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In the first part of the paper, we show a generic compiler that transformsany oracle algorithm that can query multiple oracles adaptively, i.e., candecide on which oracle to query at what point dependent on previous oracleresponses, into a static algorithm that fixes these choices at the beginning ofthe execution. Compared to naive ways of achieving this, our compiler controlsthe blow-up in query complexity for each oracle individually, and causes a verymild blow-up only.  In the second part of the paper, we use our compiler to show the security ofthe very efficient hash-based split-key PRF proposed by Giacon, Heuer andPoettering (PKC 2018), in the quantum random-oracle model. Using a split-keyPRF as the key-derivation function gives rise to a secure KEM combiner. Thus,our result shows that the hash-based construction of Giacon et al. can besafely used in the context of quantum attacks, for instance to combine awell-established but only classically-secure KEM with a candidate KEM that isbelieved to be quantum-secure.  Our security proof for the split-key PRF crucially relies on ouradaptive-to-static compiler, but we expect our compiler to be useful beyondthis particular application. Indeed, we discuss a couple of other, knownresults from the literature that would have profitted from our compiler, inthat these works had to go though serious complications in order to deal withadaptivity.

Adaptive versus Static Multi-oracle Algorithms, and Quantum Security of a Split-key PRF