On Profitability of Nakamoto double spend

TL;DR

This paper analyzes the profitability of Nakamoto double spend strategies, providing exact calculations and showing that fewer confirmations are needed to prevent profitable double spends than previously thought.

Contribution

It introduces a precise profitability model for double spend strategies and determines minimal confirmation numbers to prevent profitable attacks, improving on prior success probability estimates.

Findings

Fewer confirmations (1-2) are sufficient to prevent profitable double spends for small attacker hashrates.

The minimal profitable double spend amount is explicitly computed.

Traditional Nakamoto confirmation numbers are higher than necessary for security.

Abstract

Nakamoto double spend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability and does not make sense from the profitability point of view. The simplest strategy that can be profitable incorporates a stopping threshold when success is unlikely. We solve and compute the exact profitability for this strategy. We compute the minimal amount of the double spend that is profitable. For a given amount of the transaction, we determine the minimal number of confirmations to be requested by the recipient such that this double spend strategy is non-profitable. We find that this number of confirmations is only 1 or 2 for average transactions and a small hashrate of the attacker. This is substantially lower than the original Nakamoto numbers that are widely used and are only based on the success probability instead of the profitability.