Lower bounds and impossibility results in distributed computing are both intellectually challenging and practically important. Hundreds if not thousands of proofs appear in the literature, but surprisingly, the vast majority of them apply to deterministic algorithms only. Probabilistic protocols have been around for at least four decades and are receiving a lot of attention with the emergence of blockchain systems. Nonetheless, we are aware of only a handful of randomized lower bounds.
In this paper we provide a formal framework for reasoning about randomized distributed algorithms. We generalize the notion of indistinguishability, the most useful tool in deterministic lower bounds, to apply to a probabilistic setting. We apply this framework to prove a result of independent interest. Namely, we completely characterize the quality of decisions that protocols for a randomized multi-valued Consensus problem can guarantee in an asynchronous environment with Byzantine faults. We use the new notion to prove a lower bound on the probability at which it can be guaranteed that honest parties will not decide on a possibly bogus value. Finally, we show that the bound is tight by providing a protocol that matches it.
In the Byzantine agreement problem, n nodes with possibly different input values aim to reach agreement on a common value in the presence of t < n/3 Byzantine nodes which represent arbitrary failures in the system. This paper introduces a generalization of Byzantine agreement, where the input values of the nodes are preference rankings of three or more candidates. We show that consensus on preferences, which is an important question in social choice theory, complements already known results from Byzantine agreement. In addition preferential voting raises new questions about how to approximate …
Byzantine general problem is the core problem of the consensus algorithm, and many protocols are proposed recently to improve the decentralization level, the performance and the security of the blockchain. There are two challenging issues when the blockchain is operating in practice. First, the outcomes of the consensus algorithm are usually related to the incentive model, so whether each participant's value has an equal probability of being chosen becomes essential. However, the issues of fairness are not captured in the traditional security definition of Byzantine agreement. Second, the bloc…
Approximate byzantine consensus is a fundamental problem of distributed computing. This paper presents a novel algorithm for approximate byzantine consensus, called Relay-ABC. The algorithm allows machines to achieve approximate consensus to arbitrary exactness in the presence of byzantine failures. The algorithm relies on the usage of a relayed messaging system and signed messages with unforgeable signatures that are unique to each node. The use of signatures and relays allows the strict necessary network conditions of traditional approximate byzantine consensus algorithms to be circumvented.…
This paper describes a simple and efficient asynchronous Binary Byzantine faulty tolerant consensus algorithm. In the algorithm, non-faulty nodes perform an initial broadcast followed by a executing a series of rounds each consisting of a single message broadcast plus the computation of a global random coin using threshold signatures. Each message is accompanied by a cryptographic proof of its validity. Up to one third of the nodes can be faulty and termination is expected in a constant number of rounds. An optimization is described allowing the round message plus the coin message to be combin…
Lattice Aggregation in Distributed Verification under Crash and Byzantine Failures
Posgrado en Ciencia e Ingeniería de la Computación, Universidad Nacional Autónoma de México（墨西哥国立自治大学计算机科学与工程研究生项目）；Department of Computer Science and Engineering, Michigan State University（密歇根州立大学计算机科学工程系）；Instituto de Matemáticas, Universidad Nacional Autónoma de México（墨西哥国立自治大学数学研究所）
The celebrated result of Fischer, Lynch and Paterson is the fundamental lower bound for asynchronous fault tolerant computation: any 1-crash resilient asynchronous agreement protocol must have some (possibly measure zero) probability of not terminating. In 1994, Ben-Or, Kelmer and Rabin published a proof-sketch of a lesser known lower bound for asynchronous fault tolerant computation with optimal resilience against a Byzantine adversary: if $n\le 4t$ then any t-resilient asynchronous verifiable secret sharing protocol must have some non-zero probability of not terminating. Our main contributio…
In this paper, we study the Byzantine lattice agreement problem in synchronous systems. The lattice agreement problem in crash failure model has been studied both in synchronous and asynchronous systems, which leads to the current best upper bound of $O(\log f)$ rounds in both systems. However, very few algorithmic results are known for the lattice agreement problem in Byzantine failure model. The paper [Nowak et al., DISC, 2019] first gives an algorithm for a variant of the lattice agreement problem on cycle-free lattices that tolerates up to $f < n/(h(X) + 1)$ Byzantine faults, where $n$ is …
Exact Byzantine consensus problem requires that non-faulty processes reach agreement on a decision (or output) that is in the convex hull of the inputs at the non-faulty processes. It is well-known that exact consensus is impossible in an asynchronous system in presence of faults, and in a synchronous system, n>=3f+1 is tight on the number of processes to achieve exact Byzantine consensus with scalar inputs, in presence of up to f Byzantine faulty processes. Recent work has shown that when the inputs are d-dimensional vectors of reals, n>=max(3f+1,(d+1)f+1) is tight to achieve exact Byzantine …
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 Byzantine, 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.…
