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arXiv · 1504.06512

On the computation of rational points of a hypersurface over a finite field

Guillermo Matera·Mariana Pérez·Melina Privitelli
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Abstract

We design and analyze an algorithm for computing rational points of hypersurfaces defined over a finite field based on searches on "vertical strips", namely searches on parallel lines in a given direction. Our results show that, on average, less than two searches suffice to obtain a rational point. We also analyze the probability distribution of outputs, using the notion of Shannon entropy, and prove that the algorithm is somewhat close to any "ideal" equidistributed algorithm.

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Guillermo Matera, Mariana Pérez, Melina Privitelli. 2015-04-24. On the computation of rational points of a hypersurface over a finite field. https://arxiv.org/abs/1504.06512

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