Selfish Mining in Multi-Attacker Scenarios: An Empirical Evaluation of Nakamoto, Fruitchain, and Strongchain

TL;DR

The paper tackles the challenge of selfish mining in multi-attacker settings across PoW protocols. It develops a unified stochastic simulation framework to empirically compare Nakamoto, Fruitchain, and Strongchain under one or more selfish miners, varying the propagation factor $\\gamma$. Key findings show Strongchain achieving the highest resistance (e.g., $46\%$ single-attacker threshold and $32\%$ per attacker with two attackers), while Fruitchain substantially improves over Nakamoto (about $38$–$39\%$ single-attacker threshold) and remains largely $\\gamma$-insensitive. The work provides novel multi-attacker thresholds, reveals protocol-dependent defenses, and delivers an open platform for cross-protocol evaluation, offering practical insights for designing more robust blockchain consensus mechanisms.

Abstract

The aim of this work is to enhance blockchain security by deepening the understanding of selfish mining attacks in various consensus protocols, especially the ones that have the potential to mitigate selfish mining. Previous research was mainly focused on a particular protocol with a single selfish miner, while only limited studies have been conducted on two or more attackers. To address this gap, we proposed a stochastic simulation framework that enables analysis of selfish mining with multiple attackers across various consensus protocols. We created the model of Proof-of-Work (PoW) Nakamoto consensus (serving as the baseline) as well as models of two additional consensus protocols designed to mitigate selfish mining: Fruitchain and Strongchain. Using our framework, thresholds reported in the literature were verified, and several novel thresholds were discovered for 2 and more attackers. We made the source code of our framework available, enabling researchers to evaluate any newly added protocol with one or more selfish miners and cross-compare it with already modeled protocols.

Figures (7)

• Figure 1: Selfish mining with a single attacker on Nakamoto's consensus selfish_1.
• Figure 2: Selfish mining with 2 attackers selfish_2_b: rewards of the attacker 1 based on his mining power vs. the mining power of attacker 2.
• Figure 3: Selfish mining with 2+ independent attackers yields new scenarios: (1) multiple ties and (2) cascading release selfish_2_b.
• Figure 4: A Fruitchain's fragment with fruits and blocks fruitchain.
• Figure 5: Fruitchain: longest chain rule; block reward = 9$\times$ fruit reward.