[Paper Review] Bitcoin Blockchain Dynamics: the Selfish-Mine Strategy in the Presence of Propagation Delay

Johannes Göbel, Paul Keeler+2 more|arXiv (Cornell University)|May 20, 2015

Blockchain Technology Applications and Security8 references4 citations

TL;DR

This paper analyzes the selfish-mine strategy in Bitcoin's blockchain under propagation delay, showing that block-hiding increases orphan block rates and reduces overall block production. It demonstrates that even with high mining power, selfish pools may earn less revenue due to inefficiencies, and identifies propagation delay variability as a key factor in enabling the strategy's success through parameter γ.

ABSTRACT

In the context of the `selfish-mine' strategy proposed by Eyal and Sirer, we study the effect of propagation delay on the evolution of the Bitcoin blockchain. First, we use a simplified Markov model that tracks the contrasting states of belief about the blockchain of a small pool of miners and the `rest of the community' to establish that the use of block-hiding strategies, such as selfish-mine, causes the rate of production of orphan blocks to increase. Then we use a spatial Poisson process model to study values of Eyal and Sirer's parameter $γ$, which denotes the proportion of the honest community that mine on a previously-secret block released by the pool in response to the mining of a block by the honest community. Finally, we use discrete-event simulation to study the behaviour of a network of Bitcoin miners, a proportion of which is colluding in using the selfish-mine strategy, under the assumption that there is a propagation delay in the communication of information between miners.

Motivation & Objective

• To study the impact of propagation delay on the selfish-mine strategy in Bitcoin's blockchain.
• To analyze how block-hiding strategies affect orphan block production and network efficiency.
• To evaluate the profitability of selfish-mine under realistic network delays and varying network conditions.
• To investigate the role of parameter γ, representing honest miners' response to secret blocks, in enabling or undermining the strategy.
• To validate analytical findings using discrete-event simulation under realistic mining dynamics.

Proposed method

• A simplified Markov model tracks belief states of miners and the broader community to study block-hiding effects on orphan block rates.
• A spatial Poisson process model is used to analyze the parameter γ, representing the fraction of honest miners who mine on a secret block after a public block is discovered.
• The model incorporates propagation delay variability, showing that increased delay variance raises γ significantly.
• Discrete-event simulation models a network of miners, with a fraction using selfish-mine, under realistic communication delays.
• The simulation evaluates long-term block production rates and revenue distribution under honest and selfish mining strategies.
• The analysis assumes constant mining difficulty to isolate the effects of propagation delay and block-hiding.

Experimental results

Research questions

• RQ1 How does propagation delay affect the success rate of the selfish-mine strategy in Bitcoin?
• RQ2 To what extent does block-hiding increase the rate of orphan blocks in the blockchain?
• RQ3 How does variability in propagation delay influence the value of γ, the proportion of honest miners who respond to a secret block?
• RQ4 Under what conditions does selfish mining lead to a net reduction in block production rate despite higher relative revenue?
• RQ5 Can the broader mining community detect selfish-mine behavior through monitoring orphan block rates?

Key findings

• The rate of orphan block production increases significantly when miners use block-hiding strategies like selfish-mine.
• Propagation delay variability causes γ to increase rapidly, making it easier for selfish pools to exploit the network.
• Even with a mining power share above 25%, selfish pools may earn less revenue per hour than they would under honest mining due to reduced block production efficiency.
• The long-term block production rate decreases when selfish-mine is used, indicating a systemic inefficiency despite higher relative rewards.
• The honest community can detect selfish-mine behavior by monitoring an elevated rate of orphan blocks.
• In the absence of difficulty adjustment, selfish mining leads to lower absolute revenue for the pool, even if it captures a larger share of the total.