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Elements Of Provable High Orders In Finite Fields
 Proc. American Math. Soc
, 1997
"... A method is given for constructing elements in F q n whose orders are larger than any polynomial in n when n becomes large. As a byproduct a theorem on multiplicative independence of compositions of polynomials is proved. 1. ..."
Abstract

Cited by 12 (4 self)
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A method is given for constructing elements in F q n whose orders are larger than any polynomial in n when n becomes large. As a byproduct a theorem on multiplicative independence of compositions of polynomials is proved. 1.
Constructing nonresidues in finite fields and the extended Riemann hypothesis
 Math. Comp
, 1991
"... Abstract. We present a new deterministic algorithm for the problem of constructing kth power nonresidues in finite fields Fpn,wherepis 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 pol ..."
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Cited by 8 (0 self)
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Abstract. We present a new deterministic algorithm for the problem of constructing kth power nonresidues in finite fields Fpn,wherepis 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 other deterministic algorithms for this problem, this polynomialtime bound holds even if k is exponentially large. More generally, assuming the ERH, in time (n log p) O(n) we can construct a set of elements