On the efficiency of a general attack against the MOBS cryptosystem

TL;DR

This paper investigates the security of the MOBS cryptosystem, a variant of the semidirect key exchange protocol, and finds that the telescoping equality does not provide an effective attack due to numerous solutions.

Contribution

It provides computational evidence that the telescoping equality is not a practical attack method against MOBS, challenging previous assumptions about its vulnerability.

Findings

Telescoping equality has too many solutions for MOBS

MOBS resists attacks based on telescoping equality

The attack is not practically viable against MOBS

Abstract

All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called "telescoping equality"; in some cases, this equality has been used to construct an attack. In this report we present computational evidence suggesting that an instance of the scheme called `MOBS' is an example of a scheme where the telescoping equality has too many solutions to be a practically viable means to conduct an attack.