{"title":"Quantum circuit implementations of SM4 block cipher optimizing the number of qubits","authors":"Qing-bin Luo, Qiang Li, Xiao-yu Li, Guo-wu Yang, Jinan Shen, Minghui Zheng","doi":"10.1007/s11128-024-04394-x","DOIUrl":null,"url":null,"abstract":"<p>SM4 cryptographic algorithm is a block cipher algorithm issued by China’s state cryptographic administration and has become an international standard. We implement the quantum circuits of SM4 block cipher by optimizing the number of qubits and the value of depth-times-width. The quantum circuits of the S-box are first studied. According to the algebraic structure of the S-box, four kinds of improved quantum circuits of S-box are presented for different phases in SM4 based on composite field arithmetic. In order to optimize the number of qubits, we implement the quantum circuit of SM4 by connecting the quantum subcircuits in series. The implemented quantum circuit of SM4 only uses 260 qubits, which is the least number of qubits used not only in implementing the SM4 quantum circuit, but also in implementing the block cipher algorithms with 8-bit S-box, 128-bit plaintext and 128-bit secret key. When optimizing the value of depth-times-width, we achieve it through parallel implementation. The trade-off quantum circuit uses a total of 288 quantum bits, and the Toffoli depth is 1716. The depth-times-width is 49,4208, which is less than the existing best value 82,5792.</p>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s11128-024-04394-x","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
SM4 cryptographic algorithm is a block cipher algorithm issued by China’s state cryptographic administration and has become an international standard. We implement the quantum circuits of SM4 block cipher by optimizing the number of qubits and the value of depth-times-width. The quantum circuits of the S-box are first studied. According to the algebraic structure of the S-box, four kinds of improved quantum circuits of S-box are presented for different phases in SM4 based on composite field arithmetic. In order to optimize the number of qubits, we implement the quantum circuit of SM4 by connecting the quantum subcircuits in series. The implemented quantum circuit of SM4 only uses 260 qubits, which is the least number of qubits used not only in implementing the SM4 quantum circuit, but also in implementing the block cipher algorithms with 8-bit S-box, 128-bit plaintext and 128-bit secret key. When optimizing the value of depth-times-width, we achieve it through parallel implementation. The trade-off quantum circuit uses a total of 288 quantum bits, and the Toffoli depth is 1716. The depth-times-width is 49,4208, which is less than the existing best value 82,5792.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.