• Mathematics, Computer Science
  • Published in SIAM J. Comput. 1988
  • DOI:10.1137/0219073

Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields

@article{Grigoriev1988FastPA,
  title={Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields},
  author={Dima Grigoriev and Marek Karpinski and Michael F. Singer},
  journal={SIAM J. Comput.},
  year={1988},
  volume={19},
  pages={1059-1063}
}
The authors consider the problem of reconstructing (i.e., interpolating) a t-sparse multivariate polynomial given a black box which will produce the value of the polynomial for any value of the arguments. It is shown that, if the polynomial has coefficients in a finite field $GF[q]$ and the black box can evaluate the polynomial in the field $GF[q^{\ulcorner 2\log_{q}(nt)+3 \urcorner}]$, where n is the number of variables, then there is an algorithm to interpolate the polynomial in $O(\log^3 (nt… CONTINUE READING

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Factoring polynomials over largefinitefields

J. GRABMEIER
  • 1970