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

TL;DR

The paper tackles Byzantine consensus in partially synchronous systems where participants initially know only subsets of the global membership and do not know the fault threshold $f$. It first analyzes the BFT-CUP model under digital signatures (authenticated BFT-CUP), showing that the known graph conditions are insufficient when $f$ is unknown, and introduces a no-threshold variant BFT-CUPFT with an extended knowledge-graph notion. A novel core-based approach replaces the sink concept to guarantee a unique, identifiable core that can safely drive consensus; Discovery and Core-detection protocols enable any correct process to identify the core, after which a PBFT-like consensus on the core ensures termination, validity, and agreement for all correct processes. The work provides impossibility results for unknown $f$ with standard BFT-CUP graphs and offers a constructive protocol and proofs for solving consensus in the BFT-CUPFT model, advancing practical fault-tolerant consensus in hybrid networks. This has significant implications for scalable, permissioned-hybrid systems where full system membership and fault-tolerance parameters are not globally known a priori.

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.

Figures (4)

• Figure 1: Two knowledge connectivity graphs. In each graph, a vertex corresponds to a participant, and the outgoing edges from a vertex $i$ point to the participants that $i$ initially knows; for instance, participant $1$ initially knows participants $2$, $3$, and $4$. Participant $4$ is Byzantine, and others are correct.
• Figure 2: Processes in $\{1,2,3\}$ cannot distinguish between case a (if process $4$ remains silent) and case c (if process $4$ is slow). Likewise, Processes in $\{6,7,8\}$ cannot distinguish cases b and c.
• Figure 3: Processes in $\{2,3,4,6\}$ cannot distinguish between case a (if processes $5$ and $7$ remain silent) and case b (if process $1$ behaves like correct processes but processes $5$ and $7$ are slow).
• Figure 4: Two knowledge connectivity graphs that satisfy the requirements of the BFT-CUPFT model.

Theorems & Definitions (22)

• Definition 1: $k$-One Sink Reducibility ($k$-OSR) PD alchieri_2016
• Theorem 1: alchieri_2016
• Remark 1
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 5
• Theorem 6
• Theorem 7
• proof