Deterministic equation solving over finite fields

Authors:
Christiaan van de Woestijne
Affiliations:
Universiteit Leiden, RA Leiden, The Netherlands
Venue:
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Year:
2005

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Abstract

Deterministic algorithms are presented for the efficient solution of diagonal homogeneous equations in many variables over finite fields. As auxiliary algorithms, it is shown how to compute a field generator that is an nth power, and how to write elements as sums of nth powers, for a given integer n. All these algorithms take polynomial time in n and in the logarithm of the field size, and are practical as stated.