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Quantum circuit implementations of SM4 block cipher optimizing the number of qubits

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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.

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Acknowledgements

The authors would like to thank the editor and the referees for carefully reading the paper, and for their useful comments which helped improve the paper.

Funding

This work is supported by the Natural Sciences Foundation of Hubei Province (Grant No. 2020CFB326), the National Natural Science Foundation of China (Grant Nos.62262020,12164037), the National Key R &D Program of China (Grant No. 2018YFA0306703), and the Open Fund of Advanced Cryptography and System Security Key Laboratory of Sichuan Province (Grant No. SKLACSS-202105).

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Authors and Affiliations

  1. College of Intelligent Systems Science and Engineering, Hubei Minzu University, Enshi, 44500, China

    Qing-bin Luo, Qiang Li, Xiao-yu Li, Jinan Shen & Minghui Zheng

  2. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Qing-bin Luo

  3. Big data research Center and School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Guo-wu Yang

  4. Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu University of Information Technology, Chengdu, 610225, Sichuan, China

    Guo-wu Yang

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  1. Qing-bin Luo
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The original idea to this paper came from Qingbin Luo. All authors contributed to the preparation of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Qing-bin Luo.

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A Specific optimized quantum circuit of S-box for \({\mathcal {C}}_1\)

A Specific optimized quantum circuit of S-box for \({\mathcal {C}}_1\)

In appendix section, we present the specific optimized quantum circuit of S-box for \({\mathcal {C}}_1\), which is implemented by using Qiskit quantum computing software, and the circuit wire switchings are realized by using quantum SWAP gates. The correctness of the quantum circuit is verified by using the Aer simulator of IBM quantum platform (Fig. 20).

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Luo, Qb., Li, Q., Li, Xy. et al. Quantum circuit implementations of SM4 block cipher optimizing the number of qubits. Quantum Inf Process 23, 177 (2024). https://doi.org/10.1007/s11128-024-04394-x

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