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 of the honest network. 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 a threat as long as the chance to make 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 finitetime 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 how a DS attack at any proportion of computing power can be made profitable. Given one’s transaction value, the results can also be used to assess the risk of a DS attack. An example of profitable DS attack against BitcoinCash is provided.
Highlights
A blockchain is a distributed ledger which has originated from the desire to find a novel alternative to centralized ledgers such as transactions through third parties [1]
In a blockchain network based on the proof-of-work (PoW) mechanism, each miner verifies transactions and tries to put them into a block and mold the block to an existing chain by solving a cryptographic puzzle
From Equation (13), the probability distribution function (PDF) of TDSA requires the probabilities of two random events; one is the state progression time Ti in Equation (5); and the other is the event that a given state index i satisfies
Summary
A blockchain is a distributed ledger which has originated from the desire to find a novel alternative to centralized ledgers such as transactions through third parties [1]. In a blockchain network based on the proof-of-work (PoW) mechanism, each miner verifies transactions and tries to put them into a block and mold the block to an existing chain by solving a cryptographic puzzle. This series of processes is called mining. To double spend, attackers need to replace the status-quo chain in the network with their new one, after taking the goods or services. The presence of such computing resource rental services significantly reduce the cost of making a profit from double spending This is because renting a required computing power for a few hours is much cheaper than building such a computing network. We follow the definition of DS attack in [1,6], and we need to develop a new set of mathematical tools for precise analysis of attack profitability that we aim to report in this paper
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