## Abstract

For a given elliptic curve E over a finite field, we obtain an upper bound on incomplete character sums with power generator on E, that is, for the sequence of points

W-n = e(n)W(0),

where W-0 is an IFq rational point on E and e is an integer, relatively prime to the order of W-0.

These results complement those obtained by T. Lange and I. E. Shparlinski, where a similar bound has been established for sums over the entire period. We propose two different approaches. One of them leads to stronger results for very short sums, while the other one is stronger for almost complete sums.

Combining these bounds with some standard arguments we also derive results about the uniformity of distribution of such sequences.

Original language | English |
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Title of host publication | Finite fields and applications |

Editors | Gary L. Mullen, Daniel Panario, Igor E. Shparlinski |

Place of Publication | Providence, RI |

Publisher | American Mathematical Society |

Pages | 111-118 |

Number of pages | 8 |

ISBN (Print) | 9780821843093 |

Publication status | Published - 2008 |

Event | 8th International Conference on Finite Fields and Applications - Melbourne, Australia Duration: 9 Jul 2007 → 13 Jul 2007 |

### Publication series

Name | Contemporary mathematics series |
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Publisher | American Mathematical Society |

Volume | 461 |

ISSN (Print) | 0271-4132 |

### Conference

Conference | 8th International Conference on Finite Fields and Applications |
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Country | Australia |

City | Melbourne |

Period | 9/07/07 → 13/07/07 |

## Keywords

- REINGOLD PSEUDORANDOM FUNCTION
- EXPONENTIAL-SUMS
- CHARACTER SUMS
- FINITE-FIELDS