# Quantum trapdoor functions from classical one-way functions

arXiv: https://arxiv.org/abs/2302.12821 · HTML: https://mlsanity.com/paper/2302.12821/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Quantum Solutions to the Privacy vs. Utility Tradeoff](https://mlsanity.com/paper/2307.03118/) (2023)

## Abstract (arXiv)

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.