Asynchronous Byzantine consensus with 2f + 1 processes

IEEE Transactions on Dependable and Secure Computing, 2000

This paper is on the Consensus problem in asynchronous distributed systems where (up to f ) processes (among n) can exhibit a Byzantine behavior, i.e., can deviate arbitrarily from their specification. A way to solve the consensus problem in such a context consists of enriching the system with additional oracles that are powerful enough to cope with the uncertainty and unpredictability created by the combined effect of Byzantine behavior and asynchrony. Considering two types of such oracles, namely, an oracle that provides processes with random values, and a failure detector oracle, the paper presents two families of Byzantine asynchronous consensus protocols. Two of these protocols are particularly noteworthy: they allow the processes to decide in one communication step in favorable circumstances. The first is a randomized protocol that assumes n > 5f . The second one is a failure detector-based protocol that assumes n > 6f . These protocols are designed to be particularly simple and efficient in terms of communication steps, the number of messages they generate in each step, and the size of messages. So, although they are not optimal in the number of Byzantine processes that can be tolerated, they are particularly efficient when we consider the number of communication steps they require to decide, and the number and size of the messages they use. In that sense, they are practically appealing.

Journal of the ACM, 2015

This article is on broadcast and agreement in asynchronous message-passing systems made up of n processes, and where up to t processes may have a Byzantine Behavior. Its first contribution is a powerful, yet simple, all-to-all broadcast communication abstraction suited to binary values. This abstraction, which copes with up to t < n /3 Byzantine processes, allows each process to broadcast a binary value, and obtain a set of values such that (1) no value broadcast only by Byzantine processes can belong to the set of a correct process, and (2) if the set obtained by a correct process contains a single value v , then the set obtained by any correct process contains v . The second contribution of this article is a new round-based asynchronous consensus algorithm that copes with up to t < n /3 Byzantine processes. This algorithm is based on the previous binary broadcast abstraction and a weak common coin. In addition to being signature-free and optimal with respect to the value of ...

This paper establishes the first theorem relating resilience, round complexity and authentication in distributed computing. We give an exact measure of the time complexity of consensus algorithms that tolerate Byzantine failures and arbitrary long periods of asynchrony as in the Internet. The measure expresses the ability of processes to reach a consensus decision in a minimal number of rounds of information exchange, as a function of (a) the ability to use authentication and (b) the number of actual process failures, in those rounds, as well as of (c) the total number of failures tolerated and (d) the system configuration. The measure holds for a framework where the different roles of processes are distinguished such that we can directly derive a meaningful bound on the time complexity of implementing robust general services in practical distributed systems. To prove our theorem, we establish certain lower bounds and we give algorithms that match these bounds. The algorithms are all variants of the same generic asynchronous Byzantine consensus algorithm, which is interesting in its own right.

IEICE Transactions on Information and Systems, 2014

We propose a new method that accelerates asynchronous Byzantine Fault Tolerant (BFT) protocols designed on the principle of state machine replication. State machine replication protocols ensure consistency among replicas by applying operations in the same order to all of them. A naive way to determine the application order of the operations is to repeatedly execute the BFT consensus to determine the next executed operation, but this may introduce inefficiency caused by waiting for the completion of the previous execution of the consensus protocol. To reduce this inefficiency, our method allows parallel execution of the consensuses while keeping consistency of the consensus results at the replicas. In this paper, we also prove the correctness of our method and experimentally compare it with the existing method in terms of latency and throughput. The evaluation results show that our method makes a BFT protocol three or four times faster than the existing one when some machines or message transmissions are delayed.

Proceedings of the 2014 ACM symposium on Principles of distributed computing - PODC '14, 2014

This paper presents a new round-based asynchronous consensus algorithm that copes with up to t < n/3 Byzantine processes, where n is the total number of processes. In addition of being signature-free and optimal with respect to the value of t, this algorithm has several noteworthy properties: the expected number of rounds to decide is four, each round is composed of two or three communication steps and involves O(n 2 ) messages, and a message is composed of a round number plus a single bit. To attain this goal, the consensus algorithm relies on a common coin as defined by Rabin, and a new extremely simple and powerful broadcast abstraction suited to binary values. The main target when designing this algorithm was to obtain a cheap and simple algorithm. This was motivated by the fact that, among the first-class properties, simplicity -albeit sometimes under-estimated or even ignored-is a major one.

2009

Byzantine Quorum Systems is a replication technique used to ensure availability and consistency of replicates data even in presence of arbitrary faults. This paper presents a Byzantine Quorum Systems protocol that provides atomic semantics despite the existence of Byzantine clients and servers. Moreover, this protocol is integrated with a protocol for proactive recovery of servers.

2010

It is known that Byzantine consensus algorithms guarantee one-step decision only in favorable situations (e.g. when all processes propose the same value) and no one-step algorithm can support two-step decision. This paper presents DEX, a novel one-step Byzantine algorithm that circumvents these impossibilities using the condition-based approach. Algorithm DEX has two distinguished features: Adaptiveness and Double-expedition property. Adaptiveness makes it sensitive to only actual number of failures so that it provides fast termination for more number of inputs when there are fewer failures (a common case in practice). The double-expedition property facilitates two-step decision in addition to one-step decision by running two condition-based mechanisms in parallel. To the best of our knowledge, double-expedition property is the new concept introduced by this paper, and DEX is the first algorithm having such a feature. Although DEX takes four steps at worst in well-behaved runs while existing one-step algorithms take only three, it is expected to work efficiently because the worst-case does not occur so often in practice.

Lecture Notes in Computer Science, 2015

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 uses neither signatures nor additional computational power (such as random numbers, failure detectors, additional sheduling assumption, or additional synchrony assumption). 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 satisfying the following property: if the set of a non-faulty process is a singleton containing value v, the set of any non-faulty process contains v. 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 uses a single instance of the underlying binary consensus, and tolerates message reordering by Byzantine processes.

Acta Informatica, 2016

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 uses neither signatures nor additional computational power (such as random numbers, failure detectors, additional sheduling assumption, or additional synchrony assumption). 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 satisfying the following property: if the set of a non-faulty process is a singleton containing value v, the set of any non-faulty process contains v. 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 uses a single instance of the underlying binary consensus, and tolerates message reordering by Byzantine processes.

This paper establishes the first theorem relating resilience, time complexity and authentication in distributed computing. We study consensus algorithms that tolerate Byzantine failures and arbitrary long periods of asynchrony. We measure the ability of processes to reach a consensus decision in a minimal number of rounds of information exchange, as a function of (a) their ability to use authentication and (b) the number of actual process failures in those rounds, as well as of (c) the total number of failures tolerated and (d) the system constellation. The constellations considered distinguish different roles of processes, such that we can directly derive a meaningful bound on the time complexity of implementing robust general services using several replicas coordinated through consensus. To prove our theorem, we establish certain lower bounds and we give algorithms that match these bounds. The algorithms are all variants of the same generic asynchronous Byzantine consensus algorithm, which is interesting in its own right.