a1 Department of Mathematics, University of Texas, Austin, TX 78712, USA (email: email@example.com)
We discuss the problem of constructing elements of multiplicative high order in finite fields of large degree over their prime field. We obtain such elements by evaluating rational functions on elliptic curves, at points whose order is small with respect to their degree. We discuss several special cases, including an old construction of Wiedemann, giving the first nontrivial estimate for the order of the elements in this construction.
(Received June 03 2009)
2000 Mathematics subject classification
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Research supported by NSA grant MDA904-H98230-09-1-0070.