Ja n 20 05 Public Key Cryptography based on Semigroup Actions ∗ Gérard Maze

A generalization of the original Diffie-Hellman key exchange in (Z/pZ) found a new depth when Miller [21] and Koblitz [9] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we extend such a generalization to the setting of a semigroup action (G-action) on a finite set. We define these extended protocols, show how it is related to the general Diffie-Hellman key exchange and give some examples.