of the computation as well as compromising the privacy of other peers. For this
model we provide a fourth scheme to defend the execution of the computation
against the malicious peers. The proposed scheme has a higher complexity
relative to the semi-honest model. Overall, we provide the Peer-to-Peer network
designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA)
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