Camellia密码算法S盒的量子电路优化  

Quantum Circuit Optimization of Camellia Cryptographic Algorithm S-box

作　　者：吕轶 罗庆斌 李强[1] 郑圆梦 LYU Yi;LUO Qingbin;LI Qiang;ZHENG Yuanmeng(College of Intelligent Science and Engineering,Hubei Minzu University,Enshi,Hubei 445000,China;School of Information and Software,University of Electronic Science and Technology of China,Chengdu 610054,China;School of Mathematics and Statistics,Hubei Minzu University,Enshi,Hubei 445000,China)

机构地区：[1]湖北民族大学智能科学与工程学院,湖北恩施445000 [2]电子科技大学信息与软件学院,成都610054 [3]湖北民族大学数学与统计学院,湖北恩施445000

出　　处：《计算机科学》2024年第S01期1017-1022,共6页Computer Science

基　　金：国家自然科学基金(62262020);湖北省自然科学基金(2020CFB326);湖北民族大学研究生创新项目(MYK2023074)。

摘　　要：S盒是Camellia密码算法重要的非线性组件。使用Toffoli门、CNOT门和NOT门构建Camellia密码算法S盒的量子电路。为了降低计算的复杂度,根据S盒的代数表达式,将有限域GF(2^(8))中的乘法求逆运算同构到GF((2^(4))^(2))的复合域中的运算,构造出Camellia密码算法S盒的量子电路。在优化方面,将仿射矩阵、同构矩阵以及一组CNOT门对应的矩阵先进行乘法操作,再进行综合,使用DORCIS工具优化GF(2^(4))中乘法求逆的量子电路,运用W-Type算法优化矩阵运算的量子电路。最终得到的S盒的量子电路只需使用20个量子比特,52个Toffoli门、178个CNOT门和13个NOT门,Toffoli深度为40,电路深度为130。该量子电路的正确性通过IBM公司的Aer模拟器进行验证。相比于已有的结果,文中使用的量子资源有了进一步的减少。S-box is an important nonlinear component of Camellia cryptographic algorithm.In this paper,Toffoli gate,CNOT gate and NOT gate are used to construct the quantum circuit of Camellia cryptographic algorithm S box.In order to reduce the computational complexity,according to the algebraic expression of the S-box,the multiplication inversion operation in the finite domain GF(2^(8))isisomorphic to the operation in the complex domain GF((2^(4))^(2),and finally the quantum circuit diagram of Camellia cipher algorithm S box is synthesized.In optimization,the affine matrix,isomorphic matrix and a group of matrices corresponding to CNOT gates are first multiplied and then synthesized,and the quantum circuit of multiplication inversion in GF((2^(4))^(2) is optimized using DORCIS tool,and the quantum circuit of matrix operation is optimized using W-Type algorithm.The resulting quantum circuit of the S-box uses only 20 qubits,52 Toffoli gates,178 CNOT gates,and 13 NOT gates,Toffoli-depth is 40,with a circuit depth of 130.The correctness of the quantum circuit is verified by IBM’s Aer simulator.Compared with the existing results,the quantum resources used in this paper are further reduced.

关 键 词：量子电路 CAMELLIA S盒 复合域 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]