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

作　　者：郭运雨 向泽军 林达 曾祥勇 张莎莎[1] GUO Yun-Yu;XIANG Ze-Jun;LIN Da;ZENG Xiang-Yong;ZHANG Sha-Sha(School of Cyber Science and Technology,Hubei University,Wuhan 430062,China;State Key Laboratory of Cryptology,Beijing 100878,China;College of Science,National University of Defense Technology,Changsha 410073,China;Hubei Key Laboratory of Applied Mathematics,Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学网络空间安全学院,武汉430062 [2]密码技术全国重点实验室,北京100878 [3]国防科技大学理学院,长沙410073 [4]湖北大学数学与统计学学院应用数学湖北省重点实验室,武汉430062

出　　处：《密码学报(中英文)》2025年第1期163-179,共17页Journal of Cryptologic Research

基　　金：国家重点研发计划-青年科学家项目(2023YFA1011200);国家自然科学基金(62272147,62402511);湖北省自然科学基金(2024AFB573);湖北省自然科学基金创新群体项目(2023AFA021)。

摘　　要：本文主要研究SM4算法的低Toffoli深度以及低T深度的量子电路构造.对于SM4算法的S盒,本文以对其基于塔域分解技术得到的经典实现的重新划分为基础,通过添加量子辅助比特使每部分的Toffoli深度以及T深度达到理论上的最小值.在经典实现的重新划分中,第二部分可视为4比特S盒,本文在基于NCT门集设计其量子电路时,提出了一种Toffoli深度为2的实现方案,该方案仅消耗8个量子辅助比特.针对重新划分中的第二部分基于Clifford+T门集的实现,本文使用基于SAT的搜索算法得到该部分与门深度为2的实现,并基于此设计了其T深度为2的量子电路.上述方法能在仅添加有限量子比特的条件下,有效地降低S盒整体电路的Toffoli深度以及T深度.基于上述方法,本文分别设计了SM4算法S盒Toffoli深度为8以及T深度为4的量子电路.将上述S盒电路应用于SM4算法整体设计中,本文最终分别设计了SM4算法的Toffoli深度为264、T深度为132的量子电路.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 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]