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arXiv · 2302.12821

Quantum trapdoor functions from classical one-way functions

Andrea Coladangelo
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Abstract

We formalize and study the notion of a quantum trapdoor function. This is an efficiently computable unitary that takes as input a "public" quantum state and a classical string $x$, and outputs a quantum state. This map is such that (i) it is hard to invert, in the sense that it is hard to recover $x$ given the output state (and many copies of the public state), and (ii) there is a classical trapdoor that allows efficient inversion. We show that a quantum trapdoor function can be constructed from any quantum-secure one-way function. A direct consequence of this result is that, assuming just the existence of quantum-secure one-way functions, there exists a public-key encryption scheme with a (pure) quantum public key.

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Andrea Coladangelo. 2023-02-24. Quantum trapdoor functions from classical one-way functions. https://arxiv.org/abs/2302.12821

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