Provided is a key generation apparatus that generates, based on a generated random number, quantum gates Ui, L and R corresponding respectively to m types of unitary operations Ui corresponding to n qubits and two types of unitary operations L and R corresponding to m qubits, generates a quantum gate CU whose control is enabled such that operation of the quantum gate Ui is controlled according to an input state of the m qubits, generates a quantum gate G by adding the quantum gates L and R to the quantum gate CU, generates a public key P by obfuscating the quantum gate G, generates a quantum gate CU† and a quantum gate R*, and generates a private key S by connecting the quantum gate CU† and the quantum gate R*.