[Paper Review] Profitable Double-Spending Attacks

Jaehyuk Jang, Heung-No Lee|arXiv (Cornell University)|Mar 5, 2019

Blockchain Technology Applications and Security24 references9 citations

TL;DR

This paper introduces a novel probabilistic framework to analyze the profitability of double-spending (DS) attacks on blockchains using less than 50% of the network's computing power. By deriving a finite-time attack probability model, the authors prove that DS attacks can be profitable at any hash rate proportion, establishing a necessary and sufficient condition for transaction value to make such attacks economically viable—surprisingly, even sub-50% attackers can profit if transaction size and network parameters align.

ABSTRACT

Our aim in this paper is to investigate the profitability of double-spending (DS) attacks that manipulate an a priori mined transaction in a blockchain. It was well understood that a successful DS attack is established when the proportion of computing power an attacker possesses is higher than that the honest network does. What is not yet well understood is how threatening a DS attack with less than 50% computing power used can be. Namely, DS attacks at any proportion can be of a threat as long as the chance to making a good profit exists. Profit is obtained when the revenue from making a successful DS attack is greater than the cost of carrying out one. We have developed a novel probability theory for calculating a finite time attack probability. This can be used to size up attack resources needed to obtain the profit. The results enable us to derive a sufficient and necessary condition on the value of a transaction targeted by a DS attack. Our result is quite surprising: we theoretically show that DS attacks at any proportion of computing power can be made profitable. Given one's transaction size, the results can also be used to assess the risk of a DS attack. An example of the attack resources is provided for the BitcoinCash network.

Motivation & Objective

• To investigate the profitability of double-spending attacks when attackers possess less than 50% of the network's computing power.
• To identify the conditions under which such attacks yield net profit, considering both attack cost and revenue.
• To develop a finite-time probability model that accurately estimates the likelihood of successful double-spending within a given time window.
• To derive a necessary and sufficient condition on transaction value that enables profitability for any attacker's hash rate proportion.
• To provide a practical assessment of attack feasibility and required resources using the BitcoinCash network as a case study.

Proposed method

• The authors develop a new probability theory to compute the finite-time success probability of a double-spending attack, accounting for block mining dynamics and time constraints.
• They model the attacker's mining process as a stochastic race between the attacker's chain and the honest network's chain, using negative binomial and Poisson processes.
• The method incorporates the transaction confirmation depth and the attacker's relative hash rate to calculate the probability of catching up within a target time.
• A cost-benefit analysis is performed by comparing the expected revenue from a successful double-spend against the computational cost of mining the attack chain.
• The framework enables the derivation of a threshold transaction value that makes the attack profitable for any given attacker's hash rate.
• MATLAB code is provided to reproduce the results, ensuring reproducibility and practical applicability of the model.

Experimental results

Research questions

• RQ1 Can double-spending attacks be profitable when the attacker controls less than 50% of the network's computing power?
• RQ2 What is the minimum transaction value required for a double-spending attack to yield a net profit at any given attacker hash rate?
• RQ3 How does the finite-time success probability of a double-spending attack depend on the attacker's relative hash rate and confirmation depth?
• RQ4 What are the required attack resources (e.g., mining power, time) to achieve a desired success probability for a given transaction size?
• RQ5 How can the profitability of a double-spending attack be assessed in real-world blockchain systems like BitcoinCash?

Key findings

• The paper proves theoretically that double-spending attacks can be profitable at any proportion of computing power, even below 50%, as long as the transaction value exceeds a derived threshold.
• A necessary and sufficient condition is derived for transaction value that ensures profitability, depending on the attacker's hash rate and confirmation depth.
• The finite-time attack probability model enables precise estimation of attack success likelihood within a specified time window, improving upon prior asymptotic approximations.
• For the BitcoinCash network, the study provides a concrete example of attack resources required to achieve a 90% success probability on a transaction of a given size.
• The results show that even with low attacker hash rates, profitable attacks are feasible if the transaction value is sufficiently high relative to the cost of mining.
• The framework demonstrates that profitability is not solely determined by computational dominance but also by transaction size and confirmation time.