Universal construction of a full quantum one-way function

Classical one-way function is a fundamental part of cryptography. Its one-wayness is threatened by the emerging quantum computers. Quantum one-way function (QOWF) was proposed to solve this dilemma. It is computable but almost irreversible in quantum polynomial time. However, there is not a purely full quantum one-way function which takes quantum states as input and output and does not transform information between quantum information and classical information during execution. In this paper, we propose a universal construction of full quantum one-way function. Quantum obfuscation is the critical operation to the one-wayness of this scheme, which can hide partial information of a quantum circuits. The new full QOWF directly transforms information between quantum information and is easy to be implemented in a real quantum platform. Moreover, it is more suitable for quantum cryptographic schemes than previous QOWF. The new full QOWF is used for quantum message authentication which is proved to be secure against forgery attack. The work demonstrates that quantum obfuscation is beneficial to the construction of a full QOWF and full QOWF will further play an important role in quantum cryptography and quantum computation.