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arXiv · 2509.09896

Improved Quantum Lifting by Coherent Measure-and-Reprogram

Alexandru Cojocaru·Juan Garay·Qipeng Liu·Fang Song
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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.

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Alexandru Cojocaru, Juan Garay, Qipeng Liu, Fang Song. 2025-09-11. Improved Quantum Lifting by Coherent Measure-and-Reprogram. https://doi.org/10.1007/978-981-96-0947-5_6

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