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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Notes
- 1.
We believe this is a folklore result that to our knowledge, this bound follows from a result in [CGK+23] (Theorem 3.1). Moreover, we would like to emphasize that since our main result is a strengthening of the lifting Lemma of [YZ21], we can also show that our result concerning the bound of this problem is stronger than the bound derived from [YZ21].
- 2.
It is also equivalent to \({H_{x_k, \varTheta _k}}\). However, due to our description of the simulator, \(H_{(x_j, x_k), (\varTheta _j, \varTheta _k)}\) is more natural to work with.
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Acknowledgements
J.G. was partially supported by NSF SaTC grants no. 2001082 and 2055694. F.S. was partially supported by NSF grant no. 1942706 (CAREER). J.G. and F.S. were also partially support by Sony by means of the Sony Research Award Program. A.C. acknowledges support from the National Science Foundation grant CCF-1813814, from the AFOSR under Award Number FA9550-20-1-0108 and the support of the Quantum Advantage Pathfinder (QAP) project, with grant reference EP/X026167/1 and the UK Engineering and Physical Sciences Research Council.
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Cojocaru, A., Garay, J., Liu, Q., Song, F. (2025). Improved Quantum Lifting by Coherent Measure-and-Reprogram. In: Chung, KM., Sasaki, Y. (eds) Advances in Cryptology – ASIACRYPT 2024. ASIACRYPT 2024. Lecture Notes in Computer Science, vol 15492. Springer, Singapore. https://doi.org/10.1007/978-981-96-0947-5_6
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