ON PROFITABILITY OF NAKAMOTO DOUBLE SPEND

Nakamoto double spend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability and does not make sense from the profitability point of view. The simplest strategy that can be profitable incorporates a stopping threshold when success is unlikely. We solve and compute the exact profitability for this strategy. We compute the minimal amount of the double spend that is profitable. For a given amount of the transaction, we determine the minimal number of confirmations to be requested by the recipient such that this double spend strategy is non-profitable. We find that this number of confirmations is only 1 or 2 for average transactions and a small hashrate of the attacker. This is substantially lower than the original Nakamoto numbers that are widely used and are only based on the success probability instead of the profitability.

[1]  Cyril Grunspan,et al.  On Profitability of Trailing Mining , 2018, ArXiv.

[2]  Gavin Andresen,et al.  An Analysis of Attacks on Blockchain Consensus , 2016, ArXiv.

[3]  Peter G. Taylor,et al.  A Note on Optimal Double Spending Attacks , 2019 .

[4]  Heung-No Lee,et al.  Profitable Double-Spending Attacks , 2019, Applied Sciences.

[5]  Cyril Grunspan,et al.  On profitability of selfish mining , 2018, ArXiv.

[6]  Doron Zeilberger,et al.  A combinatorial-probabilistic analysis of bitcoin attacks* , 2018, Journal of Difference Equations and Applications.

[7]  Cyril Grunspan,et al.  On profitability of stubborn mining , 2018, ArXiv.

[8]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[9]  P. Goffard.  Fraud risk assessment within blockchain transactions , 2019, Advances in Applied Probability.

[10]  Cyril Grunspan,et al.  Double spend races , 2017, International Journal of Theoretical and Applied Finance.

[11]  Satoshi Nakamoto.  Bitcoin : A Peer-to-Peer Electronic Cash System , 2009 .

[12]  Meni Rosenfeld,et al.  Analysis of Hashrate-Based Double Spending , 2014, ArXiv.