Zhihuai Chen

Zhihuai Chen, Siyao Guo, Qian Li et al.

We show how to distinguish circuits with $\log k$ negations (a.k.a $k$-monotone functions) from uniformly random functions in $\exp\left(\tilde{O}\left(n^{1/3}k^{2/3}\right)\right)$ time using random samples. The previous best distinguisher, due to the learning algorithm by Blais, Cannone, Oliveira, Servedio, and Tan (RANDOM'15), requires $\exp\big(\tilde{O}(n^{1/2} k)\big)$ time. Our distinguishers are based on Fourier analysis on \emph{slices of the Boolean cube}. We show that some "middle" slices of negation-limited circuits have strong low-degree Fourier concentration and then we apply a variation of the classic Linial, Mansour, and Nisan "Low-Degree algorithm" (JACM'93) on slices. Our techniques also lead to a slightly improved weak learner for negation limited circuits under the uniform distribution.

Zhihuai Chen, Bo Li, Xiaohan Shan et al.

The arisen of Bitcoin has led to much enthusiasm for blockchain research and block mining, and the extensive existence of mining pools helps its participants (i.e., miners) gain reward more frequently. Recently, the mining pools are proved to be vulnerable for several possible attacks, and pool block withholding attack is one of them: one strategic pool manager sends some of her miners to other pools and these miners pretend to work on the puzzles but actually do nothing. And these miners still get reward since the pool manager can not recognize these malicious miners. In this work, we revisit the game-theoretic model for pool block withholding attacks and propose a revised approach to reallocate the reward to the miners. Fortunately, in the new model, the pool managers have strong incentive to not launch such attacks. We show that for any number of mining pools, no-pool-attacks is always a Nash equilibrium. Moreover, with only two minority mining pools participating, no-pool-attacks is actually the unique Nash equilibrium.