On Profitability of Nakamoto Double Spend

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.

Blockchain and cryptocurrencies: economic and financial research

“…Nakamoto's model represents a different paradigm, where double-spending attacks-spending the same amount twice-are unlikely, provided some requirements are met (Grunspan and Pérez-Marco 2018). Such repeated attacks prove to be unprofitable, unless one is ready to double-spend enormous amounts on a regular basis-an unreasonable assumption in practice (Grunspan 2021). This is achieved using the proof of work concept, which originates in the design of spam filters (Dwork and Naor 1993).…”