Quantum circuit implementations of SM4 block cipher optimizing the number of qubits

SM4 cryptographic algorithm is a block cipher algorithm issued by China’s state cryptographic administration and has become an international standard. We implement the quantum circuits of SM4 block cipher by optimizing the number of qubits and the value of depth-times-width. The quantum circuits of the S-box are first studied. According to the algebraic structure of the S-box, four kinds of improved quantum circuits of S-box are presented for different phases in SM4 based on composite field arithmetic. In order to optimize the number of qubits, we implement the quantum circuit of SM4 by connecting the quantum subcircuits in series. The implemented quantum circuit of SM4 only uses 260 qubits, which is the least number of qubits used not only in implementing the SM4 quantum circuit, but also in implementing the block cipher algorithms with 8-bit S-box, 128-bit plaintext and 128-bit secret key. When optimizing the value of depth-times-width, we achieve it through parallel implementation. The trade-off quantum circuit uses a total of 288 quantum bits, and the Toffoli depth is 1716. The depth-times-width is 49,4208, which is less than the existing best value 82,5792.