A. Pinar Ozisik

A. Pinar Ozisik, George Bissias, Brian Levine

We make several contributions that quantify the real-time hash rate and therefore the consensus of a blockchain. We show that by using only the hash value of blocks, we can estimate and measure the hash rate of all miners or individual miners, with quanti able accuracy. We apply our techniques to the Ethereum and Bitcoin blockchains; our solution applies to any proof-of-work-based blockchain that relies on a numeric target for the validation of blocks. We also show that if miners regularly broadcast status reports of their partial proof-of- work, the hash rate estimates are signi cantly more accurate at a cost of slightly higher bandwidth. Whether using only the blockchain, or the additional information in status reports, merchants can use our techniques to quantify in real-time the threat of double-spend attacks.

A. Pinar Ozisik, Brian Neil Levine

The fundamental attack against blockchain systems is the double-spend attack. In this tutorial, we provide a very detailed explanation of just one section of Satoshi Nakamoto's original paper where the attack's probability of success is stated. We show the derivation of the mathematics relied upon by Nakamoto to create a model of the attack. We also validate the model with a Monte Carlo simulation, and we determine which model component is not perfect.

George Bissias, Brian Neil Levine, A. Pinar Ozisik et al.

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. Our model quantifies the importance of several factors that determine the attack's success, including confirmation depth, attacker mining power, and any 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 sum of coin turned-over (between individuals) in the blocks, but more difficult by the increasing proof of work required. In recent blockchain data, we observed a median block turnover value of 6 BTC. Based on this value, a merchant requiring a single confirmation is protected against only attackers that can increase the current mining power by 1% or less. However, similar analysis shows that a merchant that requires a much longer 72 confirmations (~12 hours) will eliminate all potential profit for any double-spend attacker adding mining power less than 40% of the current mining power.