SM4密码算法S盒的量子电路优化OA北大核心CSTPCD

The S-box is an important nonlinear component in the SM4 cryptographic algorithm.The quantum circuit for SM4 can be designed by the following steps:Firstly,based on the composite field theory,the operations of the S-box over the finite field GF(28)are mapped to that over the composite field GF((24)2)with an isomorphic mapping,and then the quantum circuits of the individual operations are gradually constructed and optimized using the NCT gate library,finally,a complete S-box quantum circuit is designed.To reduce the usage of Toffoli gates,the quantum circuit that uses the least number of Toffoli gates is selected according to the algebraic expression of multiplicative operation over GF(24).In order to reduce the amount of CNOT gates,this paper focuses on three aspects of optimization:first,to synthesize the quantum circuit of the 4th order matrix using the optimal CNOT circuit.Second,to synthesize the quantum circuit of the 8th order matrix by using the substitution matrix and the optimized subcircuit.Third,to optimize the number of CNOT gates of the whole S-box by the idea of combining the calculations and then synthesizing.This S-box quantum circuit is implemented using the Qiskit Aer quantum simulator and its correctness is verified.After quantum resource analysis,the optimized S-box quantum circuit uses a total of 21 qubits,10 NOT gates,152 CNOT gates and 34 Toffoli gates,and the circuit depth is 97.Compared with the existing results,both the number of Toffoli gates,the total number of sub-logic gates and the circuit depth are greatly reduced.