arXiv:1702.02867Date: 2017-02-17Author(s): Cyril Grunspan, Ricardo Pérez-MarcoLink to PaperAbstractWe correct the double spend race analysis given in Nakamoto's foundational Bitcoin article and give a closed-form formula for the probability of success of a double spend attack using the Regularized Incomplete Beta Function. We give a proof of the exponential decay on the number of confirmations, often cited in the literature, and find an asymptotic formula. Larger number of confirmations are necessary compared to those given by Nakamoto. We also compute the probability conditional to the known validation time of the blocks. This provides a finer risk analysis than the classical one.References[1] ABRAMOVITCH, M.; STEGUN, I.A.; Hanbook of Mathematical Functions, Dover, NY, 1970.[2] DLMF; Digital Library of Mathematical Functions, http://dlmf.nist.gov[3] FELLER, W.; An introduction to probability theory and its applications, 2nd edition, Wiley, 1971.[4] GAUTSCHI, W.; Some elementary inequalities relating to the gamma and incomplete gamma function, J. Math. and Phys., 38, p.77-81, 1959.[5] GRUNSPAN, C.; PEREZ-MARCO, R.; ´ Satoshi Risk Tables, arXiv:1702.04421, 2017.[6] LOPEZ, J.L.; SESMA, J.; ´ Asymptotic expansion of the incomplete beta function for large values of the first parameter, Integral Transforms and Special Functions, 8, 3-4, p.233-236, 1999.[7] NAKAMOTO, S.; Bitcoin: A Peer-to-Peer Electronic Cash System, www.bitcoin.org/ bitcoin.pdf, 2009.[8] ROSENFELD, M.; Analysis of hashrate-based double spending, ArXiv 1402.2009v1, 2014. via /r/myrXiv http://bit.ly/2TyoUHi
