Several emerging PoW blockchain protocols rely on a "parallel-chain" architecture for scaling, where instead of a single chain, multiple chains are run in parallel and aggregated. A key requirement of practical PoW blockchains is to adapt to mining power variations over time. In this paper, we consider the design of provably secure parallel-chain protocols which can adapt to such mining power variations. The Bitcoin difficulty adjustment rule adjusts the difficulty target of block mining periodically to get a constant mean inter-block time. While superficially simple, the rule has proved itself to be sophisticated and successfully secure, both in practice and in theory. We show that natural adaptations of the Bitcoin adjustment rule to the parallel-chain case open the door to subtle, but catastrophic safety and liveness breaches. We uncover a meta-design principle that allow us to design variable mining difficulty protocols for three popular PoW blockchain proposals (Prism, OHIE, and Fruitchains) inside a common rubric. The principle has three components:(M1) a pivot chain, based on which blocks in all chains choose difficulty, (M2) a monotonicity condition for referencing pivot chain blocks and (M3) translating additional protocol aspects from using levels (depth) to using "difficulty levels". We show that protocols employing a subset of these principles may have catastrophic failures. The security of the designs is also proved using a common rubric - the key technical challenge involves analyzing the interaction between the pivot chain and the other chains, as well as bounding the sudden changes in difficulty target experienced in non-pivot chains. We empirically investigate the responsivity of the new mining difficulty rule via simulations based on historical Bitcoin data, and find that the protocol very effectively controls the forking rate across all the chains.

中文翻译：

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在可变挖掘能力下确保并行链协议的安全

几种新兴的PoW区块链协议依赖于“并行链”架构进行扩展，其中多个链而不是单链并行运行并聚集在一起。实用PoW区块链的关键要求是适应随时间变化的挖掘能力变化。在本文中，我们考虑了可适应这种挖掘能力变化的可证明安全的并行链协议的设计。比特币难度调整规则会定期调整区块挖掘的难度目标，以获取恒定的平均区块间时间。尽管从表面上看很简单，但该规则在实践和理论上都证明自己是复杂的并且成功地确保了安全性。我们显示，比特币调整规则对并行链案例的自然适应为微妙但灾难性的安全性和活力性破坏打开了大门。我们发现了一种元设计原则，该原则使我们能够为一个常见的规则内的三个流行的PoW区块链提案（Prism，OHIE和Fruitchains）设计可变的挖掘难度协议。该原理包括三个部分：（M1）枢纽链，基于该链中所有链中的块选择难度，（M2）用于引用枢纽链块的单调性条件，以及（M3）将其他协议方面从使用级别（深度）转换为使用“难度级别”。我们表明，使用这些原理的子集的协议可能会发生灾难性的故障。设计的安全性还可以通过通用的规则来证明-关键的技术挑战包括分析枢轴链与其他链之间的相互作用，以及限制非枢轴链遇到的困难目标的突然变化。