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

Hanling Lin, Xiaofeng Wang and Min Li ()
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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

Mathematics, 2023, vol. 11, issue 13, 1-12

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.

Keywords: post-quantum; braid group; Mihailova subgroup; signature scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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