Public key cryptography and semi-group actions

The traditional Diffie-Hellman and ElGamal protocols are based on the hardness of the discrete logarithm problem in a finite group.

The goal of this talk is to give a generalization of these protocols built from semi-group actions on arbitrary sets. This then results in a generalized Diffie-Hellman key exchange and a generalized ElGamal one-way trapdoor function.

Our main attention will be several interesting examples of semi-ring actions on a semi-module. Several new examples will be presented which may lead to new one-way trapdoor functions.

The presented results constitute joint work with Gerard Maze and Chris Monico.