One-way functionsOne-way function areQuantum one-way function fundamental tools for cryptography. Until now, quantum one-way functionsQuantum one-way function have several input-output categories such as ‘classical-to-classical’, ‘classical-to-quantum’, ‘quantum-to-classical’ and ‘quantum-to-quantum’, which are used for post-quantum cryptography or quantum cryptographyQuantum cryptography. The most significant functions are ‘classical-to-classical’ quantum one-way functionQuantum one-way function and ‘quantum-to-quantum’ quantumOne-way function one-wayOne-way function functionQuantum one-way function. ‘Quantum-to-quantum’ quantum one-wayOne-way function functionQuantum one-way function, also called full quantum one-wayFull Quantum One-way Function (F-QOWF) functionQuantum one-way function, can deal with quantum stateQuantum state and be easily performed on the quantum computer. ‘Classical-to-classical’ quantum one-wayOne-way function functionQuantum one-way function, which deals with classical information, can improve the security of current cryptographic systems to be secure even against quantum attacker.