Sublinear-round Byzantine agreement under corrupt majority
Byzantine agreement (BA) deals with the problem of reaching consensus in a network in the presence of faulty (and malicious) nodes. In particular, the system reaches a BA when the following conditions are satisfied: \par 1.) all honest nodes agree on the same outcome, \par 2.) all honest nodes agree on the sender's output if the sender is honest. It is known that when the number \(t\) of faulty nodes is larger than one third of the total number of nodes the BA is not possible. Nonetheless, it is possible to have an arbitrary number of faulty nodes \(t < n\), provided that an additional setup is considered and that the protocol features \(t+1\) rounds. It is also known that, although \(t+1\) is the optimal bound in the deterministic setting, randomized protocols can run in expected constant rounds when the majority of the nodes is honest, i.e.\ when \(t< n/2\). The present paper deals with the corresponding problem in the absence of an honest majority. Precisely, the authors wonder if ``randomized protocols [can] help to overcome the \((t+1)\)-round complexity lower bound when the majority of nodes can be corrupt''. The only previous results in the sense of sub-linear round complexity are related to the case when \(t=n/2+o(n)\). The authors prove here (see Theorem 1) that, under some cryptographic assumptions in the setting of a public-key infrastructure, \(t\) can be of the form \(t= (1-\varepsilon)n\) for some \(\varepsilon > 0\), provided that a specified number of rounds is considered. For the entire collection see [Zbl 1481.94004].
scientific article; zbMATH DE number 7436974
scientific article