Difficulty Adjustment Algorithms in Cryptocurrency Protocols

As of this writing, the algorithm employed for difficulty adjustment in the CryptoNote reference code is known by the Monero Research Lab to be flawed. We describe and illustrate the nature of the flaw and recommend a solution. By dishonestly reporting timestamps, attackers can gain disproportionate control over network difficulty. We verify this route of attack by auditing the CryptoNote reference difficulty adjustment code, which, we reimplement in the Python programming language. We use a stochastic model of blockchain growth to test the CryptoNote reference difficulty formula against the more traditional Bitcoin difficulty formula. This allows us to test our difficulty formula against various hash rate scenarios. This research bulletin has not undergone peer review, and reflects only the results of internal investigation.