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

We study the (quantum) security of pseudorandom generators (PRGs) constructed from random oracles. We prove a ``lifting theorem'' showing, roughly, that if such a PRG is unconditionally secure against classical adversaries making polynomially many queries to the random oracle, then it is also (unconditionally) secure against quantum adversaries in the same sense. As a result of independent interest, we also show that any pseudo-deterministic quantum-oracle algorithm (i.e., a quantum algorithm that with high probability returns the same value on repeated executions) can be simulated by a computationally unbounded but query bounded classical-oracle algorithm with only a polynomial blowup in the number of queries. This implies as a corollary that our lifting theorem holds even for PRGs that themselves make quantum queries to the random oracle.

@article{katz2025_2401.14319,
  title={ A Quantum "Lifting Theorem" for Constructions of Pseudorandom Generators from Random Oracles },
  author={ Jonathan Katz and Ben Sela },
  journal={arXiv preprint arXiv:2401.14319},
  year={ 2025 }
}