Dynamic full quantum one-way function based on quantum circuit mapping

Quantum one-way function provides security for cryptographic protocols in quantum cryptography. Full quantum one-way function is a type of quantum one-way function that maps between quantum states and deals with pure quantum information. It was initially proposed by means of concatenating ‘quantum–classical’ and ‘classical–quantum’ quantum one-way functions. The first full quantum one-way function can be applied to quantum authentication, which uses quantum states to authenticate quantum states directly. However, the concatenation format restricts the implementation and cryptographic applications of this function. Considering the advantage of quantum circuit optimization in implementing quantum circuits to physical quantum devices, we propose a dynamic full quantum one-way function based on quantum circuit mapping. Quantum circuit optimization intrinsically generates the remapped quantum circuit which maps between quantum states but does not destroy them. The dynamic process of quantum circuit mapping contributes to the one-wayness of the dynamic full quantum one-way function. The experimental results show that this function is more realizable than the concatenated full quantum one-way function. The dynamic full quantum one-way function can be employed to construct a full quantum trapdoor one-way function which is ‘easy to compute and invert’ based on a trapdoor. Meanwhile, this new full quantum one-way function is proved to be very useful in quantum cryptography, especially in quantum currency notes. Our work promotes the development from full quantum one-way functions to future quantum cryptographic applications.