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Fraud risk assessment within blockchain transactions

Part of: General field theory Stochastic processes

Published online by Cambridge University Press:  07 August 2019

Pierre-O. Goffard
Pierre-O. Goffard*
Affiliation:
University of California, Santa Barbara
*
*Postal address: Institut de Science Financière et d’Assurances, Université Lyon 1, 50 Avenue Tony Garnier, 69007 Lyon, France.
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Abstract

The probability of successfully spending twice the same bitcoins is considered. A double-spending attack consists in issuing two transactions transferring the same bitcoins. The first transaction, from the fraudster to a merchant, is included in a block of the public chain. The second transaction, from the fraudster to himself, is recorded in a block that integrates a private chain, exact copy of the public chain up to substituting the fraudster-to-merchant transaction by the fraudster-to-fraudster transaction. The double-spending hack is completed once the private chain reaches the length of the public chain, in which case it replaces it. The growth of both chains are modelled by two independent counting processes. The probability distribution of the time at which the malicious chain catches up with the honest chain, or, equivalently, the time at which the two counting processes meet each other, is studied. The merchant is supposed to await the discovery of a given number of blocks after the one containing the transaction before delivering the goods. This grants a head start to the honest chain in the race against the dishonest chain.

Keywords

Bitcoin blockchaindouble-spending problemrisk theoryorder statistic point processesrenewal processesboundary crossing problems

MSC classification

Primary: 60G55: Point processes
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 12E10: Special polynomials
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 2 , June 2019 , pp. 443 - 467
Copyright
© Applied Probability Trust 2019 

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