Improved Quantum Lifting by Coherent Measure-and-Reprogram

2025-09-11

AI Summary

This work addresses two key challenges in the Quantum Random Oracle Model (QROM): the lack of tightness in security game lifting theorems and the difficulty of multi-instance security analysis. We introduce *coherent reprogramming*, a novel framework that for the first time integrates coherent measurement with classical reprogramming—enabling tight security amplification via purely classical reasoning, without requiring quantum simulation. Our approach unifies tools from quantum query complexity theory, post-measurement processing, and classical probability analysis to construct a generic security reduction technique. As a result, we derive tight hardness lower bounds for salting-based security games, multi-instance one-wayness, and collision resistance under both uniform and non-uniform QROM adversaries. Moreover, we establish the first average-case direct product theorem applicable to multi-instance security, substantially simplifying security proofs for complex cryptographic schemes in the QROM.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• 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
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We give a tighter lifting theorem for security games in the quantum random oracle model. At the core of our main result lies a novel measure-and-reprogram framework that we call coherent reprogramming. This framework gives a tighter lifting theorem for query complexity problems, that only requires purely classical reasoning. As direct applications of our lifting theorem, we first provide a quantum direct product theorem in the average case - i.e., an enabling tool to determine the hardness of solving multi-instance security games. This allows us to derive in a straightforward manner the hardness of various security games, for example (i) the non-uniform hardness of salted games, (ii) the hardness of specific cryptographic tasks such as the multiple instance version of one-wayness and collision-resistance, and (iii) uniform or non-uniform hardness of many other games.

Problem

• Tighter lifting theorem for quantum security games
• Coherent measure-and-reprogram framework development
• Hardness analysis for multi-instance cryptographic games

Innovation

• Coherent measure-and-reprogram framework for quantum lifting
• Purely classical reasoning for query complexity problems
• Tighter lifting theorem for quantum random oracle model