DAG-based Consensus with Asymmetric Trust [Extended Version]

TL;DR

This work addresses the challenge of achieving DAG-based consensus under asymmetric trust, where each participant defines its own trust assumptions via asymmetric quorum systems. It shows that naively replacing threshold quorums in existing gather primitives fails, motivating a novel constant-round asymmetric gather and a fully asymmetric DAG-based consensus built on it. The authors introduce asymmetric common-core primitives, establish correctness and liveness proofs, and prove that the protocol achieves randomized asynchronous consensus with expected constant rounds, bounded by the smallest quorum size via $|\,\mathcal{P}\,| / c(\mathbb{Q})$. By reworking the gather, common coin, and reliable broadcast components to the asymmetric setting, the work extends the DAG-Rider framework to heterogeneous trust, offering a path toward high-throughput, permissioned-open networks. The results have practical significance for open blockchain-like systems where participants may have divergent trust relationships, enabling robust and efficient consensus under realistic trust models.

Abstract

In protocols with asymmetric trust, each participant is free to make its own individual trust assumptions about others, captured by an asymmetric quorum system. This contrasts with ordinary, symmetric quorum systems and with threshold models, where all participants share the same trust assumption. It is already known how to realize reliable broadcasts, shared-memory emulations, and binary consensus with asymmetric quorums. In this work, we introduce Directed Acyclic Graph (DAG)-based consensus protocols with asymmetric trust. To achieve this, we extend the key building-blocks of the well-known DAG-Rider protocol to the asymmetric model. Counter to expectation, we find that replacing threshold quorums with their asymmetric counterparts in the existing constant-round gather protocol does not result in a sound asymmetric gather primitive. This implies that asymmetric DAG-based consensus protocols, specifically those based on the existence of common-core primitives, need new ideas in an asymmetric-trust model. Consequently, we introduce the first asymmetric protocol for computing a common core, equivalent to that in the threshold model. This leads to the first randomized asynchronous DAG-based consensus protocol with asymmetric quorums. It decides within an expected constant number of rounds after an input has been submitted, where the constant depends on the quorum system.

Figures (4)

• Figure 1: Fail-prone system that leads to no common core in an asymmetric execution of gather. Each process (row) has only one fail-prone set, which is represented by the processes in striped red on its row. Processes in blue represent the canonical quorum associated to said fail-prone set.
• Figure 2: Values possessed by each process after one round of hearing messages coming from its quorums. Also denoted as $S$ sets
• Figure 3: Values possessed by each process after the second round of receiving messages from one of their $P \setminus F_i$. Also denoted as $T$ sets
• Figure 4: Values possessed by each process after the third round of receiving messages from the processes in $P \setminus F_i$. Also denotes as $U$ sets. Observe that there is no set $S^+$ (where $S^+$ is a quorum of a wise process) that is received by all processes. This happens because all quorums of all processes contain at least one element in the range $[16, 30]$ and as can be observed in the picture, all processes are missing at least one element from this range in their received values.

Theorems & Definitions (38)

• definition 1
• definition 2
• definition 3: $B^3$-condition
• theorem 1
• definition 4: Gather
• definition 5: Asymmetric Gather
• lemma 1
• lemma 2
• proof
• lemma 3