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We study the (quantum) security of pseudorandom generators (PRGs) constructedfrom random oracles. We prove a ``lifting theorem'' showing, roughly, that ifsuch a PRG is unconditionally secure against classical adversaries makingpolynomially many queries to the random oracle, then it is also(unconditionally) secure against quantum adversaries in the same sense. As aresult of independent interest, we also show that any pseudo-deterministicquantum-oracle algorithm (i.e., a quantum algorithm that with high probabilityreturns the same value on repeated executions) can be simulated by acomputationally unbounded but query bounded classical-oracle algorithm withonly a polynomial blowup in the number of queries. This implies as a corollarythat our lifting theorem holds even for PRGs that themselves make quantumqueries to the random oracle.

A Quantum "Lifting Theorem" for Constructions of Pseudorandom Generators from Random Oracles