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Several emerging PoW blockchain protocols rely on a "parallel-chain"architecture for scaling, where instead of a single chain, multiple chains arerun in parallel and aggregated. A key requirement of practical PoW blockchainsis to adapt to mining power variations over time. In this paper, we considerthe design of provably secure parallel-chain protocols which can adapt to suchmining power variations.  The Bitcoin difficulty adjustment rule adjusts the difficulty target of blockmining periodically to get a constant mean inter-block time. Whilesuperficially simple, the rule has proved itself to be sophisticated andsuccessfully secure, both in practice and in theory. We show that naturaladaptations of the Bitcoin adjustment rule to the parallel-chain case open thedoor to subtle, but catastrophic safety and liveness breaches. We uncover ameta-design principle that allow us to design variable mining difficultyprotocols for three popular PoW blockchain proposals (Prism, OHIE, andFruitchains) inside a common rubric.  The principle has three components:(M1) a pivot chain, based on which blocksin all chains choose difficulty, (M2) a monotonicity condition for referencingpivot chain blocks and (M3) translating additional protocol aspects from usinglevels (depth) to using "difficulty levels". We show that protocols employing asubset of these principles may have catastrophic failures. The security of thedesigns is also proved using a common rubric - the key technical challengeinvolves analyzing the interaction between the pivot chain and the otherchains, as well as bounding the sudden changes in difficulty target experiencedin non-pivot chains. We empirically investigate the responsivity of the newmining difficulty rule via simulations based on historical Bitcoin data, andfind that the protocol very effectively controls the forking rate across allthe chains.

Securing Parallel-chain Protocols under Variable Mining Power