Constructing nonresidues in finite fields

and the extended Riemann hypothesis

Authors:
Johannes Buchmann and Victor Shoup

Journal:
Math. Comp. **65** (1996), 1311-1326

MSC (1991):
Primary 11Y16

DOI:
https://doi.org/10.1090/S0025-5718-96-00751-X

MathSciNet review:
1348040

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Abstract: We present a new deterministic algorithm for the problem of constructing th power nonresidues in finite fields , where is prime and is a prime divisor of . We prove under the assumption of the Extended Riemann Hypothesis (ERH), that for fixed and , our algorithm runs in polynomial time. Unlike other deterministic algorithms for this problem, this polynomial-time bound holds even if is exponentially large. More generally, assuming the ERH, in time we can construct a set of elements that generates the multiplicative group . An extended abstract of this paper appeared in *Proc. 23rd Ann. ACM Symp. on Theory of Computing*, 1991.

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Additional Information

**Johannes Buchmann**

Affiliation:
Universität des Saarlandes, Fb 14 – Informatik, PF 151150, 66041 Saarbrücken, Germany

**Victor Shoup**

Affiliation:
Bellcore, 445 South St., Morristown, New Jersey 07960

DOI:
https://doi.org/10.1090/S0025-5718-96-00751-X

Received by editor(s):
March 19, 1993

Received by editor(s) in revised form:
February 12, 1995

Additional Notes:
This research was done while the second author was a postdoctoral fellow at the University of Toronto.

Article copyright:
© Copyright 1996
American Mathematical Society