Quantum-Computable One-Way Functions without One-Way Functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911158510813184 |
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| author | Kretschmer, William Qian, Luowen Tal, Avishay |
| author_facet | Kretschmer, William Qian, Luowen Tal, Avishay |
| contents | We construct a classical oracle relative to which $\mathsf{P} = \mathsf{NP}$ but quantum-computable quantum-secure trapdoor one-way functions exist. This is a substantial strengthening of the result of Kretschmer, Qian, Sinha, and Tal (STOC 2023), which only achieved single-copy pseudorandom quantum states relative to an oracle that collapses $\mathsf{NP}$ to $\mathsf{P}$. For example, our result implies multi-copy pseudorandom states and pseudorandom unitaries, but also classical-communication public-key encryption, signatures, and oblivious transfer schemes relative to an oracle on which $\mathsf{P}=\mathsf{NP}$. Hence, in our new relativized world, classical computers live in "Algorithmica" whereas quantum computers live in "Cryptomania," using the language of Impagliazzo's worlds.
Our proof relies on a new distributional block-insensitivity lemma for $\mathsf{AC^0}$ circuits, wherein a single block is resampled from an arbitrary distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-Computable One-Way Functions without One-Way Functions Kretschmer, William Qian, Luowen Tal, Avishay Quantum Physics Computational Complexity Cryptography and Security We construct a classical oracle relative to which $\mathsf{P} = \mathsf{NP}$ but quantum-computable quantum-secure trapdoor one-way functions exist. This is a substantial strengthening of the result of Kretschmer, Qian, Sinha, and Tal (STOC 2023), which only achieved single-copy pseudorandom quantum states relative to an oracle that collapses $\mathsf{NP}$ to $\mathsf{P}$. For example, our result implies multi-copy pseudorandom states and pseudorandom unitaries, but also classical-communication public-key encryption, signatures, and oblivious transfer schemes relative to an oracle on which $\mathsf{P}=\mathsf{NP}$. Hence, in our new relativized world, classical computers live in "Algorithmica" whereas quantum computers live in "Cryptomania," using the language of Impagliazzo's worlds. Our proof relies on a new distributional block-insensitivity lemma for $\mathsf{AC^0}$ circuits, wherein a single block is resampled from an arbitrary distribution. |
| title | Quantum-Computable One-Way Functions without One-Way Functions |
| topic | Quantum Physics Computational Complexity Cryptography and Security |
| url | https://arxiv.org/abs/2411.02554 |