### Abstract

We describe a new deterministic algorithm for the problem of constructing k-Th power nonresidues in finite fields GF(p_{n}), where p is prime and k is a prime divisor of pn - 1. We prove under the assumption of the Extended Riemann Hypothesis (ERH), that for fixed n and p + ∼, our algorithm runs in polynomial time. Unlike previous algorithms for this problem, this polynomial time bound holds even if k is very large. More generally, assuming the ERH, in time (log p)"(n) we can construct a set of elements that generates GF(p_{n}).

Original language | English (US) |
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Title of host publication | Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991 |

Publisher | Association for Computing Machinery |

Pages | 72-79 |

Number of pages | 8 |

ISBN (Electronic) | 0897913973 |

State | Published - Jan 3 1991 |

Event | 23rd Annual ACM Symposium on Theory of Computing, STOC 1991 - New Orleans, United States Duration: May 5 1991 → May 8 1991 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F130073 |

ISSN (Print) | 0737-8017 |

### Other

Other | 23rd Annual ACM Symposium on Theory of Computing, STOC 1991 |
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Country | United States |

City | New Orleans |

Period | 5/5/91 → 5/8/91 |

### ASJC Scopus subject areas

- Software

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## Cite this

Buchmann, J., & Shoup, V. (1991). Constructing nonresidues in finite fields riemann hypothesis (Preliminary Version). In

*Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991*(pp. 72-79). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F130073). Association for Computing Machinery.