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Post-Quantum Signature Scheme Based on the Root Extraction Problem over Mihailova Subgroups of Braid Groups

Author

Listed:
  • Hanling Lin

    (College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China)

  • Xiaofeng Wang

    (College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China)

  • Min Li

    (College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China)

Abstract

In this paper, by introducing an isomorphism from the Mihailova subgroup of F 2 × F 2 to the Mihailova subgroups of a braid group, we give an explicit presentation of Mihailova subgroups of a braid group. Hence, in a braid group, there are some Mihailova subgroups experiencing unsolvable subgroup membership problem. Based on this, we propose a post-quantum signature scheme of the Wang–Hu scheme, and we show that the signature scheme is free of quantum computational attack.

Suggested Citation

  • Hanling Lin & Xiaofeng Wang & Min Li, 2023. "Post-Quantum Signature Scheme Based on the Root Extraction Problem over Mihailova Subgroups of Braid Groups," Mathematics, MDPI, vol. 11(13), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2892-:d:1181029
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    References listed on IDEAS

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    1. Frank Arute & Kunal Arya & Ryan Babbush & Dave Bacon & Joseph C. Bardin & Rami Barends & Rupak Biswas & Sergio Boixo & Fernando G. S. L. Brandao & David A. Buell & Brian Burkett & Yu Chen & Zijun Chen, 2019. "Quantum supremacy using a programmable superconducting processor," Nature, Nature, vol. 574(7779), pages 505-510, October.
    2. Jiahui Chen & Jie Ling & Jianting Ning & Emmanouil Panaousis & George Loukas & Kaitai Liang & Jiageng Chen, 2020. "Post quantum proxy signature scheme based on the multivariate public key cryptographic signature," International Journal of Distributed Sensor Networks, , vol. 16(4), pages 15501477209, April.
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