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Quantum Information Processing

Universal construction of a full quantum one-way function

Yao Tang, Tao Shang, Jianwei Liu

Published Jul 26, 2022• 4 citations
Publisher
DOI
10.1007/s11128-022-03586-7

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One-way functions are fundamental tools for cryptography. Until now, quantum one-way functions have several input-output categories such as “classical-to-classical,” “classical-to-quantum,” and “quantum-to-classical,” which are used for postquantum cryptography or quantum cryptography. However, there are still no intrinsic “quantum-to-quantum” quantum one-way functions. In this article, we propose the full quantum one-way function to design full quantum cryptographic schemes. By concatenating the “quantum-classical” one-way function and the rotation operation of single qubit, the full quantum one-way function has the input and output of quantum states. We prove its one-way property from “easy computation” and “computationally difficult to invert.” Then we apply the full quantum one-way function to quantum identity authentication. Security analysis shows that the proposed quantum identity authentication scheme based on the full quantum one-way function is secure even under active attacks.

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Quantum one-way function (QOWF) was proposed for quantum cryptography, which was computable but almost irreversible in quantum polynomial time. Full quantum one-way function (F-QOWF) is one of the most important models of QOWF, which deals with quantum states. Although the universal construction of full quantum one-way function has been proposed, there is still little further discussion on the entangled input, specific function instantiation and application scenarios of F-QOWF. In this paper, we introduce quantum hypergraph states into the universal construction of F-QOWF. Quantum hypergraph states are highly entangled multi-party states constructed from the hypergraph. By applying quantum hypergraph states to the new F-QOWF, we generalize the universal construction of F-QOWF to entangled states. The application to quantum aggregate signature shows that quantum hypergraph states help the new F-QOWF be well applied to quantum multi-party cryptographic protocols.
One-way functions are fundamental tools for cryptography. Until now, quantum one-way functions have several input-output categories such as “classical-to-classical,” “classical-to-quantum,” and “quantum-to-classical,” which are used for postquantum cryptography or quantum cryptography. However, there are still no intrinsic “quantum-to-quantum” quantum one-way functions. In this article, we propose the full quantum one-way function to design full quantum cryptographic schemes. By concatenating the “quantum-classical” one-way function and the rotation operation of single qubit, the full quantum one-way function has the input and output of quantum states. We prove its one-way property from “easy computation” and “computationally difficult to invert.” Then we apply the full quantum one-way function to quantum identity authentication. Security analysis shows that the proposed quantum identity authentication scheme based on the full quantum one-way function is secure even under active attacks.