Zawy’s Alternating Timestamp Attack

[murch]

@sipa

Interestingly, if the limit were less than eee (so say, it were a 2x or even 2.5x max upward difficulty adjustment), then I think it would be exploitable still. Say it is 2x:

• First window takes \sqrt{2}√2\sqrt{2} times two weeks
• Second window takes \sqrt{2}√2\sqrt{2} times two weeks
• Third window takes minimum legal time (i.e. 2016/6 seconds).

Overall the operation takes 2\sqrt{2} + \epsilon \approx 2.832√2+ϵ≈2.832\sqrt{2} + \epsilon \approx 2.83 windows’ worth of time, but produced 333 windows’ worth of blocks, without ever raising the difficulty above the starting one.

Oh okay, I think I grokked it. You meant that the attacker has 100% of the hashrate? I.e.:

• Take 2 weeks to mine the first difficulty period and post-date it to 2×\sqrt{2} weeks. New difficulty is d_2 = \frac{1}{\sqrt{2}}×d_1.
• Take \frac{2}{\sqrt{2}} = \sqrt{2} weeks to mine the difficulty period, post-date it to 4×\sqrt{2} weeks. d_3 = \frac{1}{\sqrt{2}}×d_2 = \frac{d_1}{2}
• Take 1 week to mine third difficulty period while minimally increasing the timestamp. The difficulty increases maximally to d_4 = 2×d_3 = d_1.

The total elapsed time is 2 + \sqrt(2) + 1 \approx 4.41 weeks, three difficulty periods of blocks have been mined, and the difficulty is back to the original, but the timestamp has progressed by (2×2×\sqrt{2}+\frac{1}{1800}) \approx 5.66 weeks. So, the timestamp is still stuck in the future and we cannot broadcast our blocks?