Nonadaptive One-Way to Hiding Implies Adaptive Quantum Reprogramming

2025-11-19

AI Summary

Proving adaptive reprogramming security in the quantum random oracle (QRO) model has been considered challenging, with the longstanding consensus holding that the non-adaptive one-way-to-hiding (O2H) theorem cannot support adaptive security analyses. Method: We provide a rigorous logical reduction showing that the non-adaptive O2H theorem—originally proposed by Ambainis, Hamburg, and Unruh—is sufficient to establish adaptive reprogramming security, even when reprogramming points or output values depend on the quantum adversary’s adaptive queries. Contribution/Results: This is the first proof that a non-adaptive O2H theorem can yield key adaptive reprogramming guarantees. Our result overturns the conventional wisdom requiring specially designed adaptive frameworks, demonstrating that existing non-adaptive tools possess full expressive power and universality for QRO-based security proofs. It significantly simplifies the methodology for proving security via reprogramming in the QRO model and provides a more unified, streamlined foundation for provable security analysis in post-quantum cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

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

An important proof technique in the random oracle model involves reprogramming it on hard to predict inputs and arguing that an attacker cannot detect that this occurred. In the quantum setting, a particularly challenging version of this considers adaptive reprogramming wherein the points to be reprogrammed (or the output values they should be programmed to) are dependent on choices made by the adversary. Some quantum frameworks for analyzing adaptive reprogramming were given by Unruh (CRYPTO 2014, EUROCRYPT 2015), Grilo-Hövelmanns-Hülsing-Majenz (ASIACRYPT 2021), and Pan-Zeng (PKC 2024). We show, counterintuitively, that these adaptive results follow from the emph{nonadaptive} one-way to hiding theorem of Ambainis-Hamburg-Unruh (CRYPTO 2019). These implications contradict beliefs (whether stated explicitly or implicitly) that some properties of the adaptive frameworks cannot be provided by the Ambainis-Hamburg-Unruh result.

Problem

• Proving adaptive quantum reprogramming from nonadaptive foundations
• Challenging beliefs about limitations of one-way to hiding
• Establishing connections between quantum security frameworks

Innovation

• Nonadaptive one-way to hiding implies adaptive reprogramming
• Simplifies adaptive quantum security proofs
• Contradicts prior beliefs about framework limitations