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To get the probability the attacker could still catch up now, we multiply the Poisson density for
each amount of progress he could have made by the probability he could catch up from that point
... we proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker ...
To get the probability the attacker could still catch up now, we multiply the Poisson density for each amount of progress he could have made by the probability he could catch up from that point