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Abstract: It is shown that Gauss periods of special type give an explicit polynomial-time computation of elements of exponentially large multiplicative order in some finite fields. This can be considered as a step towards solving the celebrated problem of finding primitive roots in finite fields in polynomial time. 1 Introduction One of the most important unsolved problems in the computational theory of finite fields is to design a fast algorithm to construct primitive roots in a finite field IF q of q... (Update)
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...#) 0 depends only on p and arbitrary # 0. Several more results about the multiplicative orders of # and # # 1 can be extracted from [2, 3]. Theorem. For any fixed # 0 and su#ciently large q, for any positive divisors n and m of q 1 with nm # q 3 2 # there exists #...
...not limited to cryptography, coding theory, pseudo random number generation and combinatorial designs. Following this idea, the authors [9] have proposed some algorithms to construct elements of exponentially large order for some su#ciently dense sequence of extensions of a...
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BibTeX entry: (Update)
J. von zur Gathen and I. Shparlinski, `Orders of Gauss periods in finite fields', Appl. Algebra in Engin., Commun. and Computing , 1998, v.9, 15-24. http://citeseer.ist.psu.edu/article/vonzurgathen96orders.html More
@misc{ gathen98orders,
author = "J. Gathen and I. Shparlinski",
title = "Orders of Gauss periods in finite fields",
text = "J. von zur Gathen and I. Shparlinski, `Orders of Gauss periods in finite
fields', Appl. Algebra in Engin., Commun. and Computing , 1998, v.9, 15-24.",
year = "1998",
url = "citeseer.ist.psu.edu/article/vonzurgathen96orders.html" }
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