Abstract
We study the quantum query complexity of finding a collision for a function f whose outputs are chosen according to a distribution with min-entropy k. We prove that \(\varOmega (2^{k/9})\) quantum queries are necessary to find a collision for function f. This is needed in some security proofs in the quantum random oracle model (e.g. Fujisaki-Okamoto transform).
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Acknowledgments
We would like to thank the anonymous reviewers for their comments. This work was supported by the Estonian ICT program 2011–2015 (3.2.1201.13-0022), the European Union through the European Regional Development Fund through the sub-measure “Supporting the development of R&D of info and communication technology”, by the European Social Fund’s Doctoral Studies and Internationalisation Programme DoRa, by the Estonian Centre of Excellence in Computer Science, EXCS.
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Targhi, E.E., Tabia, G.N., Unruh, D. (2016). Quantum Collision-Resistance of Non-uniformly Distributed Functions. In: Takagi, T. (eds) Post-Quantum Cryptography. PQCrypto 2016. Lecture Notes in Computer Science(), vol 9606. Springer, Cham. https://doi.org/10.1007/978-3-319-29360-8_6
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DOI: https://doi.org/10.1007/978-3-319-29360-8_6
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