Optimized quantum implementations of SM3 with low T-depth and low width

SM3 is a hash algorithm independently developed by China. This work mainly studies the quantum circuit implementation of SM3 based on the Clifford+T gate set, and proposes two quantum implementation structures for optimizing the T-depth and width of the circuit, respectively. For the design of quantum circuits with lower T-depth, this paper implements multiple modulo adders applied in parallel, and designs an implementation of quantum circuits for nonlinear components with lower T-depth by utilizing the QAND gate and its conjugate transpose. Based on this, the paper proposes two quantum circuit implementations of the SM3 according to the out-of-place and in-place structures of the nonlinear component, with T-depths of 7040 and 7136, respectively. Compared with the existing circuit with the lowest T-depth, the proposed circuit reduces the T-depth by 72%. For the design of quantum circuits with lower width, this paper groups the constants and variables in the constant modulo addition step, leading to the implementation of the constant modulo operation based on 32 bits only consumes 11 ancilla qubits when the size of group is 4 or 8. Based on this, the paper proposes a quantum circuit implementation of the SM3 that consumes 779 qubits, including 11 ancilla qubits. Compared with the existing circuit with the least consumption of ancilla qubits, the proposed circuit reduces the consumption of ancilla qubits by 67%.