On profitability of selfish mining

Abstract

We review the so called selfish mining strategy in the Bitcoin network and compare its profitability to honest mining. We build a rigorous profitability model for repetition games. The time analysis of the attack has been ignored in the previous literature based on a Markov model, but is critical. Using martingale's techniques and Doob Stopping Time Theorem we compute the expected duration of attack cycles. We discover a remarkable property of the bitcoin network: no strategy is more profitable than the honest strategy before a difficulty adjustment. So selfish mining can only become profitable afterwards, thus it is an attack on the difficulty adjustment algorithm. We propose an improvement of Bitcoin protocol making it immune to selfish mining attacks. We also study miner's attraction to selfish mining pools. We calculate the expected duration time before profit for the selfish miner, a computation that is out of reach by the previous Markov models.

Proof-of-Reputation: An Alternative Consensus Mechanism for Blockchain Systems

“…Selfish Mining attacks [36], [37], [38] is a mining strategy where a group of miners collude to exert power over the entire blockchain in order to increase their revenue. In selfish mining attacks, two groups exist side-by-side: an honest group of miners following the standard protocol and a colluding group that follows the selfish mining strategy.…”

Bitcoin Selfish Mining and Dyck Words

“…Selfish mining (in short SM) is a particular non-stop strategy of block withholding strategy described in [1] which exploits a flaw in the Bitcoin protocol in the difficulty adjustment formula [4]. The strategy is made of attack cycles.…”

“…As explained in [4] the good objective function based on sound economics principles in order to compare profitabilities of mining strategies with repetition is the revenue ratio…”

“…In [1], first a stationary probability is computed for a Markov chain. In [4] we use martingale techniques and consider Poisson processes and associated stopping times. The revenue ratio is then computed at once using Doob's stopping time theorem.…”

On profitability of stubborn mining

“…In our previous article [3] we gave a rigorous foundation for the profitability analysis of alternative mining strategies in the Bitcoin network [6]. As for games with repetition, it depends on the proper analysis of the revenue and the duration over attack cycles.…”