Knowledge Connectivity Requirements for Solving BFT Consensus with Unknown Participants and Fault Threshold (Extended Version)

TL;DR

This paper investigates the conditions under which Byzantine Fault Tolerant (BFT) consensus can be achieved in distributed systems where participants have limited initial knowledge and are unaware of the fault threshold, extending previous models.

Contribution

It introduces a new model for BFT consensus without requiring participants to know the fault threshold, and defines necessary and sufficient conditions for knowledge connectivity graphs to solve this problem.

Findings

Identified insufficiency of previous knowledge connectivity conditions for BFT-CUPFT

Proposed new conditions for knowledge connectivity graphs to solve BFT-CUPFT

Designed a protocol for achieving BFT consensus without participants knowing the fault threshold

Abstract

Consensus stands as a fundamental building block for constructing reliable and fault-tolerant distributed services. The increasing demand for high-performance and scalable blockchain protocols has brought attention to solving consensus in scenarios where each participant joins the system knowing only a subset of participants. In such scenarios, the participants' initial knowledge about the existence of other participants can collectively be represented by a directed graph known as knowledge connectivity graph. The Byzantine Fault Tolerant Consensus with Unknown Participants (BFT-CUP) problem aims to solve consensus in those scenarios by identifying the necessary and sufficient conditions that the knowledge connectivity graphs must satisfy when a fault threshold is provided to all participants. This work extends BFT-CUP by eliminating the requirement to provide the fault threshold to the participants. We indeed address the problem of solving BFT consensus in settings where each participant initially knows a subset of participants, and although a fault threshold exists, no participant is provided with this information -- referred to as BFT Consensus with Unknown Participants and Fault Threshold (BFT-CUPFT). With this aim, we first demonstrate that the conditions for knowledge connectivity graphs identified by BFT-CUP are insufficient to solve BFT-CUPFT. Accordingly, we introduce a new type of knowledge connectivity graphs by determining the necessary and sufficient conditions they must satisfy to solve BFT-CUPFT. Furthermore, we design a protocol for solving BFT-CUPFT.