Optimal-Selfish-Mining-Strategies-in-Bitcoin

This is an implementation of the Financial Crypto 2016 paper "Optimal Selfish Mining Strategies in Bitcoin" by Ayelet Sapirshtein, Yonatan Sompolinsky, and Aviv Zohar. It computes the optimal selfish mining strategy and the maximum relative revenue of the selfish miner under a given set of parameters: alphaPower, selfish miner's mining power share, and gammaRatio, the proportion of honest mining power that would work on the selfish chain during a tie. As the program can only compute block races up to a certain length, the relative revenue is approached by a pair of strict lower and upper bounds.

If you are implementing a selfish mining defense, the developer Ren Zhang would appreciate if you can compare the performance of your defense with his "Publish or Perish" (evaluation code) defense and future defenses. He will put the papers describing future defenses on his google scholar page, and the evaluation code in his github repository.

Quick Start

If you only need the results:

1. Make sure you have matlab.
2. Download the MDP toolbox for matlab, decompress it, put it in a directory such as '/users/yourname/Desktop/matlab/MDPtoolbox/fsroot/MDPtoolbox', copy the path.
3. Download the code, open Matlab, change the working dir to the dir of the code.
4. Open Init.m, paste your MDP toolbox path in the first line

addpath('/users/yourname/Desktop/matlab/MDPtoolbox/fsroot/MDPtoolbox');

5. Modify alphaPower and gammaRatio in Init.m, make sure 0<alphaPower<=0.49, 0<=gammaRatio<=1.
6. Run Init.m.

Implementation

Structure

• Init.m The portal of the program. The parameters are defined here.
• st2stnum.m A state in the paper is denoted as a tuple (a, h, fork). However in MDP, a state needs to be encoded as a number. This function converts a state tuple into the relevant number.
• stnum2st.m This function does the reverse conversion.
• SolveStrategy.m The code that actually computes the optimal selfish mining strategies. The structure of the code follows the paper.

Variants

Some simple modifications of the code allow us to compute the maximum relative revenue of some certain strategies, or within certain defenses.

• SM1 strategy outlined in the FC'13 paper "Majority is not Enough: Bitcoin Mining is Vulnerable" by Ittay Eyal and Emin Gun Sirer: force the attacker to override when h>1 and a-h=1, force the attacker to adopt when h>a, force the attacker to match when h>1 and a=h.
• The uniform tie breaking defense in the FC'13 paper: fix gammaRatio=0.5, allow the attacker to match even if fork~=relevant.

Citation

Sapirshtein A., Sompolinsky Y., Zohar A. (2017) Optimal Selfish Mining Strategies in Bitcoin. In: Grossklags J., Preneel B. (eds) Financial Cryptography and Data Security. FC 2016. Lecture Notes in Computer Science, vol 9603. Springer, Berlin, Heidelberg

@inproceedings{sapirshtein2015optimal,
  title={Optimal Selfish Mining Strategies in {B}itcoin},
  author={Sapirshtein, Ayelet and Sompolinsky, Yonatan and Zohar, Aviv},
  booktitle={International Conference on Financial Cryptography and Data Security},
  pages={515--532},
  year={2016},
  organization={Springer}
}

Chadès, I., Chapron, G., Cros, M. J., Garcia, F., & Sabbadin, R. (2014). MDPtoolbox: a multi‐platform toolbox to solve stochastic dynamic programming problems. Ecography, 37(9), 916-920.

@article{chades2014mdptoolbox,
  title={MDPtoolbox: a multi-platform toolbox to solve stochastic dynamic programming problems},
  author={Chad{\`e}s, Iadine and Chapron, Guillaume and Cros, Marie-Jos{\'e}e and Garcia, Fr{\'e}d{\'e}rick and Sabbadin, R{\'e}gis},
  journal={Ecography},
  volume={37},
  number={9},
  pages={916--920},
  year={2014},
  publisher={Wiley Online Library}
}

Disclaimer

Any mistake in the code is due to the developer.

License

This code is licensed under GNU GPLv3.