A Course in Mathematical Cryptography

12 Further Applications Using Group Theory

12.1 Finitely Presented Groups and Cryptography

In the previous several chapters we have seen how group theory, specifically the combinatorial group theory of finitely presented groups, can be utilized in a cryptographic setting. 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. The body of knowledge, learned in more than 150 years of intense study of finitely presented groups, provides a far reaching tool when applied to cryptology.

Numbers and words are often used as a means of identification, authorization, access to information, record keeping, the control of devices and so on. They ...