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

• URL: http://arxiv.org/abs/2401.14319v3
• Date: Tue, 30 Jan 2024 01:59:39 GMT
• Title: A Quantum "Lifting Theorem" for Constructions of Pseudorandom Generators from Random Oracles
• Authors: Jonathan Katz, Ben Sela,
• Abstract summary: 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 unboundedly many queries to the random oracle, then it is also (unconditionally) secure against quantum adversaries in the same sense.
• Score: 7.454028086083526
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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