Mathematics, Vol. 11, Pages 2892: Post-Quantum Signature Scheme Based on the Root Extraction Problem over Mihailova Subgroups of Braid Groups

Mathematics, Vol. 11, Pages 2892: Post-Quantum Signature Scheme Based on the Root Extraction Problem over Mihailova Subgroups of Braid Groups

Mathematics doi: 10.3390/math11132892

Authors: Hanling Lin Xiaofeng Wang Min Li

In this paper, by introducing an isomorphism from the Mihailova subgroup of F2×F2 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.