Using semidirect product of (semi)groups in public key cryptography
This work addresses the need for enhanced cryptographic security in key exchange, though it appears incremental as it builds upon existing Diffie-Hellman concepts with new mathematical frameworks.
The paper tackles the problem of designing secure and efficient key exchange protocols by proposing a general protocol based on semidirect products of (semi)groups, which generalizes the Diffie-Hellman protocol and offers improved features when using non-commutative structures.
In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This protocol can be based on any group or semigroup, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when this protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. The focus then shifts to selecting an optimal platform (semi)group, in terms of security and efficiency. We show, in particular, that one can get a variety of new security assumptions by varying an automorphism used for a (semi)group extension.