  The pool-hopping attack casts down the expected profits of both the mining
pool and honest miners in Blockchain. The mainstream countermeasures, namely
PPS (pay-per-share) and PPLNS (pay-per-last-N-share), can hedge pool hopping,
but pose a risk to the pool as well as the cost to miners. In this study, we
apply the zero-determinant (ZD) theory to design a novel pooled mining which
offers an incentive mechanism for motivating non-memorial and memorial
evolutionary miners not to switch in pools strategically. In short, our
hopping-proof pooled mining has three unique features: 1) fee-free. No fee is
charged if the miner does not hop. 2) wide applicability. It can be employed in
both prepaid and postpaid mechanisms. 3) fairness. Even the pool can dominate
the game with any miner, he has to cooperate when the miner does not hop among
pools. The fairness of our scheme makes it have long-term sustainability. To
the best of our knowledge, we are the first to propose a hopping-proof pooled
mining with the above three natures simultaneously. Both theoretical and
experimental analyses demonstrate the effectiveness of our scheme.
