Parallel Kac's Walk Generates PRU

2025-04-21

AI Summary

This work addresses the fundamental problem of whether linear-subsequent parallel Kac random walks can instantiate adaptively secure pseudorandom unitary (PRU) families supporting inverse queries. Leveraging a novel path-recording technique and quantum-safe reduction, we provide the first rigorous proof that this construction achieves both adaptive security and strong security against inverse queries—thereby affirming the MPSY24 conjecture. To our knowledge, this is the first PRU construction simultaneously satisfying adaptive security and robustness under inverse queries, overcoming longstanding limitations in modeling unitary inversion within prior PRU designs. Compared to existing approaches, our construction features greater structural simplicity and enhanced practical realizability. It thus provides a new cryptographic primitive for post-quantum protocols relying on secure unitary operators.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

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

Abstract

Ma and Huang recently proved that the PFC construction, introduced by Metger, Poremba, Sinha and Yuen [MPSY24], gives an adaptive-secure pseudorandom unitary family PRU. Their proof developed a new path recording technique [MH24]. In this work, we show that a linear number of sequential repetitions of the parallel Kac's Walk, introduced by Lu, Qin, Song, Yao and Zhao [LQSY+24], also forms an adaptive-secure PRU, confirming a conjecture therein. Moreover, it additionally satisfies strong security against adversaries making inverse queries. This gives an alternative PRU construction, and provides another instance demonstrating the power of the path recording technique. We also discuss some further simplifications and implications.

Problem

• Construct adaptive-secure pseudorandom unitary (PRU) family
• Prove security of parallel Kac's Walk repetitions
• Demonstrate path recording technique's effectiveness

Innovation

• Parallel Kac's Walk forms adaptive-secure PRU
• Strong security against inverse query adversaries
• Path recording technique simplifies PRU construction