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

2024-01-25

arXiv.org

AI Summary

This work investigates the quantum security of pseudorandom generators (PRGs) constructed in the random oracle (RO) model: if such a PRG is unconditionally secure against classical polynomial-query adversaries, does it remain secure against quantum adversaries? Method: The authors establish the first general quantum lifting theorem—demonstrating that classical unconditional security directly implies quantum unconditional security. Their key technical insight is that pseudodeterministic quantum RO algorithms can be efficiently simulated by classical algorithms with asymptotically matching query complexity; they further extend this simulation result to the broader setting where the PRG itself may be queried quantumly. Contribution/Results: This yields the first rigorous, generic security guarantee for RO-based post-quantum cryptographic constructions—including hash functions and key derivation functions—bridging the theoretical gap between classical security analyses and realistic quantum threats.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

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.

Problem

• Study quantum security of PRGs from random oracles
• Prove lifting theorem for classical-to-quantum PRG security
• Simulate quantum-oracle algorithms with classical queries

Innovation

• Quantum lifting theorem for PRG security
• Classical simulation of quantum-oracle algorithms
• Security against quantum adversaries with queries