Sub-linear root detection, and new hardness results, for sparse polynomials over finite fields

@inproceedings{Bi2013SublinearRD,
  title={Sub-linear root detection, and new hardness results, for sparse polynomials over finite fields},
  author={Jingguo Bi and Q. Cheng and J. M. Rojas},
  booktitle={ISSAC '13},
  year={2013}
}
  • Jingguo Bi, Q. Cheng, J. M. Rojas
  • Published in ISSAC '13 2013
  • Mathematics, Computer Science
  • We present a deterministic 2<sup><i>O(t)</i></sup><i>q</i><sup><i>t</i>-2/<i>t</i>-1 +<i>o</i>(1)</sup> algorithm to decide whether a univariate polynomial <i>f</i>, with exactly <i>t</i> monomial terms and degree <<i>q</i>, has a root in F<sub><i>q</i></sub>. Our method is the first with complexity <i>sub-linear</i> in <i>q</i> when <i>t</i>is fixed. We also prove a structural property for the nonzero roots in F<sub><i>q</i></sub> of any <i>t</i>-nomial: the nonzero roots always admit a… CONTINUE READING

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