Camellia密码算法S盒的量子电路优化
Quantum Circuit Optimization of Camellia Cryptographic Algorithm S-box
吕轶 1罗庆斌 2李强 1郑圆梦3
作者信息
- 1. 湖北民族大学智能科学与工程学院 湖北恩施 445000
- 2. 湖北民族大学智能科学与工程学院 湖北恩施 445000;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
- 折叠
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(28)中的乘法求逆运算同构到GF((24)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(24)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.
Abstract
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 compu-tational complexity,according to the algebraic expression of the S-box,the multiplication inversion operation in the finite domain GF(28)isisomorphic to the operation in the complex domain GF((24)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((24)2 is opti-mized using DORCIS tool,and the quantum circuit of matrix operation is optimized using W-Type algorithm.The resulting quan-tum 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 cir-cuit 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Key words
Quantum circuit/Camellia/S-box/Composite field引用本文复制引用
基金项目
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)
出版年
2024
NETL
NSTL
万方数据