### Abstract

We describe a hashing function from the elements of the finite field double-struck F_{q} into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. For ordinary Hessian curves, this function is 2:1 for almost all points. More precisely, for odd q, the cardinality of the image set of the function is exactly given by (q + i + 2)/2 for some i = - 1,1. Next, we present an injective hashing function from the elements of ℤ_{m} into points on a Hessian curve over double-struck F_{q} with odd q and m = (q + i)/2 for some i = - 1,1,3.

Original language | English |
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Title of host publication | Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings |

Editors | Abderrahmane Nitaj, David Pointcheval |

Pages | 278-289 |

Number of pages | 12 |

Volume | 6737 LNCS |

DOIs | |

Publication status | Published - 2011 |

Event | 4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011 - Dakar, Senegal Duration: 5 Jul 2011 → 7 Jul 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6737 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011 |
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Country | Senegal |

City | Dakar |

Period | 5/07/11 → 7/07/11 |

### Keywords

- Elliptic curve cryptography
- hashing
- Hessian curve

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## Cite this

*Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings*(Vol. 6737 LNCS, pp. 278-289). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6737 LNCS). https://doi.org/10.1007/978-3-642-21969-6_17