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ON PROFITABILITY OF NAKAMOTO DOUBLE SPEND

Published online by Cambridge University Press:  15 February 2021

Cyril Grunspan Open the ORCID record for Cyril Grunspan [Opens in a new window]  and
Ricardo Pérez-Marco
Cyril Grunspan
Affiliation:
Léonard de Vinci, Pôle University, Research Center, Paris-La Défense, France E-mail: [email protected]
Ricardo Pérez-Marco
Affiliation:
CNRS, IMJ-PRG, Paris, France E-mail: [email protected]
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Abstract

Nakamoto doublespend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability. The simplest strategy that avoids this risk incorporates a stopping threshold when success is unlikely. We compute the exact profitability and the minimal double spend that is profitable for this strategy. For a given amount of the transaction, we determine the minimal number of confirmations to be requested by the recipient that makes the double-spend strategy non-profitable. This number of confirmations is only 1 or 2 for average transactions and for a small relative hashrate of the attacker. This is substantially lower than the original Nakamoto number, which is about six confirmations and is widely used. Nakamoto analysis is only based on the success probability of the attack instead of on a profitability analysis that we carry out.

Keywords

BitcoinblockchainGambler's ruinmartingaleproof-of-workrandom walk
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 732 - 746
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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