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Selfish Mining and Dyck Words in Bitcoin and Ethereum Networks

Authors Cyril Grunspan, Ricardo Pérez-Marco

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Markov processes
Keywords
  • Bitcoin
  • Blockchain
  • Ethereum
  • Proof-of-Work
  • Selfish Mining
  • Stubborn Mining
  • Apparent Hashrate
  • Revenue Ratio
  • Catalan Distributions
  • Dyck Words
  • Random Walk

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Abstract

The main goal of this article is to present a direct approach for the formula giving the long-term apparent hashrates of Selfish Mining strategies using only elementary probabilities and combinatorics, more precisely, Dyck words. We can avoid computing stationary probabilities on Markov chain, nor stopping times for Poisson processes as in previous analysis. We do apply these techniques to other bockwithholding strategies in Bitcoin, and then, we consider also selfish mining in Ethereum.

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Cyril Grunspan and Ricardo Pérez-Marco. Selfish Mining and Dyck Words in Bitcoin and Ethereum Networks. In International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2019). Open Access Series in Informatics (OASIcs), Volume 71, pp. 11:1-11:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/OASIcs.Tokenomics.2019.11

Author Details

Cyril Grunspan
  • Léonard de Vinci, Research Center, Paris - La Défense, France
Ricardo Pérez-Marco
  • CNRS, IMJ-PRG, Univ. Paris 7, Paris, France

References

  1. I. Eyal and E. G. Sirer. Majority is not enough: bitcoin mining is vulnerable. Commun. ACM, 61(7):95-102, 2018. URL: https://doi.org/10.1145/3212998.
  2. C. Grunspan and R. Pérez-Marco. On profitability of Selfish mining. arXiv, 2018. URL: http://arxiv.org/abs/1805.08281.
  3. C. Grunspan and R. Pérez-Marco. On profitability of Stubborn mining. arXiv, 2018. URL: http://arxiv.org/abs/1808.01041.
  4. C. Grunspan and R. Pérez-Marco. On profitability of Trailing mining. arXiv, 2018. URL: http://arxiv.org/abs/1811.09322.
  5. C. Grunspan and R. Pérez-Marco. Selfish mining in Ethereum. arXiv, 2019. URL: http://arxiv.org/abs/1904.13330.
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  8. K. Nayak, S. Kumar, A. Miller, and E. Shi. Stubborn Mining: Generalizing Selfish Mining and Combining with an Eclipse Attack. In IEEE European Symposium on Security and Privacy, EuroS&P 2016, Saarbrücken, Germany, March 21-24, 2016, pages 305-320. IEEE, 2016. URL: https://doi.org/10.1109/EuroSP.2016.32.
  9. J. Niu and C. Feng. Selfish Mining in Ethereum. arXiv, 2019. URL: http://arxiv.org/abs/1901.04620.
  10. F. Ritz and A. Zugenmaier. The Impact of Uncle Rewards on Selfish Mining in Ethereum. In 2018 IEEE European Symposium on Security and Privacy Workshops, EuroS&P Workshops 2018, London, United Kingdom, April 23-27, 2018, pages 50-57. IEEE, 2018. URL: https://doi.org/10.1109/EuroSPW.2018.00013.
  11. Y. Sompolinsky and A. Zohar. Secure High-Rate Transaction Processing in Bitcoin. In Rainer Böhme and Tatsuaki Okamoto, editors, Financial Cryptography and Data Security - 19th International Conference, FC 2015, San Juan, Puerto Rico, January 26-30, 2015, Revised Selected Papers, volume 8975 of Lecture Notes in Computer Science, pages 507-527. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-47854-7_32.
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