Constructing nonresidues in finite fields riemann hypothesis (Preliminary Version)

Johannes Buchmann, Victor Shoup

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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).

Original languageEnglish (US)
Title of host publicationProceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991
PublisherAssociation for Computing Machinery
Pages72-79
Number of pages8
VolumePart F130073
ISBN (Electronic)0897913973
StatePublished - Jan 3 1991
Event23rd Annual ACM Symposium on Theory of Computing, STOC 1991 - New Orleans, United States
Duration: May 5 1991May 8 1991

Other

Other23rd Annual ACM Symposium on Theory of Computing, STOC 1991
CountryUnited States
CityNew Orleans
Period5/5/915/8/91

Fingerprint

Polynomials

ASJC Scopus subject areas

  • Software

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 (Vol. Part F130073, pp. 72-79). Association for Computing Machinery.

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

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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. 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.
Buchmann J, Shoup V. Constructing nonresidues in finite fields riemann hypothesis (Preliminary Version). In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991. Vol. Part F130073. Association for Computing Machinery. 1991. p. 72-79
Buchmann, Johannes ; Shoup, Victor. / Constructing nonresidues in finite fields riemann hypothesis (Preliminary Version). Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991. Vol. Part F130073 Association for Computing Machinery, 1991. pp. 72-79
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