[Paper Review] A Deep Dive into Blockchain Selfish Mining

Qianlan Bai, Xinyan Zhou+4 more|arXiv (Cornell University)|Nov 1, 2018

Blockchain Technology Applications and Security4 references4 citations

TL;DR

This paper proposes a Markov chain-based model to analyze selfish mining in blockchains with multiple colluding mining pools, showing that the minimum profitable hash rate drops to 21.48% when two selfish miners are symmetric, but increases under asymmetric conditions. It further reveals that profitable returns require a delay of up to 714 days (51 rounds) at 22% hash rate, decreasing to 70 days (5 rounds) at 33%.

ABSTRACT

This paper studies a fundamental problem regarding the security of blockchain on how the existence of multiple misbehaving pools influences the profitability of selfish mining. Each selfish miner maintains a private chain and makes it public opportunistically for the purpose of acquiring more rewards incommensurate to his Hashrate. We establish a novel Markov chain model to characterize all the state transitions of public and private chains. The minimum requirement of Hashrate together with the minimum delay of being profitable is derived in close-form. The former reduces to 21.48% with the symmetric selfish miners, while their competition with asymmetric Hashrates puts forward a higher requirement of the profitable threshold. The profitable delay increases with the decrease of the Hashrate of selfish miners, making the mining pools more cautious on performing selfish mining.

Motivation & Objective

• To investigate how the presence of multiple selfish mining pools affects the profitability threshold of selfish mining.
• To model the transient behavior of selfish mining, including the impact of blockchain difficulty adjustments.
• To determine the minimum hash rate required for selfish mining to be profitable in a competitive environment with multiple misbehaving pools.
• To analyze the time delay until profitability, considering dynamic difficulty adjustments in real-world blockchains like Bitcoin.

Proposed method

• Develops a novel Markov chain model to capture state transitions between public and private chains in a multi-miner environment.
• Models the system with one honest mining pool (Henry) and two selfish mining pools (Alice and Bob), assuming no coordination between them.
• Derives closed-form expressions for the steady-state distribution of chain states and the resulting revenue share for selfish miners.
• Incorporates blockchain difficulty adjustment into the transient analysis to model real-world time delays before profitability.
• Uses mathematical analysis and simulation to validate theoretical thresholds and revenue dynamics.
• Applies a convergence analysis to determine the stable profitable hash rate threshold under symmetric and asymmetric conditions.

Experimental results

Research questions

• RQ1 How does the existence of multiple selfish mining pools affect the minimum hash rate required for profitable selfish mining?
• RQ2 What is the transient time delay until selfish mining becomes profitable, considering difficulty adjustments?
• RQ3 How does asymmetry in hash power between selfish miners influence the profitability threshold?
• RQ4 What is the impact of long private chains on detection risk and revenue in selfish mining?
• RQ5 Can the difficulty adjustment mechanism be exploited or mitigated in the context of multi-pool selfish mining?

Key findings

• The minimum profitable hash rate for two symmetric selfish miners is 21.48%, derived in closed-form using Markov chain modeling.
• When selfish miners have asymmetric hash rates, the profitable threshold increases due to intensified competition.
• Profitability requires a delay of 51 rounds (714 days in Bitcoin) when each selfish miner holds 22% of the total hash rate.
• The profitable delay decreases significantly to 5 rounds (70 days) when each selfish miner’s hash rate increases to 33%.
• Selfish mining is inefficient during the first difficulty adjustment period regardless of hash rate, but becomes profitable after several adjustment cycles.
• The model confirms that the relative and absolute revenue measures are equivalent within acceptable error margins, validating the theoretical approach.