Though designed with security in mind, blockchains are vulnerable to various kinds of attacks, especially when the network computational power is low. Selfish mining is one of the most rudimentary and notorious attacks, which maliciously renders blocks found by honest miners orphaned by strategically withholding and revealing the found blocks. In this paper, we analyze the profitability of selfish mining under the checkpoint mechanism—a mechanism that has been adopted as a finality gadget by many blockchains like Ethereum and Bitcoin Cash. We develop a rigorous analysis method and conduct quantitative evaluations in various scenarios to explore the mechanism's suppression effect on selfish mining. The results illustrate that the checkpoint mechanism can restrict the profit of selfish mining and increase the threshold of computational power that makes selfish mining profitable, suggesting that it is a practical defense mechanism against selfish mining.

We study the maximin share (MMS) fair allocation of $m$ indivisible tasks to $n$ agents who have costs for completing the assigned tasks. It is known that exact MMS fairness cannot be guaranteed, and so far the best-known approximation for additive cost functions is $\frac{13}{11}$ by Huang and Segal-Halevi [EC, 2023]; however, beyond additivity, very little is known. In this work, we first prove that no algorithm can ensure better than $\min\{n,\frac{\log m}{\log \log m}\}$-approximation if the cost functions are submodular. This result also shows a sharp contrast with the allocation of goods where constant approximations exist as shown by Barman and Krishnamurthy [TEAC, 2020] and Ghodsi et al. [AIJ, 2022]. We then prove that for subadditive costs, there always exists an allocation that is $\min\{n,\lceil\log m\rceil\}$-approximation, and thus the approximation ratio is asymptotically tight. Besides multiplicative approximation, we also consider the ordinal relaxation, 1-out-of-$d$ MMS, which was recently proposed by Hosseini et al. [JAIR and AAMAS, 2022]. Our impossibility result implies that for any $d\ge 2$, a 1-out-of-$d$ MMS allocation may not exist. Due to these hardness results for general subadditive costs, we turn to studying two specific subadditive costs, namely, bin packing and job scheduling. For both settings, we show that constant approximate allocations exist for both multiplicative and ordinal relaxations of MMS.

A smart contract cannot be modified once deployed. Bugs in deployed smart contracts may cause devastating consequences. For example, the infamous reentrancy bug in the DAO contract allows attackers to arbitrarily withdraw ethers, which caused millions of dollars loss. Currently, the main countermeasure against contract bugs is to thoroughly detect and verify contracts before deployment, which, however, cannot defend against unknown bugs. These detection methods also suffer from possible false negative results.