Temporary Power Adjusting Withholding Attack

We consider the block withholding attacks on pools, more specifically the state-of-the-art Power Adjusting Withholding (PAW) attack. We propose a generalization called Temporary PAW (T-PAW) where the adversary withholds a fPoW from pool mining at most $T$-time even when no other block is mined. We show that PAW attack corresponds to $T\to\infty$ and is not optimal. In fact, the extra reward of T-PAW compared to PAW improves by an unbounded factor as adversarial hash fraction $\alpha$, pool size $\beta$ and adversarial network influence $\gamma$ decreases. For example, the extra reward of T-PAW is 22 times that of PAW when an adversary targets a pool with $(\alpha,\beta,\gamma)=(0.05,0.05,0)$. We show that honest mining is sub-optimal to T-PAW even when there is no difficulty adjustment and the adversarial revenue increase is non-trivial, e.g., for most $(\alpha,\beta)$ at least $1\%$ within $2$ weeks in Bitcoin even when $\gamma=0$ (for PAW it was at most $0.01\%$). Hence, T-PAW exposes a significant structural weakness in pooled mining-its primary participants, small miners, are not only contributors but can easily turn into potential adversaries with immediate non-trivial benefits.