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.

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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.

## 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.

## Citations

## Altmetrics

## Additional indexing

Other titles: | IEEE International Symposium on Information Theory, LAUSANNE, SWITZERLAND, JUN 30-JUL 05, 2002 |
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Item Type: | Book Section, refereed, original work |

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | Diffie-Hellman key exchange , ElGamal protocol , G-action , abelian semigroup , elliptic curve , protocol , public key cryptosystem , semigroup action |

Language: | English |

Date: | 2002 |

Deposited On: | 03 Feb 2010 13:52 |

Last Modified: | 05 Apr 2016 13:25 |

Publisher: | IEEE Operations Center |

ISBN: | 0-7803-7501-7 |

Free access at: | Related URL. An embargo period may apply. |

Publisher DOI: | 10.1109/ISIT.2002.1023538 |

Related URLs: | http://www.math.uzh.ch/aa/fileadmin/user/rosen/publikation/ma02p.pdf |

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