Elaboration of selfish-mine strategy

A. V. Cheremushkin

Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 71-77.

Résumé

As it was shown by Ittay Eyal and Emin Gün Sirer, the Bitcoin mining protocol is not incentive-compatible, because there exists an attack in which colluding miners obtain a revenue larger than their fair share. We describe an elaboration of Selfish-Mine Strategy and present an extended model of selfish mining based on independency hypothesis: both groups are made their work independently from each other. We describe a new state machine modelling selfish pool strategy. Let the selfish pool has mining power of $p$, $0$, and the others of $(1-p)$. We also consider the situation in which the others mine a block on the previously private branch (frequency $\gamma(1-p)$), and the others mine a block on the public branch (frequency $(1-\gamma)(1-p)$). Main result is an elaboration of an interval, in which selfish miners will earn more than their relative mining power: 1) for a given $p$, a pool of size $p$ obtains a revenue larger than its relative size for $p$ in the following range: $0 p \le 0{.}429$ (the left bound coinsides with $\gamma =1$, and the right bound coinsides with $\gamma =0$); 2) for a given $p$, a pool of size $p$ obtains a revenue larger than a revenue of other group in the following range: $0{.}358 \le p \le 0{.}449$.

Détail

Keywords: blockchain, mining, Markov model, state machine.

Bibliographie

[1] Ittay E., Emin G. S., Majority is Not Enough: Bitcoin Mining is Vulnerable, 2013, arXiv: 1311.0243 | Zbl

[2] Ittay E., Emin G. S., “Majority is not enough: bitcoin mining is vulnerable”, Financial Cryptography and Data Security, 18th Intern. Conf. (Christ Church, Barbados, March 3–7, 2014), 436–454 | Zbl

[3] Ittay E., Emin G. S., “Majority is not enough: bitcoin mining is vulnerable”, Commun. ACM, 61:7 (2018), 95–102 | DOI