Difficulty

Difficulty is a measure used to keep block production at a constant rate, it is the average amount of hashes before a solution is found.

Checking A Block's Proof Of Work

To check a block's PoW hash you interpret the hash as a little endian integer and multiply it by the difficulty, if the result does not overflow the hash is valid¹:

\(Hash * difficulty <= MAXu256 \)

Calculating Difficulty

To calculate difficulty, Monero keeps a window of the last 735² timestamps and cumulative difficulties, if there are not enough blocks, then you just use as many as possible.

The genesis block is skipped for these calculations³ so should not be included in the timestamp / CD list but it is included in the cumulative difficulty of the chain.

If the amount of blocks is less than or equal to 1 then 1 is returned as the difficulty⁴.

The timestamps and cumulative difficulties are then shortened to 720⁵ blocks so that calculations lag 15 blocks behind the chain.

The timestamps are then sorted, in ascending order. We now need to get a time span value to do this we first remove the outliers:

If the number of timestamps is less than or equal to the amount of blocks we are accounting for (600: 720 - 2 * 60) then the lower is set to 0 and the upper is set to the length of timestamps. Otherwise, if we have enough timestamps, the lower and upper is calculated by⁶:

\(lower = \frac{len(timestamps) - 600+1}{2} \)

\(upper = lower + 600 \)

We then get the timestamp at position lower and take this away from the timestamp at position upper -1 to get timeSpan. If timeSpan is 0 we set it to 1⁷.

We also get the cumulative difficulty at position lower and take this away from the cumulative difficulty at position upper -1 to get totalWork.

The next difficulty is then calculated by⁸:

\(difficulty = \frac{totalWork * targetSeconds + timeSpan -1}{timeSpan} \)