Quantum circuit implementations of SM4 block cipher based on different gate sets

In recent years, the quantum implementation of symmetric ciphers has received much attention. In this paper, we investigate the construction of quantum circuits based on different gate sets for the SM4 block cipher, which is the national standard of commercial cryptography of China and is standardized in ISO/IEC. First, we construct reversible circuits using Pauli-X gates, CNOT gates and Toffoli gates (i.e., the NCT gate set) for the SM4 S-box, based on which we design two circuits for the SM4 S-box with Clifford+T gates by applying the quantum And gate and existing decomposition scheme of the Toffoli gate, respectively. In addition, we propose a new in-place 1 implementation for the linear transformation in the SM4 round function. Finally, taking the qubit consumption and the \(T{\cdot } M\) value (the product of qubit consumption and nonlinear gate depth of a quantum circuit) as metrics, we investigate the application of various circuits we designed to the construction of quantum circuits for SM4. The results show that we can always construct a subroutine/stand-alone circuit based on the NCT gate set, or based on Clifford+T gates for SM4 with fewer qubits or lower \(T {\cdot } M\) value than existing state-of-the-art implementations.