计算机科学

计算机科学 ›› 2024, Vol. 51 ›› Issue (6A): 230900051-6.doi: 10.11896/jsjkx.230900051

• 信息安全 • 上一篇    下一篇

Camellia密码算法S盒的量子电路优化

吕轶1, 罗庆斌1,2, 李强1, 郑圆梦3   

  1. 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
  • 发布日期:2024-06-06
  • 通讯作者: 罗庆斌(qingbinluo@126.com)
  • 作者简介:(lvzxiong002@gmail.com)
  • 基金资助:
    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)

Quantum Circuit Optimization of Camellia Cryptographic Algorithm S-box

LYU Yi1, LUO Qingbin1,2, LI Qiang1, ZHENG Yuanmeng3   

  1. 1 College of Intelligent Science and Engineering,Hubei Minzu University,Enshi,Hubei 445000,China
    2 School of Information and Software,University of Electronic Science and Technology of China,Chengdu 610054,China
    3 School of Mathematics and Statistics,Hubei Minzu University,Enshi,Hubei 445000,China
  • Published:2024-06-06
  • About author:LYU Yi,born in 1997,postgraduate.His main research interests include quantum circuits and security analysis.
    LUO Qingbin,born in 1987,Ph.D.His main research interests include quantum computing and quantum cryptography.
  • Supported by:
    National Natural Science Foundation of China(62262020),Hubei Provincial Natural Science Foundation(2020CFB326) and Hubei Minzu University Graduate Innovation Project(MYK2023074).

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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。

关键词: 量子电路, Camellia, S盒, 复合域

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 computational 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 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.

Key words: Quantum circuit, Camellia, S-box, Composite field

中图分类号: 

  • TP309
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