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A Nonhomogeneous Poisson Process Modeling for Double Spending Problems of Bitcoin Blockchain



Bitcoin is the most expensive cryptocurrency in the world. It uses the technology of blockchain which functions on the Internet. This system is secured and works by solving the proof of work algorithm that is called mining. This technology uses the Internet to add time-stamp on all online payment transactions, and incorporates an ever-extending proof of work chain as the transaction record. Unless all the proofs of work are updated, the formed transaction records cannot be changed. The double spending problem can be regarded as a race between the attacker and honest nodes. A successful attack happens when the attacker mines blocks faster than the honest nodes do. In this article, we model the cumulative occurrences using a nonhomogeneous Poisson process with two different intensity functions, a power law process and a log linear process. The parameters are estimated by a maximum likelihood method based on real-world data that have not been previously published. We collected observed data from https://btc.com/block, and simulated cumulative occurrences of the attacker and honest nodes respectively in order to find out the empirical probability. It shows that the probability of a successful attack is 0.003 after 36 hours. It is safer for a transaction to wait for 48 hours. It is against the bitcoin protocol that a transaction is not regarded as valid until the transaction is 6 blocks deep. This research provides us better understanding of the probability of a double spending attack, therefore the bitcoin community may institute new and better policies on the basis of our research.

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