Quantum-Computable One-Way Functions without One-Way Functions

• URL: http://arxiv.org/abs/2411.02554v1
• Date: Mon, 04 Nov 2024 19:40:01 GMT
• Title: Quantum-Computable One-Way Functions without One-Way Functions
• Authors: William Kretschmer, Luowen Qian, Avishay Tal,
• Abstract summary: We construct a classical oracle relative to which $mathsfP = mathsfNP$ but quantum-computable quantum-secure trapdoor one-way functions exist. Our result implies multi-copy pseudorandom states and pseudorandom unitaries, but also classical-communication public-key encryption, signatures, and oblivious transfer schemes.
• Score: 0.6349503549199401
• License:
• Abstract: 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.

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