Double spend races

Cyril Grunspan (1) , Ricardo Pérez-Marco (2, 3)

1 ESILV - École Supérieure d'Ingénierie Léonard de Vinci
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 CNRS - Centre National de la Recherche Scientifique

We correct the double spend race analysis given in Nakamoto's foun-dational 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 the first proof of the exponential decay on the number of confirmations and find an asymptotic formula. Larger number of confirmations are necessary compared to those given by Nakamoto.

Mots clés: mining; proof-of-work; Regularized Incomplete Beta Function; Bitcoin; blockchain; double spend

Domaines: Cryptographie et sécurité [cs.CR]; Probabilités [math.PR]; Finance quantitative [q-fin.CP]; Gestion des risques [q-fin.RM]

Cyril Grunspan, Ricardo Pérez-Marco. Double spend races. International Journal of Theoretical and Applied Finance, 2018. ⟨hal-01456773⟩