By setting the timestamp of the first block in every period to the previous block's timestamp minus a predefined grace period, and assigning minimal legal timestamps to subsequent blocks within the same period, the attacker can artificially adjust the perceived duration it takes to mine a series of blocks. Specifically, for the bulk of the blocks in a period, the timestamps are set to the lowest possible value, essentially zero, except for the last block which is stamped with the current time. This manipulation results in the calculation of the difficulty adjustment being based on the actual mining time of the last 2016 blocks plus the grace period.

The difficulty adjustment formula incorporates this manipulated time span, adjusting the mining difficulty based on the total time observed, which includes the grace period. The efficiency of this attack method is quantified through simulations that demonstrate how the average block interval can be subtly altered. For instance, with a grace period of 600 seconds, the simulation yields an average block interval just slightly below the intended 600-second target. Increasing the grace period to 7200 seconds further decreases the average interval, illustrating the potential impact of this strategy on the blockchain's operation.

This analysis sheds light on a theoretical vulnerability in blockchain protocols, suggesting that even with mechanisms in place to prevent drastic fluctuations in mining difficulty, there exists the possibility for manipulation through coordinated actions by a powerful attacker. The implications of such an attack could extend beyond mere adjustments to the mining difficulty, potentially affecting the security and reliability of the blockchain itself.