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Block withholding resilience

Author

Listed:
  • Cyril Grunspan

    (De Vinci Research Center)

  • Ricardo Pérez-Marco

    (IMJ-PRG)

Abstract

It has been known for some time that the Nakamoto consensus as implemented in the Bitcoin protocol is not totally aligned with the individual interests of the participants. More precisely, it has been shown that block withholding mining strategies can exploit the difficulty adjustment algorithm of the protocol and obtain an unfair advantage. However, we show that a modification of the difficulty adjustment formula taking into account orphan blocks makes honest mining the only optimal strategy. Surprisingly, this is still true when orphan blocks are rewarded with an amount smaller to the official block reward. This gives an incentive to signal orphan blocks. The results are independent of the connectivity of the attacker.

Suggested Citation

  • Cyril Grunspan & Ricardo Pérez-Marco, 2025. "Block withholding resilience," Digital Finance, Springer, vol. 7(1), pages 43-60, March.
    • Handle: RePEc:spr:digfin:v:7:y:2025:i:1:d:10.1007_s42521-025-00124-9
    DOI: 10.1007/s42521-025-00124-9
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    References listed on IDEAS

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    1. Albrecher Hansjoerg & Goffard Pierre-Olivier, 2022. "On the Profitability of Selfish Blockchain Mining Under Consideration of Ruin," Operations Research, INFORMS, vol. 70(1), pages 179-200, January.
    2. Cyril Grunspan & Ricardo Pérez-Marco, 2023. "Profit Lag and Alternate Network Mining," Lecture Notes in Operations Research, in: Panos Pardalos & Ilias Kotsireas & William J. Knottenbelt & Stefanos Leonardos (ed.), Mathematical Research for Blockchain Economy, pages 115-132, Springer.
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      More about this item

      Keywords

      Bitcoin; Blockchain; Proof-of-work; Selfish mining; Martingale;
      All these keywords.

      JEL classification:

      • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
      • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
      • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Sytsems; Standards; Regimes; Government and the Monetary System
      • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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