An Analysis of Attacks on Blockchain Consensus

We present and validate a novel mathematical model of the blockchain mining process and use it to conduct an economic evaluation of the double-spend attack, which is fundamental to all blockchain systems. Our analysis focuses on the value of transactions that can be secured under a conventional double-spend attack, both with and without a concurrent eclipse attack. We account for an attacker capable of increasing profits by targeting multiple merchants simultaneously. Our model quantifies the importance of several factors that determine the attack’s success, including confirmation depth, attacker mining power, and a confirmation deadline set by the merchant. In general, the security of a transaction against a double-spend attack increases roughly logarithmically with the depth of the block, made easier by the increasing potential profits, but more difficult by the increasing proof of work required. We find that a merchant requiring a single confirmation is protected against attackers that possess as much as 10% of the mining power, but only provided that the total value of goods at risk for double-spend is less than 100 BTC. A merchant that requires a much longer 55 confirmations (≈9 hours) will prevent an attacker from breaking even unless he possesses more than 35% of the current mining power, or the value of goods at risk exceeds 1M BTC.