arXiv:1701.03977Date: 2017-01-15Author(s): A. Pinar Ozisik, Brian Neil LevineLink to PaperAbstractThe fundamental attack against blockchain systems is the double-spend attack. In this tutorial, we provide a very detailed explanation of just one section of Satoshi Nakamoto's original paper where the attack's probability of success is stated. We show the derivation of the mathematics relied upon by Nakamoto to create a model of the attack. We also validate the model with a Monte Carlo simulation, and we determine which model component is not perfect.References[1] A. W. F. Edwards. Pascal’s problem: The ‘gambler’s ruin’. Revue Internationale de Statistique, 51(1):73–79 (http://bit.ly/2CRUxpL), Apr 1983.[2] W. Feller. An Introduction to Probability Theory and its Applications: Volume I, volume 3. John Wiley & Sons London-New York-Sydney-Toronto, 1968.[3] M. J. Fischer, N. A. Lynch, and M. S. Paterson. Impossibility of distributed consensus with one faulty process. Journal of the ACM (JACM), 32(2):374–382, 1985.[4] S. Nakamoto. Bitcoin: A Peer-to-Peer Electronic Cash System. http://bit.ly/1d4HkH2, May 2009.[5] A. P. Ozisik, G. Andresen, G. Bissias, A. Houmansadr, and B. Levine. A Secure, Efficient, and Transparent Network Architecture for Bitcoin. Technical Report UM-CS-2016-006, University of Massachusetts Amherst, 2016.[6] L. Rey-Bellet. Gambler’s ruin and bold play. http://bit.ly/2CRaJYr, June 7 2016.[7] K. Sigman. Gambler’s ruin problem. http://bit.ly/2Tvx8j8, June 7 2016.[8] R. E. Walpole, R. H. Myers, S. L. Myers, and K. Ye. Probability & Statistics for Engineers & Scientists. Prentice Hall, (See pg. 161 for a discussion of Poisson experiments), 9th edition, 2012. via /r/myrXiv http://bit.ly/2CRXSVH
