密码学报（中英文）2025，Vol.12Issue(1)：163-179,17.DOI:10.13868/j.cnki.jcr.000755
SM4算法基于不同逻辑门集的量子优化实现
Optimized Quantum Implementations of SM4 Based on Different Gate Sets
摘要
Abstract
This work mainly studies the construction of quantum circuit with low Toffoli-depth and low T-depth of SM4.For the S-box of SM4,based on the reclassification of its classical implementation obtained by using the tower field technique,the theoretical minimum of Toffoli-depth and T-depth of each part can be achieved by adding ancilla qubits.Among the rearranged operations of the classical implementation,the second part can be regarded as a 4-bit S-box.To construct quantum circuit for the second part,an NCT-based circuit with Toffoli-depth 2 that consumes 8 ancilla qubits is designed.For the construction of the Clifford+T-based circuit,the SAT-based method is applied and a T-depth-2 circuit of the second part is obtained.The above methods can effectively reduce the Toffoli-depth and T-depth of the complete circuit of the S-box under the condition of only adding finite qubits.Based on the above methods,the quantum circuit of the S-box of SM4 can be designed with Toffoli-depth of 8 and T-depth of 4,respectively.Finally,applying the above S-box circuit to the overall circuit of SM4,quantum circuit of SM4 with Toffoli-depth of 264 and T-depth of 132 is designed,respectively.关键词
SM4算法/塔域分解/S盒/量子实现Key words
SM4/Tower field/S-box/Quantum circuit分类
信息技术与安全科学引用本文复制引用
郭运雨,向泽军,林达,曾祥勇,张莎莎..SM4算法基于不同逻辑门集的量子优化实现[J].密码学报（中英文）,2025,12(1):163-179,17.基金项目
国家重点研发计划-青年科学家项目(2023YFA1011200) （2023YFA1011200）
国家自然科学基金(62272147,62402511) （62272147,62402511）
湖北省自然科学基金(2024AFB573) （2024AFB573）
湖北省自然科学基金创新群体项目(2023AFA021)Young Scientist Program of National Key Research and Development Program of China(2023YFA1011200) （2023AFA021）
National Natural Science Foundation of China(62272147,62402511) （62272147,62402511）
Natural Science Founda-tion of Hubei Province(2024AFB573) （2024AFB573）
Innovation Group Project of Natural Science Foundation of Hubei Province(2023AFA021) （2023AFA021）
