### 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 |

Volume | Part F130073 |

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 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Software

### Cite this

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

**Constructing nonresidues in finite fields riemann hypothesis (Preliminary Version).** / Buchmann, Johannes; Shoup, Victor.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991.*vol. Part F130073, Association for Computing Machinery, pp. 72-79, 23rd Annual ACM Symposium on Theory of Computing, STOC 1991, New Orleans, United States, 5/5/91.

}

TY - GEN

T1 - Constructing nonresidues in finite fields riemann hypothesis (Preliminary Version)

AU - Buchmann, Johannes

AU - Shoup, Victor

PY - 1991/1/3

Y1 - 1991/1/3

N2 - We describe a new deterministic algorithm for the problem of constructing k-Th power nonresidues in finite fields GF(pn), 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(pn).

AB - We describe a new deterministic algorithm for the problem of constructing k-Th power nonresidues in finite fields GF(pn), 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(pn).

UR - http://www.scopus.com/inward/record.url?scp=85031905133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031905133&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85031905133

VL - Part F130073

SP - 72

EP - 79

BT - Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991

PB - Association for Computing Machinery

ER -