This paper presents a novel leaderless protocol (FPC-BI: Fast Probabilistic Consensus within Byzantine Infrastructures) with a low communicational complexity and which allows a set of nodes to come to a consensus on a value of a single bit. The paper makes the assumption that part of the nodes are , and are thus controlled by an adversary who intends to either delay the consensus, or break it. This defines that at least a couple of honest nodes come to different conclusions. We prove that, nevertheless, the protocol works with high probability when its parameters are suitably chosen. Along this the paper also provides explicit estimates on the probability that the protocol finalizes in the consensus state in a given time. This protocol could be applied to reaching consensus in decentralized cryptocurrency systems. A special feature of it is that it makes use of a sequence of random numbers which are either provided by a trusted source or generated by the nodes themselves using some decentralized random number generating protocol. This increases the overall trustworthiness of the infrastructure. A core contribution of the paper is that it uses a consensus to obtain a consensus on the value of a bit, and which can relate to the validity of a transaction.
There is a wide range of classical work on (probabilistic) Byzantine consensus protocols @cite_10 @cite_24 @cite_0 @cite_6 @cite_2 @cite_17 . The disadvantage of the approach of these papers is, however, that they typically require that the nodes exchange @math messages in each round (which means @math messages for each node). In the situation where the communicational complexity matters, this can be a major barrier.
@cite_6 @cite_24 @cite_0 @cite_2 @cite_10 @cite_17
2030698973 2553854225 2058322902 2077963568
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. One 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. This paper presents two kinds of Byzantine asynchronous consensus protocols using two types of oracles, namely, a common coin that provides processes with random values and a failure detector oracle. Both allow the processes to decide in one communication step in favorable circumstances. The first is a randomized protocol for an oblivious scheduler model that assumes n > 6f. The second one is a failure detector-based protocol that assumes n > tif. 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. While several consensus algorithms exist for the Byzantine Generals Problem, specifically as it pertains to distributed payment systems, many suffer from high latency induced by the requirement that all nodes within the network communicate synchronously. In this work, we present a novel consensus algorithm that circumvents this requirement by utilizing collectively-trusted subnetworks within the larger network. We show that the “trust” required of these subnetworks is in fact minimal and can be further reduced with principled choice of the member nodes. In addition, we show that minimal connectivity is required to maintain agreement throughout the whole network. The result is a low-latency consensus algorithm which still maintains robustness in the face of Byzantine failures. We present this algorithm in its embodiment in the Ripple Protocol. We present the first protocol that reaches asynchronous Byzantine consensus in two communication steps in the common case. We prove that our protocol is optimal in terms of both number of communication steps and number of processes for two-step consensus. The protocol can be used to build a replicated state machine that requires only three communication steps per request in the common case. Further, we show a parameterized version of the protocol that is safe despite f Byzantine failures and, in the common case, guarantees two-step execution despite some number t of failures (t les f). We show that this parameterized two-step consensus protocol is also optimal in terms of both number of communication steps and number of processes Byzantine Agreement has become increasingly important in establishing distributed properties when errors may exist in the systems. Recent polynomial algorithms for reaching Byzantine Agreement provide us with feasible solutions for obtaining coordination and synchronization in distributed systems. In this paper the amount of information exchange necessary to ensure Byzantine Agreement is studied. This is measured by the total number of messages the participating processors have to send in the worst case. In algorithms that use a signature scheme, the number of signatures appended to messages are also counted. First it is shown that O( nt ) is a lower bound for the number of signatures for any algorithm using authentication, where n denotes the number of processors and t the upper bound on the number of faults the algorithm is supposed to handle. For algorithms that reach Byzantine Agreement without using authentication this is even a lower bound for the total number of messages. If n is large compared to t , these bounds match the upper bounds from previously known algorithms. For the number of messages in the authenticated case we prove the lower bound O( n + t 2 ). Finally algorithms that achieve this bound are presented.