Remarks on MOBS and cryptosystems using semidirect products

Recently, several cryptosystems have been proposed based semidirect products of various algebraic structures. Efficient attacks against several of them have already been given, along with a very general attack. The purpose of this note is to provide an observation that can be used as a point-of-attack for similar systems, and show how it can be used to efficiently cryptanalyze the MOBS system.