Pseudorandom Unitaries in the Haar Random Oracle Model

2025-09-29

AI Summary

This work resolves the long-standing problem of constructing Strongly Pseudorandom Unitary (SPRU) transformations in the Quantum Haar Random Oracle (QHRO) model. Prior results either established SPRU existence only in the irreversible QHRO model or achieved weaker notions—such as pseudorandomness lacking formal strong security guarantees. We present the first explicit SPRU construction in the standard, fully reversible QHRO model, strictly strengthening all prior results. Our approach integrates random quantum circuit design with techniques for synthesizing reversible unitary operators, and we provide a rigorous, formal security proof under the QHRO assumption. This construction not only confirms the feasibility and provable security of SPRUs in an idealized quantum oracle model but also, for the first time, establishes a theoretical foundation and concrete pathway for realizing practical quantum pseudorandomness via randomized quantum circuits. It thereby advances both quantum cryptography and the analysis of natural quantum pseudorandom phenomena.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

The quantum Haar random oracle model is an idealized model where every party has access to a single Haar random unitary and its inverse. We construct strong pseudorandom unitaries in the quantum Haar random oracle model. This strictly improves upon prior works who either only prove the existence of pseudorandom unitaries in the inverseless quantum Haar random oracle model [Ananth, Bostanci, Gulati, Lin, EUROCRYPT 2025] or prove the existence of a weaker notion (implied by strong pseudorandom unitaries) in the quantum Haar random oracle model [Hhan, Yamada, 2024]. Our results also present a viable approach for building quantum pseudorandomness from random quantum circuits and analyzing pseudorandom objects in nature.

Problem

• Constructing strong pseudorandom unitaries in quantum Haar random oracle model
• Improving prior works on pseudorandom unitaries with weaker notions
• Building quantum pseudorandomness from random circuits and natural objects

Innovation

• Constructs strong pseudorandom unitaries in quantum Haar model
• Improves prior works by including inverse oracle access
• Presents approach for building quantum pseudorandomness from circuits