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Difficulty control for blockchain-based consensus systems


Crypto-currencies like Bitcoin have recently attracted a lot of interest. A crucial ingredient into such systems is the “mining” of a Nakamoto blockchain. We model mining as a Poisson process with time-dependent intensity and use this model to derive predictions about block times for various hash-rate scenarios (exponentially rising hash rate being the most important). We also analyse Bitcoin’s method to update the “network difficulty” as a mechanism to keep block times stable. Since it yields systematically too fast blocks for exponential hash-rate growth, we propose a new method to update difficulty. Our proposed method performs much better at ensuring stable average block times over longer periods of time, which we verify both in simulations of artificial growth scenarios and with real-world data. Besides Bitcoin itself, this has practical benefits particularly for systems like Namecoin. It can be used to make name expiration times more predictable, preventing accidental loss of names.

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The author would like to thank the Bitcoin and Namecoin communities for valuable input as well as pointing out that more stable name expiration times are an interesting research question in the first place. This work is supported by the Austrian Science Fund (FWF) and the International Research Training Group IGDK 1754.

Author information

Correspondence to Daniel Kraft.


Appendix A: Notation used in the models

Table 3

Appendix B:: Compliance with ethical standards


This work was funded by the Austrian Science Fund (FWF). No funding was received in relation to this work apart from the author’s employment at the University of Graz.

Conflict of Interest::

The author currently serves voluntarily as the main developer of the Namecoin project. No salary is received as part of that involvement.

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Kraft, D. Difficulty control for blockchain-based consensus systems. Peer-to-Peer Netw. Appl. 9, 397–413 (2016).

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  • Crypto-currency
  • Bitcoin mining
  • Namecoin
  • Nakamoto blockchain
  • Poisson process