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Paper: Unifying Presampling via Concentration Bounds

Authors:
Siyao Guo
Qian Li
Qipeng Liu
Jiapeng Zhang
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DOI: 10.1007/978-3-030-90459-3_7
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Abstract: Auxiliary-input (AI) idealized models, such as auxiliary-input random oracle model (AI-ROM) and auxiliary-input random permutation model (AI-PRM), play a critical role in assessing non-uniform security of symmetric key and hash function constructions. However, obtaining security bounds in these models is often much more challenging. The presampling technique, introduced by Unruh (CRYPTO' 07), generically reduces security proofs in the auxiliary-input models to much simpler bit-fixing models. This technique has been further optimized by Coretti, Dodis, Guo, Steinberger (EUROCRYPT' 18), and generalized by Coretti, Dodis, Guo (CRYPTO' 18), resulting in powerful tools for proving non-uniform security bounds in various idealized models. We study the possibility of leveraging the presampling technique to the quantum world. To this end, (*) We show that such leveraging will {resolve a major open problem in quantum computing, which is closely related to the famous Aaronson-Ambainis conjecture (ITCS' 11). (*) Faced with this barrier, we give a new but equivalent bit-fixing model and a simple proof of presampling techniques for arbitrary oracle distribution in the classical setting, including AI-ROM and AI-RPM. Our theorem matches the best-known security loss and unifies previous presampling techniques. (*) Finally, we leverage our new classical presampling techniques to a novel ``quantum bit-fixing'' version of presampling. It matches the optimal security loss of the classical presampling. Using our techniques, we give the first post-quantum non-uniform security for salted Merkle-Damgard hash functions and reprove the tight non-uniform security for function inversion by Chung et al. (FOCS' 20).
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BibTeX
@article{tcc-2021-31547,
  title={Unifying Presampling via Concentration Bounds},
  booktitle={Theory of Cryptography;19th International Conference},
  publisher={Springer},
  doi={10.1007/978-3-030-90459-3_7},
  author={Siyao Guo and Qian Li and Qipeng Liu and Jiapeng Zhang},
  year=2021
}