Abstract
We consider the problem of interpolating and zero testing sparse multivariate polynomials over finite fields from their values given by a black box. We give an estimate of the size of a test set constructed by Clausen, Dress, Grabmeier, and Karpinski [2] and improve the previously known lower bounds on the size of a minimal test set. Further, we present for arbitrary finite fields a new interpolation algorithm that uses only evaluations over the ground field, thereby answering an open question of Dür and Grabmeier [3].
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Werther, K. The complexity of sparse polynomial interpolation over finite fields. AAECC 5, 91–103 (1994). https://doi.org/10.1007/BF01438278
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DOI: https://doi.org/10.1007/BF01438278