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Maze, G; Monico, C; Rosenthal, J (2002). A public key cryptosystem based on actions by semigroups. In: IEEE. ISIT: 2002 IEEE International Symposium on Information Theory. Proceedings. Piscataway, N.J.: IEEE Operations Center, 266.

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Abstract

A generalization of the original Diffie-Hellman key exchange in Fp found a new depth when Miller (1986) and Koblitz (1987) suggested that such a protocol could be used with the group over an elliptic curve. In the present article, we extend such a generalization to the setting of a semigroup action (G-action) on a finite set. We define this extended protocol, show how it is related to the general Diffie-Hellman key exchange and give some examples. The interesting thing is that every action by an abelian semigroup gives rise to a Diffie-Hellman key exchange. With an additional assumption it is also possible to extend the ElGamal protocol.