213 research outputs found
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 âgoâ signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a âfireâ signal. Moreover, no node should generate a âfireâ signal without some correct node having previously received a âgoâ 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
Near-optimal self-stabilising counting and firing squads
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 âgoâ signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a âfireâ signal. Moreover, no node should generate a âfireâ signal without some correct node having previously received a âgoâ 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
Asynchronous Byzantine Systems: From Multivalued to Binary Consensus with t < n/3, O(nÂČ) Messages, O(1) Time, and no Signature
International audienceThis paper presents a new algorithm that reduces multivalued consensus to binary consensus in an asyn-chronous message-passing system made up of n processes where up to t may commit Byzantine failures. This algorithm has the following noteworthy properties: it assumes t < n/3 (and is consequently optimal from a resilience point of view), uses O(nÂČ) messages, has a constant time complexity, and does not use signatures. The design of this reduction algorithm relies on two new all-to-all communication abstractions. The first one allows the non-faulty processes to reduce the number of proposed values to c, where c is a small constant. The second communication abstraction allows each non-faulty process to compute a set of (proposed) values such that, if the set of a non-faulty process contains a single value, then this value belongs to the set of any non-faulty process. Both communication abstractions have an O(nÂČ) message complexity and a constant time complexity. The reduction of multivalued Byzantine consensus to binary Byzantine consensus is then a simple sequential use of these communication abstractions. To the best of our knowledge, this is the first asynchronous message-passing algorithm that reduces multivalued consensus to binary consensus with O(nÂČ) messages and constant time complexity (measured with the longest causal chain of messages) in the presence of up to t < n/3 Byzantine processes, and without using cryptography techniques. Moreover, this reduction algorithm tolerates message reordering by Byzantine processes
Distributed Consensus in Networks
Distributed algorithms have gained a lot of attention during recent years. Their
application in industry, particularly in wireless sensor networks has motivated researchers
to try to design them in order to be less resource-consuming (e.g. memory
and power), faster, and more reliable. There have been numerous distributed algorithms
for different types of problems in the context of distributed algorithms. We
are interested in a fundamental coordination problem namely the majority consensus problem. In the majority consensus problem nodes try to find the opinion of
the majority in a network of interest. As our first contribution and motivated by
the distributed binary consensus problem in [1] we propose a distributed algorithm
for multivalued consensus in complete graphs. As our second contribution we propose
an algorithm for the optimization of the binary interval consensus algorithm
pioneered by Ben ezit et al in [2]. Finally we use binary interval consensus algorithm
to design a framework for error-free consensus in dynamic networks using
which nodes can leave or join the network during or after the consensus process.Open Acces
Asynchronous Byzantine Systems: From Multivalued to Binary Consensus with t < n/3, O(n 2 ) Messages, O(1) Time, and no Signature
This paper presents a new algorithm that reduces multivalued consensus to binary consensus in an asynchronous message-passing system made up of n processes where up to t may commit Byzantine failures. This algorithm has the following noteworthy properties: it assumes t < n/3 (and is consequently optimal from a resilience point of view), uses O(n 2) messages, has a constant time complexity, and does not use signatures. The design of this reduction algorithm relies on two new all-to-all communication abstractions. The first one allows the non-faulty processes to reduce the number of proposed values to c, where c is a small constant. The second communication abstraction allows each non-faulty process to compute a set of (proposed) values such that, if the set of a non-faulty process contains a single value, then this value belongs to the set of any non-faulty process. Both communication abstractions have an O(n 2) message complexity and a constant time complexity. The reduction of multivalued Byzantine consensus to binary Byzantine consensus is then a simple sequential use of these communication abstractions. To the best of our knowledge, this is the first asynchronous message-passing algorithm that reduces multivalued consensus to binary consensus with O(n 2) messages and constant time complexity (measured with the longest causal chain of messages) in the presence of up to t < n/3 Byzantine processes, and without using cryptography techniques. Moreover, this reduction algorithm tolerates message re-ordering by Byzantine processes. Une rĂ©duction du consensus multivaluĂ© au consensus binaire en prĂ©sence d'asynchronisme, de t < n/3 processus byzantins, avec un temps constant, O(n 2) messages, et pas de signatures RĂ©sumĂ© : Cet article prĂ©sente un algorithme rĂ©parti qui, dans un systĂšme asynchrone de n processus qui communiquent par passage de messages, et qui comprend jusqu'Ă t processus byzantins, ramĂšne le problĂšme du consensus multivaluĂ© au problĂšme du consensus binaire. Cette rĂ©duction est optimale par rapport Ă t (t < n/3), requiert un temps constant et O(n 2) messages, et n'utilise aucun Ă©lĂ©ment cryptographique (i.e., pas de signatures). Elle considĂšre donc un adversaire donc la la puissance de calcul peut ĂȘtre illimitĂ©e
Network-Agnostic Security Comes (Almost) for Free in DKG and MPC
Distributed key generation (DKG) protocols are an essential building block for threshold cryptosystems. Many DKG protocols tolerate up to corruptions assuming a well-behaved synchronous network, but become insecure as soon as the network delay becomes unstable. On the other hand, solutions in the asynchronous model operate under arbitrary network conditions, but only tolerate corruptions, even when the network is well-behaved.
In this work, we ask whether one can design a protocol that achieves security guarantees in either scenario. We show a complete characterization of network-agnostic DKG protocols, showing that the tight bound is . As a second contribution, we provide an optimized version of the network-agnostic MPC protocol by Blum, Liu-Zhang and Loss [CRYPTO\u2720] which improves over the communication complexity of their protocol by a linear factor. Moreover, using our DKG protocol, we can instantiate our MPC protocol in the plain PKI model, i.e., without the need to assume an expensive trusted setup.
Our protocols incur the same communication complexity as state-of-the-art DKG and MPC protocols with optimal resilience in their respective purely synchronous and asynchronous settings, thereby showing that network-agnostic security comes (almost) for free
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