Remarks on MOBS and cryptosystems using semidirect products

TL;DR

This paper analyzes cryptosystems based on semidirect products, providing a general attack method that efficiently cryptanalyzes the MOBS system and highlights vulnerabilities in similar cryptosystems.

Contribution

It introduces a novel point-of-attack technique applicable to cryptosystems using semidirect products, demonstrating its effectiveness on the MOBS system.

Findings

The attack efficiently breaks the MOBS cryptosystem.

Semidirect product-based cryptosystems are vulnerable to the proposed attack.

The method can be generalized to other similar cryptosystems.

Abstract

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.