Abstract
We show that Gauss periods of special type give an explicit polynomial-time construction of elements of exponentially large multiplicative order in some finite fields. It can be considered as a step towards solving the celebrated problem of finding primitive roots in finite fields in polynomial time.
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© 1995 Springer-Verlag Berlin Heidelberg
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von zur Gathen, J., Shparlinski, I. (1995). Orders of Gauss periods in finite fields. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015425
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DOI: https://doi.org/10.1007/BFb0015425
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