A Meta-Complexity Characterization of Quantum Cryptography
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916425351823360 |
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| author | Cavalar, Bruno P. Goldin, Eli Gray, Matthew Hall, Peter |
| author_facet | Cavalar, Bruno P. Goldin, Eli Gray, Matthew Hall, Peter |
| contents | We prove the first meta-complexity characterization of a quantum cryptographic primitive. We show that one-way puzzles exist if and only if there is some quantum samplable distribution of binary strings over which it is hard to approximate Kolmogorov complexity. Therefore, we characterize one-way puzzles by the average-case hardness of a uncomputable problem. This brings to the quantum setting a recent line of work that characterizes classical cryptography with the average-case hardness of a meta-complexity problem, initiated by Liu and Pass. Moreover, since the average-case hardness of Kolmogorov complexity over classically polynomial-time samplable distributions characterizes one-way functions, this result poses one-way puzzles as a natural generalization of one-way functions to the quantum setting. Furthermore, our equivalence goes through probability estimation, giving us the additional equivalence that one-way puzzles exist if and only if there is a quantum samplable distribution over which probability estimation is hard. We also observe that the oracle worlds of defined by Kretschmer et. al. rule out any relativizing characterization of one-way puzzles by the hardness of a problem in NP or QMA, which means that it may not be possible with current techniques to characterize one-way puzzles with another meta-complexity problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Meta-Complexity Characterization of Quantum Cryptography Cavalar, Bruno P. Goldin, Eli Gray, Matthew Hall, Peter Cryptography and Security Computational Complexity Quantum Physics We prove the first meta-complexity characterization of a quantum cryptographic primitive. We show that one-way puzzles exist if and only if there is some quantum samplable distribution of binary strings over which it is hard to approximate Kolmogorov complexity. Therefore, we characterize one-way puzzles by the average-case hardness of a uncomputable problem. This brings to the quantum setting a recent line of work that characterizes classical cryptography with the average-case hardness of a meta-complexity problem, initiated by Liu and Pass. Moreover, since the average-case hardness of Kolmogorov complexity over classically polynomial-time samplable distributions characterizes one-way functions, this result poses one-way puzzles as a natural generalization of one-way functions to the quantum setting. Furthermore, our equivalence goes through probability estimation, giving us the additional equivalence that one-way puzzles exist if and only if there is a quantum samplable distribution over which probability estimation is hard. We also observe that the oracle worlds of defined by Kretschmer et. al. rule out any relativizing characterization of one-way puzzles by the hardness of a problem in NP or QMA, which means that it may not be possible with current techniques to characterize one-way puzzles with another meta-complexity problem. |
| title | A Meta-Complexity Characterization of Quantum Cryptography |
| topic | Cryptography and Security Computational Complexity Quantum Physics |
| url | https://arxiv.org/abs/2410.04984 |