Quote from: DannyHamilton on Today at 07:28:28 PM

Maybe. I'm not 100% convinced yet, but I'm coming around.

Here's how it would work.

For this, it is important to know that block timestamps are governed by a lower bound of the median timestamp of the last 11 blocks plus one second, and an upper bound of 2 hours in the future.

Let's say I am a miner with a small percentage of the hashrate. I mine my own competing chain in secret. It takes me longer than 10 minutes per block, but that's ok. Let's start at the beginning of the next difficulty epoch for the sake of this example.

I mine a block and give it time x. The next block that I mine, I give time x+1 second. The block after that, x+2 seconds. And so on, for 2,015 blocks, up to x+2,015 seconds. The last block of the difficulty epoch I give a timestamp of the current time.

Let's say it took me 60 days to mine those 2,016 blocks. The difficulty now drops by a factor of 4, the maximum allowable change in one retarget. I keep mining, but now consider the timestamps of the last 11 blocks I just found. The last block I just found has a timestamp of the current time, but the 10 blocks before that all have a timestamp of x plus a few seconds, which is now 60 days ago. If we take the median of those 11 blocks, then we still have a timestamp which is 60 days ago.

So I can keep mining blocks, and continue giving all the blocks I find a timestamp of x+1 second, which is 60 days ago. I do this for another 2,015 blocks, and then the last block of the epoch I set to the current time. This time, let's say it took me 15 days to mine those blocks, since the difficulty was lowered by a factor of 4. However, the first block of these 2,016 blocks still has a timestamp of x+some seconds, which is now 75 days ago. So the protocol thinks it took me 75 days to mine these 2,016 blocks, and he difficulty is lowered by another factor of 4. Now consider again the timestamp of the last 11 blocks. The last block has a timestamp of the current time, and the 10 before that have a timestamp of 75 days ago. The median timestamp is still 75 days ago.

So I repeat the process again. Every difficulty epoch I mine 2,015 blocks incrementing the time by 1 second only, and then the last block at the current time. This is all within the rules set out above. Each time we hit a retargeting, the protocol thinks it has taken me longer and longer to find the last 2,016 blocks, and the difficulty drops by a factor of 4 each time. And each time, the median timestamp of my last 11 blocks never moves by more than a few seconds.

Very quickly I can drop the difficulty to 1 and keep it their. I can churn out a block a second for as long as I want. If the rule was to follow the longest chain, then I have now successfully taken over the entire network indefinitely.