The mathematics of Bitcoin

We survey recent results on the mathematical stability of Bitcoin protocol. Profitability and probability of a double spend are estimated in closed form with classical special functions. The stability of Bitcoin mining rules is analyzed and several theorems are proved using martingale and combinatorics techniques. In particular, the empirical observation of the stability of the Bitcoin protocol is proved. This survey article on the mathematics of Bitcoin is published by the Newsletter of the European Mathematical Society, vol.115, 2020, p.31-37. Continuation of arXiv:1601.05254 (EMS Newsletter, 100, 2016 p.32).

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

[2]  Cyril Grunspan,et al.  Selfish Mining in Ethereum , 2019, ArXiv.

[3]  Cyril Grunspan,et al.  ON PROFITABILITY OF NAKAMOTO DOUBLE SPEND , 2019, Probability in the Engineering and Informational Sciences.

[4]  Cyril Grunspan,et al.  Bitcoin Selfish Mining and Dyck Words , 2019, ArXiv.

[5]  Chen Feng,et al.  Selfish Mining in Ethereum , 2019, 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS).

[6]  Kartik Nayak,et al.  Stubborn Mining: Generalizing Selfish Mining and Combining with an Eclipse Attack , 2016, 2016 IEEE European Symposium on Security and Privacy (EuroS&P).

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

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

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

[10]  Ricardo Pérez-Marco,et al.  Bitcoin and Decentralized Trust Protocols , 2016, ArXiv.

[11]  Emin Gün Sirer,et al.  Majority is not enough , 2013, Financial Cryptography.

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

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

[14]  Cyril Grunspan,et al.  Satoshi Risk Tables , 2017, ArXiv.

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