A Key Exchange Construction using Mihailova Subgroups in Braid groups

Abstract

In this paper, we propose a modified Anshel-Anshel-Goldfeld (AAG) key exchange construction.The algebraic motivation underlying this construction comes from the membership problem for Mihailova subgroups of the braid group, a problem that is algorithmically unsolvable. We show that this perspective leads naturally to a quotient-group formulation involving Mihailova subgroups modulo the center of Bn. We also explain, however,that these algebraic facts do not by themselves provide a complete security proof for the protocol,because recovering a functionally equivalent conjugator modulo the center may already suffice for an adversary. Thus, the construction should be regarded as an algebraically motivated candidate whose full cryptographic security requires further study.