@article{Kopparty2008DetectingRP, title={Detecting Rational Points on Hypersurfaces over Finite Fields}, author={Swastik Kopparty and Sergey Yekhanin}, journal={2008 23rd Annual IEEE Conference on Computational Complexity}, year={2008}, pages={311-320} }

- Published 2008 in 2008 23rd Annual IEEE Conference on Computational…
DOI:10.1109/CCC.2008.36

We study the complexity of deciding whether a given homogeneous multivariate polynomial has a non- trivial root over a finite field. Given a homogeneous algebraic circuit C that computes an n- variate polynomial p(x) of degree d over a finite field Fq, we wish to determine if there exists a nonzero xisinFq n with C(x)=0. For constant n there are known algorithms for doing this efficiently. However for linear n, the problem becomes NP hard. In this paper, using interesting algebraic techniques… CONTINUE READING

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