以低成本实现Camellia算法S盒的量子电路  

Quantum circuit for implementing Camellia S-box with low costs

作　　者：李振强 高飞[1] 秦素娟[1] 温巧燕[1] LI ZhenQiang;GAO Fei;QIN SuJuan;WEN QiaoYan(State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing100876,China;Henan Key Laboratory of Network Cryptography Technology,Zhengzhou 450001,China)

机构地区：[1]北京邮电大学网络与交换技术国家重点实验室,北京100876 [2]河南省网络密码技术重点实验室,郑州450001

出　　处：《中国科学：物理学、力学、天文学》2023年第4期17-25,共9页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:62272056,61972048,61976024);河南省网络密码技术重点实验室开放课题(编号:LNCT2021-A10)资助项目。

摘　　要：Camellia是继AES后最具有竞争优势的分组密码算法之一,它在信息安全的很多领域已经有了广泛的应用.S盒是Camellia算法中唯一的非线性组件.本文研究如何用较少的资源实现Camellia算法S盒的量子电路.首先通过映射矩阵使得有限域F_(2^(8))的乘法逆可以通过F_(2^(4))的(乘法和)乘法逆运算得到,进而以更少的量子比特给出实现后者的量子电路.然后应用PLU分解和消元法,通过CNOT门和NOT门实现S盒的仿射变换.最后,结合所提出的量子电路,给出需要20个量子比特、54个Toffoli门、196个CNOT门以及Toffoli门深度为42的实现S盒的量子电路.与之前需要23个量子比特、67个Toffoli门、308个CNOT门以及Toffoli门深度为53的研究相比,本文S盒量子电路需要的资源更少.此外,本文的S盒量子电路可减少实现Camellia时所需的资源,进而降低Grover算法对其攻击时所需的量子电路规模.Camellia,after AES,is one of the most competitive block cipher algorithms.It has been widely used in many fields of information security.Camellia's distinctive nonlinear component is the S-box.This paper studies how to build the quantum circuit of the Camellia S-box at lower costs.First,the multiplicative inversion in F_(2^(8)) can be obtained by the multiplicative inversion(and multiplication)in F_(2^(4)) via a mapping matrix,and the latter can be implemented by the automation tool LIGHTER-R.The afine transformation of the S-box is then implemented with CNOT and NOT gates using the PLU decomposition and elimination approach.Finally,the Camellia S-box quantum circuit is built with 20 qubits,54 Toffoli gates,196 CNOT gates,13 NOT gates,and a Toffoli depth of 42.In comparison with the previous study,which required 23 qubits,67 Toffoli,and 38 CNOT gates,and a Toffoli depth of 53,the S-box quantum circuit in this paper requires fewer resources.Furthermore,the S-box quantum circuit used in the study can reduce the quantum resources in implementing Camellia,reducing the quantum circuit scale required to attack Camellia by the Grover algorithm.

关 键 词：CAMELLIA S盒 乘法逆 组合域 

分 类 号：O413[理学—理论物理] TN918.4[理学—物理]