以低成本实现Serpent算法的量子电路  

Quantum circuit for implementing Serpent algorithm with low costs

作　　者：陈慧楠 朱彦莹 蔡彬彬 刘晓芬[1] CHEN HuiNan;ZHU YanYing;CAI BinBin;LIU XiaoFen(College of Computer and Cyber Security,Fujian Normal University,Fuzhou 350117,China;Digital Fujian Internet-of-Things Laboratory of Environmental Monitoring,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学计算机与网络空间安全学院,福州350117 [2]福建师范大学数字福建环境监测物联网实验室,福州350117

出　　处：《中国科学:物理学、力学、天文学》2025年第4期116-128,共13页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:62171131,61976053);福建省自然科学基金(编号:2022J01186,2023J01533);福建省中青年教师教育科研项目(编号:JAT231018)资助。

摘　　要：Serpent是AES候选算法之一,以其高安全性和抗攻击性著称,适用于对信息安全要求较高的领域.S盒是Serpent算法中唯一的非线性结构.本文研究如何使用较少的资源实现Serpent算法的量子电路.以更少的量子比特和量子门实现S盒的量子电路,结合S盒的逆量子电路,可构造密钥扩展的量子电路.并且通过对S盒的量子电路中出现的3控制非门进行分解,并对分解后的量子电路进行优化,进一步减少Toffoli门的使用.结合所提出的量子电路,给出需要448个量子比特、92288个T门和需要384个量子比特、118944个T门两种实现Serpent算法的量子电路.与之前需要800个量子比特和132608个T门的研究相比,本文实现Serpent算法量子电路需要的资源更少.此外,本文的S盒与密钥扩展的量子电路可减少实现Serpent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.Serpent,one of the AES candidate algorithms,is known for its high security and attack resistance.It is suitable for areas with high information security requirements.Serpent’s distinctive nonlinear structure is the S-boxes.This paper studies how to build the quantum circuit for Serpent algorithm with lower costs.By combining with the quantum circuits of Sboxes with fewer qubits and quantum gates and the inverse quantum circuits of S-boxes,the key expansion quantum circuit can be constructed.Moreover,by decomposing the 3-controlled CNOT gates appearing in the quantum circuits of the S-boxes and optimizing the decomposed quantum circuits,the number of Toffoli gates is further reduced.In conjunction with the proposed quantum circuits,two types of quantum circuits requiring 448 qubits and 92288 T gates and 384 qubits and 118944 T gates are given to realize the Serpent algorithm.In comparison with the previous study,which required 800 qubits and 132608 T gates,the quantum circuit in this paper requires fewer resources.Furthermore,the S-boxes and key expansion quantum circuits used in the study can reduce the quantum resources in implementing Serpent,reducing the quantum circuit scale required to attack Serpent by the Grover algorithm.

关 键 词：Serpent S盒 量子电路 GROVER算法 资源估计 

分 类 号：O413[理学—理论物理]