Further potential applications of group theory in information security

Abstract

Group theory, specifically the combinatorial group theory of finitely presented groups,has been utilized effectively in cryptology. Several new public key cryptosystems have been developed and this has ushered a new area in cryptography called group based cryptography. Braid groups have been suggested as possible platforms and this has led to what is called braid group cryptography. This has also had a profound effect on theoretical group theory as techniques have been found to analyse these group-based cryptosystems.The basic idea is that a finitely presented group can be described by a finite amount of data.This provides techniques to enormously compress and hide information. This suggests that we have only barely scraped the surface of using finitely presented groups for data control, security and storage. For example, we describe a far-reaching extension for controlling access to files which could be relevant in medical records.